[{"data":1,"prerenderedAt":5161},["ShallowReactive",2],{"evidence-index":3,"evidence-doc-higgs-field":314},[4,19,31,44,58,71,84,95,108,120,132,143,154,168,178,189,202,213,223,233,243,255,266,277,289,303],{"path":5,"title":6,"description":7,"keywords":8,"field":17,"order":18},"\u002Fevidence\u002Fmaxwells-equations","Maxwell's Equations","Four equations that joined electricity, magnetism and light, and set physics on the road to relativity.",[9,10,11,12,13,14,15,16],"electromagnetism","electric fields","magnetic fields","electromagnetic waves","light","Gauss law","Faraday law","Ampere law","Physical",1,{"path":20,"title":21,"description":22,"keywords":23,"field":30,"order":18},"\u002Fevidence\u002Fnumerology-origin","Numerology Origin","How ancient number symbolism, built to describe cosmic order and interpret sacred texts, became modern personality numerology.",[24,25,26,27,28,29],"number symbolism","Pythagoras","gematria","sacred numbers","divination","history of mathematics","Historical",{"path":32,"title":33,"description":34,"keywords":35,"field":43,"order":18},"\u002Fevidence\u002Forigin-of-life","Origin of Life","What chemistry, geology and genomics currently tell us about how non-living matter became the first living cells.",[36,37,38,39,40,41,42],"abiogenesis","RNA world","Miller-Urey experiment","prebiotic chemistry","hydrothermal vents","protocells","LUCA","Biological",{"path":45,"title":46,"description":47,"keywords":48,"field":57,"order":18},"\u002Fevidence\u002Fsuffering","Suffering","How Siddhartha Gautama tested both luxury and severe self-denial, and what his diagnosis of suffering became.",[49,50,51,52,53,54,55,56],"Buddhism","Buddha","Siddhartha Gautama","dukkha","Four Noble Truths","Middle Way","Eightfold Path","craving","Cultural",{"path":59,"title":60,"description":61,"keywords":62,"field":70,"order":18},"\u002Fevidence\u002Fthe-evolution-of-trust","The Evolution of Trust","How the prisoner's dilemma, Axelrod's tournaments, and later models explain when cooperation beats selfishness, and when it does not.",[63,64,65,66,67,68,69],"game theory","prisoners dilemma","cooperation","Robert Axelrod","tit for tat","reciprocity","evolutionary dynamics","Social",{"path":72,"title":73,"description":74,"keywords":75,"field":43,"order":83},"\u002Fevidence\u002Fplacebo","Placebo","How an inert treatment can change pain, symptoms and brain chemistry, why it works, and where its power ends.",[76,77,78,79,80,81,82],"placebo effect","nocebo","expectation","conditioning","pain relief","clinical trials","endogenous opioids",2,{"path":85,"title":86,"description":87,"keywords":88,"field":70,"order":83},"\u002Fevidence\u002Fpuer-aeternus","Puer Aeternus","The Jungian \"eternal youth\" archetype, what it describes, what empirical psychology can and cannot say about it, and where such people thrive or struggle.",[89,90,91,92,93,94],"Carl Jung","Jungian psychology","eternal youth","archetype","Peter Pan","adulthood",{"path":96,"title":97,"description":98,"keywords":99,"field":57,"order":83},"\u002Fevidence\u002Ftaoism","Taoism","What the Dao, wu wei and naturalness mean, and why Daoist texts separate caring for something from clinging to it.",[100,101,102,103,104,105,106,107],"Daoism","Laozi","Zhuangzi","Daodejing","Tao Te Ching","wu wei","yin and yang","attachment",{"path":109,"title":110,"description":111,"keywords":112,"field":17,"order":83},"\u002Fevidence\u002Ftime-dilation","Time Dilation","Why moving clocks and clocks deeper in gravity tick slower, and how the twin paradox resolves.",[113,114,115,116,117,118,119],"special relativity","general relativity","twin paradox","Lorentz factor","proper time","atomic clocks","GPS",{"path":121,"title":122,"description":123,"keywords":124,"field":17,"order":131},"\u002Fevidence\u002Fhiggs-field","Higgs Field","How an invisible field filling all of space gives mass to fundamental particles, and how it was found in 2012.",[125,126,127,128,129,130],"Higgs boson","particle physics","Standard Model","CERN","Large Hadron Collider","symmetry breaking",3,{"path":133,"title":134,"description":135,"keywords":136,"field":43,"order":131},"\u002Fevidence\u002Fmeditation","Meditation","What meditation trains, how it seems to work in the brain, and how strong the evidence really is.",[137,138,139,140,141,142],"mindfulness","attention","neuroscience","brain","stress","contemplative practice",{"path":144,"title":145,"description":146,"keywords":147,"field":57,"order":131},"\u002Fevidence\u002Fthe-god-of-the-gaps","The God of the Gaps","Why explaining unknowns by appeal to God keeps losing ground, and why many theologians reject the move themselves.",[148,149,150,151,152,153],"theology","religion and science","argument from ignorance","naturalism","cosmological argument","fine-tuning",{"path":155,"title":156,"description":157,"keywords":158,"field":43,"order":167},"\u002Fevidence\u002Fif-the-world-was-vegan","If the World Was Vegan","A scenario analysis of whether global agriculture could feed everyone without animals, and what it would mean for land, soil and ecosystems.",[159,160,161,162,163,164,165,166],"veganism","plant-based diet","agriculture","livestock","food security","soil fertility","biodiversity","nutrition",4,{"path":169,"title":170,"description":171,"keywords":172,"field":17,"order":167},"\u002Fevidence\u002Fkaluza-klein-reduction","Kaluza–Klein Reduction","How one extra, curled-up dimension turns Einstein's gravity into gravity plus electromagnetism, and why we have not seen it.",[173,174,175,9,176,177],"extra dimensions","compactification","gravity","unification","charge quantization",{"path":179,"title":180,"description":181,"keywords":182,"field":17,"order":188},"\u002Fevidence\u002F13-dimensional-models","13-Dimensional Models","Where the number 13 comes from in theoretical physics, why a universe with two time dimensions is mathematically possible, and why none of it is confirmed.",[183,184,185,186,173,187,174],"string theory","M-theory","F-theory","S-theory","two-time physics",5,{"path":190,"title":191,"description":192,"keywords":193,"field":57,"order":188},"\u002Fevidence\u002F1984","1984","What Orwell's Nineteen Eighty-Four is about, why he wrote it, and why rival governments have banned or challenged it as propaganda for the other side.",[194,195,196,197,198,199,200,201],"George Orwell","Nineteen Eighty-Four","dystopia","totalitarianism","surveillance","Big Brother","Newspeak","censorship",{"path":203,"title":204,"description":205,"keywords":206,"field":17,"order":212},"\u002Fevidence\u002Ftachyons","Tachyons","Hypothetical particles that always move faster than light, why they would carry messages into the past, and why modern physics reads them as a sign of instability instead.",[207,208,209,210,211,113],"faster than light","superluminal","causality","imaginary mass","instability",6,{"path":214,"title":215,"description":216,"keywords":217,"field":17,"order":222},"\u002Fevidence\u002Fclosed-timelike-curves","Closed Timelike Curves","How Einstein's equations permit paths through spacetime that return to their own past, and why no one has ever found one.",[218,114,209,219,220,221],"time travel","wormholes","Godel","chronology protection",7,{"path":224,"title":225,"description":226,"keywords":227,"field":17,"order":232},"\u002Fevidence\u002Fnovikov-self-consistency-principle","Novikov Self-Consistency Principle","Why a journey into the past might never change it, and why that need not require any force preventing change.",[218,228,229,230,209,231],"grandfather paradox","causal loops","closed timelike curves","consistency",8,{"path":234,"title":235,"description":236,"keywords":237,"field":17,"order":242},"\u002Fevidence\u002Fbootstrap-paradox","Bootstrap Paradox","Causal loops in which an object or idea exists only because it was carried into its own past, and whether physics can tolerate them.",[218,238,239,209,240,241],"causal loop","information paradox","entropy","self-consistency",9,{"path":244,"title":245,"description":246,"keywords":247,"field":17,"order":254},"\u002Fevidence\u002Fblock-universe","Block Universe","The view, motivated by relativity, that past, present and future all exist and time does not flow.",[248,249,250,251,252,253],"eternalism","spacetime","relativity","simultaneity","presentism","arrow of time",10,{"path":256,"title":257,"description":258,"keywords":259,"field":17,"order":265},"\u002Fevidence\u002Fdeterminism","Determinism","Whether the present fixes the entire future, what physics says about it, and why free will may survive either way.",[260,209,261,262,263,264],"free will","Laplace demon","compatibilism","chaos","quantum mechanics",11,{"path":267,"title":268,"description":269,"keywords":270,"field":17,"order":276},"\u002Fevidence\u002Fbig-bounce","Big Bounce","The idea that our universe began not from nothing but from the collapse of a previous one, and what physics can and cannot say about it.",[271,272,273,274,240,275],"cosmology","Big Bang","cyclic universe","loop quantum cosmology","eternal return",12,{"path":278,"title":279,"description":280,"keywords":281,"field":17,"order":288},"\u002Fevidence\u002Fgolden-ratio","Golden Ratio","Why one number, the golden ratio, keeps turning up in sunflowers, and why many famous claims about it are myths.",[282,283,284,285,286,287],"phi","Fibonacci","phyllotaxis","spirals","irrational numbers","geometry",13,{"path":290,"title":291,"description":292,"keywords":293,"field":17,"order":302},"\u002Fevidence\u002Fsha-256-encryption","SHA-256 Hashing","How the SHA-256 hash function works, why it cannot be run backwards, and what reversing it would actually require.",[294,295,296,297,298,299,300,301],"cryptography","hash function","SHA256","encryption","preimage resistance","collisions","Bitcoin","brute force",14,{"path":304,"title":305,"description":306,"keywords":307,"field":17,"order":313},"\u002Fevidence\u002Fgrovers-algorithm","Grover's Algorithm","How a quantum computer can search N possibilities in about √N steps, and why that is both remarkable and far less than popular accounts claim.",[308,309,310,311,312,294],"quantum computing","quantum search","qubits","amplitude amplification","oracle",15,{"id":315,"title":122,"body":316,"description":123,"extension":5154,"field":17,"keywords":5155,"meta":5156,"navigation":5157,"order":131,"path":121,"seo":5158,"stem":5159,"__hash__":5160},"evidence\u002Fevidence\u002Fhiggs-field.md",{"type":317,"value":318,"toc":5126},"minimark",[319,323,327,347,354,361,366,373,376,384,388,393,396,407,410,414,417,427,430,434,447,455,489,492,495,499,503,554,856,859,1079,1137,1170,1600,1637,1641,1771,2410,2423,2431,2435,2441,2610,2700,2704,2707,2979,3345,3356,3360,3363,3460,3467,3470,3474,3478,3481,3491,3495,3502,3769,3772,3784,3788,3794,4151,4154,4158,4161,4165,4200,4204,4408,4420,4424,4564,4579,4594,4598,4624,4628,4631,4634,4637,4640,4644,4666,4684,4702,4720,4739,4759,4776,4793,4812,4830,4849,4867,4886,4904,4921,4936,4954,4978,4998,5016,5035,5054,5073,5091,5110],[320,321,122],"h1",{"id":322},"higgs-field",[324,325,326],"p",{},"By the early 1960s, particle physicists had a beautiful idea and an ugly fact that seemed to contradict it.",[324,328,329,330,334,335,339,340,346],{},"The idea was ",[331,332,333],"strong",{},"gauge symmetry",". Electromagnetism, described by ",[336,337,338],"a",{"href":5},"Maxwell's equations",", could be derived from a single requirement: that the laws of physics stay unchanged under a certain kind of local \"re-labelling\" of the electron's quantum phase. Demand that symmetry, and the photon, together with its properties, falls out of the mathematics almost automatically. In 1954 Chen-Ning Yang and Robert Mills generalised this recipe to more complicated symmetries ",[341,342,345],"sup",{"className":343},[344],"c-cite","[1]",". It looked like a template for every force of nature.",[324,348,349,350,353],{},"The ugly fact was the ",[331,351,352],{},"weak nuclear force",", responsible for radioactive beta decay. Unlike electromagnetism, which reaches across the universe, the weak force acts only across distances far smaller than an atomic nucleus. A short-range force means the particle carrying it must be heavy. But the gauge recipe had an unavoidable consequence: its force carriers had to be exactly massless. Adding a mass by hand destroyed the very symmetry that made the theory work, and with it the mathematical consistency of the theory at high energies.",[324,355,356,357,360],{},"So the template that explained electromagnetism so elegantly seemed unable to describe the weak force at all. The resolution, found in 1964, was the idea now called the ",[331,358,359],{},"Higgs field",". Its confirmation took another 48 years and the largest machine ever built.",[362,363,365],"h2",{"id":364},"empty-space-with-a-value","Empty Space with a Value",[324,367,368,369,372],{},"The central proposal is simple to state and strange to accept: ",[331,370,371],{},"space is not empty",". Everywhere, including the deepest vacuum between galaxies, there is a field with a constant, nonzero value.",[324,374,375],{},"Particles that interact with this field behave as though they have mass. Particles that do not interact with it, such as the photon, remain massless and travel at the speed of light. The stronger a particle's interaction with the field, the heavier it appears.",[324,377,378,379,383],{},"A common analogy compares the Higgs field to molasses that slows particles down. The analogy is imperfect in an important way. Molasses causes ",[380,381,382],"em",{},"drag",", which depends on speed and dissipates energy; a particle moving at constant velocity through the Higgs field experiences no drag at all. What the field does is subtler: it changes the way the particle's quantum wave propagates, so that it can no longer travel at the speed of light and acquires inertia, a resistance to being accelerated. Mass, in this picture, is not something a particle carries around inside itself. It is a consequence of the particle's constant interaction with its surroundings.",[362,385,387],{"id":386},"how-it-works-symmetry-that-hides-itself","How It Works: Symmetry That Hides Itself",[389,390,392],"h3",{"id":391},"a-scenario-the-pencil-on-its-tip","A Scenario: The Pencil on Its Tip",[324,394,395],{},"Balance a pencil perfectly upright on its point. The situation is completely symmetric: no direction is special. But the balance is unstable. The slightest disturbance makes the pencil fall, and once it lies on the table, it points in one particular direction.",[324,397,398,399,402,403,406],{},"The law of gravity did not change. It is still symmetric. The ",[380,400,401],{},"state"," the system ended up in is not. Physicists call this ",[331,404,405],{},"spontaneous symmetry breaking",": the rules are symmetric, but the lowest-energy state is not.",[324,408,409],{},"The same thing happens when a hot piece of iron cools. Above a certain temperature, the atomic magnets point randomly. Below it, they align, all choosing the same arbitrary direction. The underlying physics has no preferred direction, yet the magnet does.",[389,411,413],{"id":412},"the-mexican-hat-potential","The Mexican-Hat Potential",[324,415,416],{},"For the Higgs field, the \"table\" is a graph of energy against the field's value. Picture the shape of a sombrero, or the bottom of a wine bottle: a bump in the middle, surrounded by a circular trough.",[418,419,420,424],"ul",{},[421,422,423],"li",{},"At the centre, where the field is zero, the situation is symmetric but sits on top of the bump. Like the upright pencil, it is unstable.",[421,425,426],{},"The lowest energy lies somewhere in the trough, at a nonzero value of the field. Every point around the trough has the same energy, so the choice of point is arbitrary. But some point must be chosen.",[324,428,429],{},"The universe, in this picture, rolled off the central bump early in its history and settled into the trough. We now live in that valley, surrounded by a field that has a nonzero value everywhere.",[389,431,433],{"id":432},"the-goldstone-obstacle-and-the-gauge-escape","The Goldstone Obstacle and the Gauge Escape",[324,435,436,437,441,442,446],{},"This mechanism was first understood outside particle physics. Yoichiro Nambu recognised that superconductivity involves a spontaneously broken symmetry ",[341,438,440],{"className":439},[344],"[2]",". Jeffrey Goldstone then showed that such breaking generically produces massless particles, corresponding to the free, costless motion of the ball around the trough ",[341,443,445],{"className":444},[344],"[3]",". That seemed to make things worse: the aim was to give particles mass, and symmetry breaking appeared to create new massless ones that had never been seen.",[324,448,449,450,454],{},"The escape came from superconductors again. Philip Anderson pointed out in 1963 that inside a superconductor the photon effectively acquires a mass, which is why magnetic fields are expelled from the material, and suggested the massless modes could disappear in a gauge theory ",[341,451,453],{"className":452},[344],"[4]",". In 1964, three independent groups showed how this works in relativistic field theory:",[418,456,457,468,478],{},[421,458,459,462,463,467],{},[331,460,461],{},"François Englert and Robert Brout"," (Brussels), in a paper published in August 1964 ",[341,464,466],{"className":465},[344],"[5]",";",[421,469,470,473,474,467],{},[331,471,472],{},"Peter Higgs"," (Edinburgh), in two papers that year, the second of which explicitly pointed to a new massive scalar particle as a consequence ",[341,475,477],{"className":476},[344],"[6,7]",[421,479,480,483,484,488],{},[331,481,482],{},"Gerald Guralnik, Carl Hagen and Tom Kibble"," (London), later in 1964 ",[341,485,487],{"className":486},[344],"[8]",".",[324,490,491],{},"The result is that when the broken symmetry is a gauge symmetry, the would-be massless Goldstone particles do not appear as separate particles. Instead they are absorbed by the gauge bosons, which become massive. A massless force carrier, like the photon, can only vibrate in two directions perpendicular to its motion. A massive one can vibrate in three. The Goldstone mode supplies the third direction. Physicists often say that the gauge boson \"eats\" the Goldstone boson.",[324,493,494],{},"The gauge symmetry is not destroyed by this process. It is hidden in the vacuum state, and the theory keeps the mathematical good behaviour that the symmetry guaranteed.",[362,496,498],{"id":497},"the-formal-description","The Formal Description",[389,500,502],{"id":501},"the-potential","The Potential",[324,504,505,506,553],{},"In the Standard Model, the Higgs field ",[507,508,511,534],"span",{"className":509},[510],"katex",[507,512,515],{"className":513},[514],"katex-mathml",[516,517,519],"math",{"xmlns":518},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[520,521,522,529],"semantics",{},[523,524,525],"mrow",{},[526,527,528],"mi",{},"ϕ",[530,531,533],"annotation",{"encoding":532},"application\u002Fx-tex","\\phi",[507,535,539],{"className":536,"ariaHidden":538},[537],"katex-html","true",[507,540,543,548],{"className":541},[542],"base",[507,544],{"className":545,"style":547},[546],"strut","height:0.8889em;vertical-align:-0.1944em;",[507,549,528],{"className":550},[551,552],"mord","mathnormal"," is a pair of complex numbers at every point in space (an SU(2) doublet). Its energy density is governed by the potential",[555,556,558],"equation",{"label":557},"Higgs potential",[507,559,562],{"className":560},[561],"katex-display",[507,563,565,644],{"className":564},[510],[507,566,568],{"className":567},[514],[516,569,571],{"xmlns":518,"display":570},"block",[520,572,573,641],{},[523,574,575,578,583,585,588,591,594,604,608,615,617,620,623,625,627,633,635],{},[526,576,577],{},"V",[579,580,582],"mo",{"stretchy":581},"false","(",[526,584,528],{},[579,586,587],{"stretchy":581},")",[579,589,590],{},"=",[579,592,593],{},"−",[595,596,597,600],"msup",{},[526,598,599],{},"μ",[601,602,603],"mn",{},"2",[605,606,607],"mtext",{}," ",[595,609,610,612],{},[526,611,528],{},[579,613,614],{},"†",[526,616,528],{},[579,618,619],{},"+",[526,621,622],{},"λ",[605,624,607],{},[579,626,582],{"stretchy":581},[595,628,629,631],{},[526,630,528],{},[579,632,614],{},[526,634,528],{},[595,636,637,639],{},[579,638,587],{"stretchy":581},[601,640,603],{},[530,642,643],{"encoding":532},"V(\\phi) = -\\mu^2\\,\\phi^\\dagger\\phi + \\lambda\\,(\\phi^\\dagger\\phi)^2",[507,645,647,681,779],{"className":646,"ariaHidden":538},[537],[507,648,650,654,658,662,665,669,674,678],{"className":649},[542],[507,651],{"className":652,"style":653},[546],"height:1em;vertical-align:-0.25em;",[507,655,577],{"className":656,"style":657},[551,552],"margin-right:0.2222em;",[507,659,582],{"className":660},[661],"mopen",[507,663,528],{"className":664},[551,552],[507,666,587],{"className":667},[668],"mclose",[507,670],{"className":671,"style":673},[672],"mspace","margin-right:0.2778em;",[507,675,590],{"className":676},[677],"mrel",[507,679],{"className":680,"style":673},[672],[507,682,684,688,691,732,736,767,770,773,776],{"className":683},[542],[507,685],{"className":686,"style":687},[546],"height:1.0935em;vertical-align:-0.1944em;",[507,689,593],{"className":690},[551],[507,692,694,697],{"className":693},[551],[507,695,599],{"className":696},[551,552],[507,698,701],{"className":699},[700],"msupsub",[507,702,705],{"className":703},[704],"vlist-t",[507,706,709],{"className":707},[708],"vlist-r",[507,710,714],{"className":711,"style":713},[712],"vlist","height:0.8641em;",[507,715,717,722],{"style":716},"top:-3.113em;margin-right:0.05em;",[507,718],{"className":719,"style":721},[720],"pstrut","height:2.7em;",[507,723,729],{"className":724},[725,726,727,728],"sizing","reset-size6","size3","mtight",[507,730,603],{"className":731},[551,728],[507,733],{"className":734,"style":735},[672],"margin-right:0.1667em;",[507,737,739,742],{"className":738},[551],[507,740,528],{"className":741},[551,552],[507,743,745],{"className":744},[700],[507,746,748],{"className":747},[704],[507,749,751],{"className":750},[708],[507,752,755],{"className":753,"style":754},[712],"height:0.8991em;",[507,756,757,760],{"style":716},[507,758],{"className":759,"style":721},[720],[507,761,763],{"className":762},[725,726,727,728],[507,764,614],{"className":765},[766,728],"mbin",[507,768,528],{"className":769},[551,552],[507,771],{"className":772,"style":657},[672],[507,774,619],{"className":775},[766],[507,777],{"className":778,"style":657},[672],[507,780,782,786,789,792,795,824,827],{"className":781},[542],[507,783],{"className":784,"style":785},[546],"height:1.1491em;vertical-align:-0.25em;",[507,787,622],{"className":788},[551,552],[507,790],{"className":791,"style":735},[672],[507,793,582],{"className":794},[661],[507,796,798,801],{"className":797},[551],[507,799,528],{"className":800},[551,552],[507,802,804],{"className":803},[700],[507,805,807],{"className":806},[704],[507,808,810],{"className":809},[708],[507,811,813],{"className":812,"style":754},[712],[507,814,815,818],{"style":716},[507,816],{"className":817,"style":721},[720],[507,819,821],{"className":820},[725,726,727,728],[507,822,614],{"className":823},[766,728],[507,825,528],{"className":826},[551,552],[507,828,830,833],{"className":829},[668],[507,831,587],{"className":832},[668],[507,834,836],{"className":835},[700],[507,837,839],{"className":838},[704],[507,840,842],{"className":841},[708],[507,843,845],{"className":844,"style":713},[712],[507,846,847,850],{"style":716},[507,848],{"className":849,"style":721},[720],[507,851,853],{"className":852},[725,726,727,728],[507,854,603],{"className":855},[551,728],[324,857,858],{},"where:",[418,860,861,931,1020],{},[421,862,863,930],{},[507,864,866,886],{"className":865},[510],[507,867,869],{"className":868},[514],[516,870,871],{"xmlns":518},[520,872,873,883],{},[523,874,875,881],{},[595,876,877,879],{},[526,878,528],{},[579,880,614],{},[526,882,528],{},[530,884,885],{"encoding":532},"\\phi^\\dagger\\phi",[507,887,889],{"className":888,"ariaHidden":538},[537],[507,890,892,896,927],{"className":891},[542],[507,893],{"className":894,"style":895},[546],"height:1.0435em;vertical-align:-0.1944em;",[507,897,899,902],{"className":898},[551],[507,900,528],{"className":901},[551,552],[507,903,905],{"className":904},[700],[507,906,908],{"className":907},[704],[507,909,911],{"className":910},[708],[507,912,915],{"className":913,"style":914},[712],"height:0.8491em;",[507,916,918,921],{"style":917},"top:-3.063em;margin-right:0.05em;",[507,919],{"className":920,"style":721},[720],[507,922,924],{"className":923},[725,726,727,728],[507,925,614],{"className":926},[766,728],[507,928,528],{"className":929},[551,552]," is the squared magnitude of the field;",[421,932,933,1019],{},[507,934,936,960],{"className":935},[510],[507,937,939],{"className":938},[514],[516,940,941],{"xmlns":518},[520,942,943,957],{},[523,944,945,951,954],{},[595,946,947,949],{},[526,948,599],{},[601,950,603],{},[579,952,953],{},">",[601,955,956],{},"0",[530,958,959],{"encoding":532},"\\mu^2 > 0",[507,961,963,1009],{"className":962,"ariaHidden":538},[537],[507,964,966,970,1000,1003,1006],{"className":965},[542],[507,967],{"className":968,"style":969},[546],"height:1.0085em;vertical-align:-0.1944em;",[507,971,973,976],{"className":972},[551],[507,974,599],{"className":975},[551,552],[507,977,979],{"className":978},[700],[507,980,982],{"className":981},[704],[507,983,985],{"className":984},[708],[507,986,989],{"className":987,"style":988},[712],"height:0.8141em;",[507,990,991,994],{"style":917},[507,992],{"className":993,"style":721},[720],[507,995,997],{"className":996},[725,726,727,728],[507,998,603],{"className":999},[551,728],[507,1001],{"className":1002,"style":673},[672],[507,1004,953],{"className":1005},[677],[507,1007],{"className":1008,"style":673},[672],[507,1010,1012,1016],{"className":1011},[542],[507,1013],{"className":1014,"style":1015},[546],"height:0.6444em;",[507,1017,956],{"className":1018},[551]," sets the depth of the trough (the minus sign creates the central bump);",[421,1021,1022,1074,1075,1078],{},[507,1023,1025,1043],{"className":1024},[510],[507,1026,1028],{"className":1027},[514],[516,1029,1030],{"xmlns":518},[520,1031,1032,1040],{},[523,1033,1034,1036,1038],{},[526,1035,622],{},[579,1037,953],{},[601,1039,956],{},[530,1041,1042],{"encoding":532},"\\lambda > 0",[507,1044,1046,1065],{"className":1045,"ariaHidden":538},[537],[507,1047,1049,1053,1056,1059,1062],{"className":1048},[542],[507,1050],{"className":1051,"style":1052},[546],"height:0.7335em;vertical-align:-0.0391em;",[507,1054,622],{"className":1055},[551,552],[507,1057],{"className":1058,"style":673},[672],[507,1060,953],{"className":1061},[677],[507,1063],{"className":1064,"style":673},[672],[507,1066,1068,1071],{"className":1067},[542],[507,1069],{"className":1070,"style":1015},[546],[507,1072,956],{"className":1073},[551]," is the field's ",[331,1076,1077],{},"self-coupling",", which makes the energy rise again at large field values.",[324,1080,1081,1082,1133,1134,1136],{},"The minus sign is the crucial ingredient. At ",[507,1083,1085,1103],{"className":1084},[510],[507,1086,1088],{"className":1087},[514],[516,1089,1090],{"xmlns":518},[520,1091,1092,1100],{},[523,1093,1094,1096,1098],{},[526,1095,528],{},[579,1097,590],{},[601,1099,956],{},[530,1101,1102],{"encoding":532},"\\phi = 0",[507,1104,1106,1124],{"className":1105,"ariaHidden":538},[537],[507,1107,1109,1112,1115,1118,1121],{"className":1108},[542],[507,1110],{"className":1111,"style":547},[546],[507,1113,528],{"className":1114},[551,552],[507,1116],{"className":1117,"style":673},[672],[507,1119,590],{"className":1120},[677],[507,1122],{"className":1123,"style":673},[672],[507,1125,1127,1130],{"className":1126},[542],[507,1128],{"className":1129,"style":1015},[546],[507,1131,956],{"className":1132},[551]," the field behaves as though it had a negative mass squared, the kind of \"tachyonic\" instability discussed in ",[336,1135,204],{"href":203},". It does not produce faster-than-light particles. It simply means the zero-field state is unstable and rolls away to the true minimum.",[324,1138,1139,1140,1169],{},"Setting the derivative of ",[507,1141,1143,1156],{"className":1142},[510],[507,1144,1146],{"className":1145},[514],[516,1147,1148],{"xmlns":518},[520,1149,1150,1154],{},[523,1151,1152],{},[526,1153,577],{},[530,1155,577],{"encoding":532},[507,1157,1159],{"className":1158,"ariaHidden":538},[537],[507,1160,1162,1166],{"className":1161},[542],[507,1163],{"className":1164,"style":1165},[546],"height:0.6833em;",[507,1167,577],{"className":1168,"style":657},[551,552]," to zero gives the minimum at",[507,1171,1173],{"className":1172},[561],[507,1174,1176,1247],{"className":1175},[510],[507,1177,1179],{"className":1178},[514],[516,1180,1181],{"xmlns":518,"display":570},[520,1182,1183,1244],{},[523,1184,1185,1188,1194,1196,1199,1201,1213,1216,1219,1221,1223,1232,1235,1238,1241],{},[579,1186,1187],{"stretchy":581},"⟨",[595,1189,1190,1192],{},[526,1191,528],{},[579,1193,614],{},[526,1195,528],{},[579,1197,1198],{"stretchy":581},"⟩",[579,1200,590],{},[1202,1203,1204,1211],"mfrac",{},[595,1205,1206,1209],{},[526,1207,1208],{},"v",[601,1210,603],{},[601,1212,603],{},[579,1214,1215],{"separator":538},",",[672,1217],{"width":1218},"2em",[526,1220,1208],{},[579,1222,590],{},[1202,1224,1225,1227],{},[526,1226,599],{},[1228,1229,1230],"msqrt",{},[526,1231,622],{},[579,1233,1234],{},"≈",[601,1236,1237],{},"246",[605,1239,1240],{}," GeV",[526,1242,488],{"mathvariant":1243},"normal",[530,1245,1246],{"encoding":532},"\\langle\\phi^\\dagger\\phi\\rangle = \\frac{v^2}{2}, \\qquad v = \\frac{\\mu}{\\sqrt{\\lambda}} \\approx 246\\ \\text{GeV}.",[507,1248,1250,1303,1434,1576],{"className":1249,"ariaHidden":538},[537],[507,1251,1253,1256,1259,1288,1291,1294,1297,1300],{"className":1252},[542],[507,1254],{"className":1255,"style":785},[546],[507,1257,1187],{"className":1258},[661],[507,1260,1262,1265],{"className":1261},[551],[507,1263,528],{"className":1264},[551,552],[507,1266,1268],{"className":1267},[700],[507,1269,1271],{"className":1270},[704],[507,1272,1274],{"className":1273},[708],[507,1275,1277],{"className":1276,"style":754},[712],[507,1278,1279,1282],{"style":716},[507,1280],{"className":1281,"style":721},[720],[507,1283,1285],{"className":1284},[725,726,727,728],[507,1286,614],{"className":1287},[766,728],[507,1289,528],{"className":1290},[551,552],[507,1292,1198],{"className":1293},[668],[507,1295],{"className":1296,"style":673},[672],[507,1298,590],{"className":1299},[677],[507,1301],{"className":1302,"style":673},[672],[507,1304,1306,1310,1411,1415,1419,1422,1425,1428,1431],{"className":1305},[542],[507,1307],{"className":1308,"style":1309},[546],"height:2.1771em;vertical-align:-0.686em;",[507,1311,1313,1317,1408],{"className":1312},[551],[507,1314],{"className":1315},[661,1316],"nulldelimiter",[507,1318,1320],{"className":1319},[1202],[507,1321,1324,1399],{"className":1322},[704,1323],"vlist-t2",[507,1325,1327,1394],{"className":1326},[708],[507,1328,1331,1344,1355],{"className":1329,"style":1330},[712],"height:1.4911em;",[507,1332,1334,1338],{"style":1333},"top:-2.314em;",[507,1335],{"className":1336,"style":1337},[720],"height:3em;",[507,1339,1341],{"className":1340},[551],[507,1342,603],{"className":1343},[551],[507,1345,1347,1350],{"style":1346},"top:-3.23em;",[507,1348],{"className":1349,"style":1337},[720],[507,1351],{"className":1352,"style":1354},[1353],"frac-line","border-bottom-width:0.04em;",[507,1356,1358,1361],{"style":1357},"top:-3.677em;",[507,1359],{"className":1360,"style":1337},[720],[507,1362,1364],{"className":1363},[551],[507,1365,1367,1371],{"className":1366},[551],[507,1368,1208],{"className":1369,"style":1370},[551,552],"margin-right:0.0359em;",[507,1372,1374],{"className":1373},[700],[507,1375,1377],{"className":1376},[704],[507,1378,1380],{"className":1379},[708],[507,1381,1383],{"className":1382,"style":988},[712],[507,1384,1385,1388],{"style":917},[507,1386],{"className":1387,"style":721},[720],[507,1389,1391],{"className":1390},[725,726,727,728],[507,1392,603],{"className":1393},[551,728],[507,1395,1398],{"className":1396},[1397],"vlist-s","​",[507,1400,1402],{"className":1401},[708],[507,1403,1406],{"className":1404,"style":1405},[712],"height:0.686em;",[507,1407],{},[507,1409],{"className":1410},[668,1316],[507,1412,1215],{"className":1413},[1414],"mpunct",[507,1416],{"className":1417,"style":1418},[672],"margin-right:2em;",[507,1420],{"className":1421,"style":735},[672],[507,1423,1208],{"className":1424,"style":1370},[551,552],[507,1426],{"className":1427,"style":673},[672],[507,1429,590],{"className":1430},[677],[507,1432],{"className":1433,"style":673},[672],[507,1435,1437,1441,1567,1570,1573],{"className":1436},[542],[507,1438],{"className":1439,"style":1440},[546],"height:2.0376em;vertical-align:-0.93em;",[507,1442,1444,1447,1564],{"className":1443},[551],[507,1445],{"className":1446},[661,1316],[507,1448,1450],{"className":1449},[1202],[507,1451,1453,1555],{"className":1452},[704,1323],[507,1454,1456,1552],{"className":1455},[708],[507,1457,1460,1533,1541],{"className":1458,"style":1459},[712],"height:1.1076em;",[507,1461,1463,1466],{"style":1462},"top:-2.1778em;",[507,1464],{"className":1465,"style":1337},[720],[507,1467,1469],{"className":1468},[551],[507,1470,1473],{"className":1471},[551,1472],"sqrt",[507,1474,1476,1524],{"className":1475},[704,1323],[507,1477,1479,1521],{"className":1478},[708],[507,1480,1483,1498],{"className":1481,"style":1482},[712],"height:0.9322em;",[507,1484,1488,1491],{"className":1485,"style":1487},[1486],"svg-align","top:-3em;",[507,1489],{"className":1490,"style":1337},[720],[507,1492,1495],{"className":1493,"style":1494},[551],"padding-left:0.833em;",[507,1496,622],{"className":1497},[551,552],[507,1499,1501,1504],{"style":1500},"top:-2.8922em;",[507,1502],{"className":1503,"style":1337},[720],[507,1505,1509],{"className":1506,"style":1508},[1507],"hide-tail","min-width:0.853em;height:1.08em;",[1510,1511,1517],"svg",{"xmlns":1512,"width":1513,"height":1514,"viewBox":1515,"preserveAspectRatio":1516},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1518,1519],"path",{"d":1520},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[507,1522,1398],{"className":1523},[1397],[507,1525,1527],{"className":1526},[708],[507,1528,1531],{"className":1529,"style":1530},[712],"height:0.1078em;",[507,1532],{},[507,1534,1535,1538],{"style":1346},[507,1536],{"className":1537,"style":1337},[720],[507,1539],{"className":1540,"style":1354},[1353],[507,1542,1543,1546],{"style":1357},[507,1544],{"className":1545,"style":1337},[720],[507,1547,1549],{"className":1548},[551],[507,1550,599],{"className":1551},[551,552],[507,1553,1398],{"className":1554},[1397],[507,1556,1558],{"className":1557},[708],[507,1559,1562],{"className":1560,"style":1561},[712],"height:0.93em;",[507,1563],{},[507,1565],{"className":1566},[668,1316],[507,1568],{"className":1569,"style":673},[672],[507,1571,1234],{"className":1572},[677],[507,1574],{"className":1575,"style":673},[672],[507,1577,1579,1582,1585,1589,1597],{"className":1578},[542],[507,1580],{"className":1581,"style":1165},[546],[507,1583,1237],{"className":1584},[551],[507,1586,1588],{"className":1587},[672]," ",[507,1590,1593],{"className":1591},[551,1592],"text",[507,1594,1596],{"className":1595},[551],"GeV",[507,1598,488],{"className":1599},[551],[324,1601,1602,1603,1632,1633,1636],{},"The quantity ",[507,1604,1606,1619],{"className":1605},[510],[507,1607,1609],{"className":1608},[514],[516,1610,1611],{"xmlns":518},[520,1612,1613,1617],{},[523,1614,1615],{},[526,1616,1208],{},[530,1618,1208],{"encoding":532},[507,1620,1622],{"className":1621,"ariaHidden":538},[537],[507,1623,1625,1629],{"className":1624},[542],[507,1626],{"className":1627,"style":1628},[546],"height:0.4306em;",[507,1630,1208],{"className":1631,"style":1370},[551,552]," is the ",[331,1634,1635],{},"vacuum expectation value",": the value the field takes in empty space. Its size is not a guess. It is fixed by the measured strength of the weak interaction, through the Fermi constant.",[389,1638,1640],{"id":1639},"masses-of-the-w-and-z","Masses of the W and Z",[324,1642,1643,1644,1672,1673,1703,1704,1770],{},"When the field sits at ",[507,1645,1647,1660],{"className":1646},[510],[507,1648,1650],{"className":1649},[514],[516,1651,1652],{"xmlns":518},[520,1653,1654,1658],{},[523,1655,1656],{},[526,1657,1208],{},[530,1659,1208],{"encoding":532},[507,1661,1663],{"className":1662,"ariaHidden":538},[537],[507,1664,1666,1669],{"className":1665},[542],[507,1667],{"className":1668,"style":1628},[546],[507,1670,1208],{"className":1671,"style":1370},[551,552],", its interaction with the electroweak gauge fields produces mass terms. With ",[507,1674,1676,1690],{"className":1675},[510],[507,1677,1679],{"className":1678},[514],[516,1680,1681],{"xmlns":518},[520,1682,1683,1688],{},[523,1684,1685],{},[526,1686,1687],{},"g",[530,1689,1687],{"encoding":532},[507,1691,1693],{"className":1692,"ariaHidden":538},[537],[507,1694,1696,1700],{"className":1695},[542],[507,1697],{"className":1698,"style":1699},[546],"height:0.625em;vertical-align:-0.1944em;",[507,1701,1687],{"className":1702,"style":1370},[551,552]," and ",[507,1705,1707,1727],{"className":1706},[510],[507,1708,1710],{"className":1709},[514],[516,1711,1712],{"xmlns":518},[520,1713,1714,1724],{},[523,1715,1716],{},[595,1717,1718,1720],{},[526,1719,1687],{},[579,1721,1723],{"mathvariant":1243,"lspace":1722,"rspace":1722},"0em","′",[530,1725,1726],{"encoding":532},"g'",[507,1728,1730],{"className":1729,"ariaHidden":538},[537],[507,1731,1733,1737],{"className":1732},[542],[507,1734],{"className":1735,"style":1736},[546],"height:0.9463em;vertical-align:-0.1944em;",[507,1738,1740,1743],{"className":1739},[551],[507,1741,1687],{"className":1742,"style":1370},[551,552],[507,1744,1746],{"className":1745},[700],[507,1747,1749],{"className":1748},[704],[507,1750,1752],{"className":1751},[708],[507,1753,1756],{"className":1754,"style":1755},[712],"height:0.7519em;",[507,1757,1758,1761],{"style":917},[507,1759],{"className":1760,"style":721},[720],[507,1762,1764],{"className":1763},[725,726,727,728],[507,1765,1767],{"className":1766},[551,728],[507,1768,1723],{"className":1769},[551,728]," the coupling strengths of the two parts of the electroweak symmetry, one finds",[507,1772,1774],{"className":1773},[561],[507,1775,1777,1887],{"className":1776},[510],[507,1778,1780],{"className":1779},[514],[516,1781,1782],{"xmlns":518,"display":570},[520,1783,1784,1884],{},[523,1785,1786,1795,1797,1809,1811,1814,1816,1818,1820,1827,1829,1861,1863,1866,1868,1870,1872,1879,1881],{},[1787,1788,1789,1792],"msub",{},[526,1790,1791],{},"m",[526,1793,1794],{},"W",[579,1796,590],{},[1202,1798,1799,1807],{},[523,1800,1801,1803,1805],{},[526,1802,1687],{},[605,1804,607],{},[526,1806,1208],{},[601,1808,603],{},[579,1810,1234],{},[601,1812,1813],{},"80.4",[605,1815,1240],{},[579,1817,1215],{"separator":538},[672,1819],{"width":1218},[1787,1821,1822,1824],{},[526,1823,1791],{},[526,1825,1826],{},"Z",[579,1828,590],{},[1202,1830,1831,1859],{},[523,1832,1833,1855,1857],{},[1228,1834,1835],{},[523,1836,1837,1843,1845],{},[595,1838,1839,1841],{},[526,1840,1687],{},[601,1842,603],{},[579,1844,619],{},[595,1846,1847,1849],{},[526,1848,1687],{},[523,1850,1851,1853],{},[579,1852,1723],{"mathvariant":1243},[601,1854,603],{},[605,1856,607],{},[526,1858,1208],{},[601,1860,603],{},[579,1862,1234],{},[601,1864,1865],{},"91.2",[605,1867,1240],{},[579,1869,1215],{"separator":538},[672,1871],{"width":1218},[1787,1873,1874,1876],{},[526,1875,1791],{},[526,1877,1878],{},"γ",[579,1880,590],{},[601,1882,1883],{},"0.",[530,1885,1886],{"encoding":532},"m_W = \\frac{g\\,v}{2} \\approx 80.4\\ \\text{GeV}, \\qquad m_Z = \\frac{\\sqrt{g^2 + g'^2}\\,v}{2} \\approx 91.2\\ \\text{GeV}, \\qquad m_\\gamma = 0.",[507,1888,1890,1950,2034,2112,2321,2401],{"className":1889,"ariaHidden":538},[537],[507,1891,1893,1897,1941,1944,1947],{"className":1892},[542],[507,1894],{"className":1895,"style":1896},[546],"height:0.5806em;vertical-align:-0.15em;",[507,1898,1900,1903],{"className":1899},[551],[507,1901,1791],{"className":1902},[551,552],[507,1904,1906],{"className":1905},[700],[507,1907,1909,1932],{"className":1908},[704,1323],[507,1910,1912,1929],{"className":1911},[708],[507,1913,1916],{"className":1914,"style":1915},[712],"height:0.3283em;",[507,1917,1919,1922],{"style":1918},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[507,1920],{"className":1921,"style":721},[720],[507,1923,1925],{"className":1924},[725,726,727,728],[507,1926,1794],{"className":1927,"style":1928},[551,552,728],"margin-right:0.1389em;",[507,1930,1398],{"className":1931},[1397],[507,1933,1935],{"className":1934},[708],[507,1936,1939],{"className":1937,"style":1938},[712],"height:0.15em;",[507,1940],{},[507,1942],{"className":1943,"style":673},[672],[507,1945,590],{"className":1946},[677],[507,1948],{"className":1949,"style":673},[672],[507,1951,1953,1957,2025,2028,2031],{"className":1952},[542],[507,1954],{"className":1955,"style":1956},[546],"height:1.7936em;vertical-align:-0.686em;",[507,1958,1960,1963,2022],{"className":1959},[551],[507,1961],{"className":1962},[661,1316],[507,1964,1966],{"className":1965},[1202],[507,1967,1969,2014],{"className":1968},[704,1323],[507,1970,1972,2011],{"className":1971},[708],[507,1973,1975,1986,1994],{"className":1974,"style":1459},[712],[507,1976,1977,1980],{"style":1333},[507,1978],{"className":1979,"style":1337},[720],[507,1981,1983],{"className":1982},[551],[507,1984,603],{"className":1985},[551],[507,1987,1988,1991],{"style":1346},[507,1989],{"className":1990,"style":1337},[720],[507,1992],{"className":1993,"style":1354},[1353],[507,1995,1996,1999],{"style":1357},[507,1997],{"className":1998,"style":1337},[720],[507,2000,2002,2005,2008],{"className":2001},[551],[507,2003,1687],{"className":2004,"style":1370},[551,552],[507,2006],{"className":2007,"style":735},[672],[507,2009,1208],{"className":2010,"style":1370},[551,552],[507,2012,1398],{"className":2013},[1397],[507,2015,2017],{"className":2016},[708],[507,2018,2020],{"className":2019,"style":1405},[712],[507,2021],{},[507,2023],{"className":2024},[668,1316],[507,2026],{"className":2027,"style":673},[672],[507,2029,1234],{"className":2030},[677],[507,2032],{"className":2033,"style":673},[672],[507,2035,2037,2041,2044,2047,2053,2056,2059,2062,2103,2106,2109],{"className":2036},[542],[507,2038],{"className":2039,"style":2040},[546],"height:0.8778em;vertical-align:-0.1944em;",[507,2042,1813],{"className":2043},[551],[507,2045,1588],{"className":2046},[672],[507,2048,2050],{"className":2049},[551,1592],[507,2051,1596],{"className":2052},[551],[507,2054,1215],{"className":2055},[1414],[507,2057],{"className":2058,"style":1418},[672],[507,2060],{"className":2061,"style":735},[672],[507,2063,2065,2068],{"className":2064},[551],[507,2066,1791],{"className":2067},[551,552],[507,2069,2071],{"className":2070},[700],[507,2072,2074,2095],{"className":2073},[704,1323],[507,2075,2077,2092],{"className":2076},[708],[507,2078,2080],{"className":2079,"style":1915},[712],[507,2081,2082,2085],{"style":1918},[507,2083],{"className":2084,"style":721},[720],[507,2086,2088],{"className":2087},[725,726,727,728],[507,2089,1826],{"className":2090,"style":2091},[551,552,728],"margin-right:0.0715em;",[507,2093,1398],{"className":2094},[1397],[507,2096,2098],{"className":2097},[708],[507,2099,2101],{"className":2100,"style":1938},[712],[507,2102],{},[507,2104],{"className":2105,"style":673},[672],[507,2107,590],{"className":2108},[677],[507,2110],{"className":2111,"style":673},[672],[507,2113,2115,2119,2312,2315,2318],{"className":2114},[542],[507,2116],{"className":2117,"style":2118},[546],"height:2.3208em;vertical-align:-0.686em;",[507,2120,2122,2125,2309],{"className":2121},[551],[507,2123],{"className":2124},[661,1316],[507,2126,2128],{"className":2127},[1202],[507,2129,2131,2301],{"className":2130},[704,1323],[507,2132,2134,2298],{"className":2133},[708],[507,2135,2138,2149,2157],{"className":2136,"style":2137},[712],"height:1.6348em;",[507,2139,2140,2143],{"style":1333},[507,2141],{"className":2142,"style":1337},[720],[507,2144,2146],{"className":2145},[551],[507,2147,603],{"className":2148},[551],[507,2150,2151,2154],{"style":1346},[507,2152],{"className":2153,"style":1337},[720],[507,2155],{"className":2156,"style":1354},[1353],[507,2158,2159,2162],{"style":1357},[507,2160],{"className":2161,"style":1337},[720],[507,2163,2165,2292,2295],{"className":2164},[551],[507,2166,2168],{"className":2167},[551,1472],[507,2169,2171,2283],{"className":2170},[704,1323],[507,2172,2174,2280],{"className":2173},[708],[507,2175,2178,2263],{"className":2176,"style":2177},[712],"height:0.9578em;",[507,2179,2182,2186],{"className":2180,"style":2181},[1486],"top:-3.2em;",[507,2183],{"className":2184,"style":2185},[720],"height:3.2em;",[507,2187,2190,2221,2224,2227,2230],{"className":2188,"style":2189},[551],"padding-left:1em;",[507,2191,2193,2196],{"className":2192},[551],[507,2194,1687],{"className":2195,"style":1370},[551,552],[507,2197,2199],{"className":2198},[700],[507,2200,2202],{"className":2201},[704],[507,2203,2205],{"className":2204},[708],[507,2206,2209],{"className":2207,"style":2208},[712],"height:0.7401em;",[507,2210,2212,2215],{"style":2211},"top:-2.989em;margin-right:0.05em;",[507,2213],{"className":2214,"style":721},[720],[507,2216,2218],{"className":2217},[725,726,727,728],[507,2219,603],{"className":2220},[551,728],[507,2222],{"className":2223,"style":657},[672],[507,2225,619],{"className":2226},[766],[507,2228],{"className":2229,"style":657},[672],[507,2231,2233,2236],{"className":2232},[551],[507,2234,1687],{"className":2235,"style":1370},[551,552],[507,2237,2239],{"className":2238},[700],[507,2240,2242],{"className":2241},[704],[507,2243,2245],{"className":2244},[708],[507,2246,2248],{"className":2247,"style":2208},[712],[507,2249,2250,2253],{"style":2211},[507,2251],{"className":2252,"style":721},[720],[507,2254,2256],{"className":2255},[725,726,727,728],[507,2257,2259],{"className":2258},[551,728],[507,2260,2262],{"className":2261},[551,728],"′2",[507,2264,2266,2269],{"style":2265},"top:-2.9178em;",[507,2267],{"className":2268,"style":2185},[720],[507,2270,2273],{"className":2271,"style":2272},[1507],"min-width:1.02em;height:1.28em;",[1510,2274,2277],{"xmlns":1512,"width":1513,"height":2275,"viewBox":2276,"preserveAspectRatio":1516},"1.28em","0 0 400000 1296",[1518,2278],{"d":2279},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[507,2281,1398],{"className":2282},[1397],[507,2284,2286],{"className":2285},[708],[507,2287,2290],{"className":2288,"style":2289},[712],"height:0.2822em;",[507,2291],{},[507,2293],{"className":2294,"style":735},[672],[507,2296,1208],{"className":2297,"style":1370},[551,552],[507,2299,1398],{"className":2300},[1397],[507,2302,2304],{"className":2303},[708],[507,2305,2307],{"className":2306,"style":1405},[712],[507,2308],{},[507,2310],{"className":2311},[668,1316],[507,2313],{"className":2314,"style":673},[672],[507,2316,1234],{"className":2317},[677],[507,2319],{"className":2320,"style":673},[672],[507,2322,2324,2328,2331,2334,2340,2343,2346,2349,2392,2395,2398],{"className":2323},[542],[507,2325],{"className":2326,"style":2327},[546],"height:0.9694em;vertical-align:-0.2861em;",[507,2329,1865],{"className":2330},[551],[507,2332,1588],{"className":2333},[672],[507,2335,2337],{"className":2336},[551,1592],[507,2338,1596],{"className":2339},[551],[507,2341,1215],{"className":2342},[1414],[507,2344],{"className":2345,"style":1418},[672],[507,2347],{"className":2348,"style":735},[672],[507,2350,2352,2355],{"className":2351},[551],[507,2353,1791],{"className":2354},[551,552],[507,2356,2358],{"className":2357},[700],[507,2359,2361,2383],{"className":2360},[704,1323],[507,2362,2364,2380],{"className":2363},[708],[507,2365,2368],{"className":2366,"style":2367},[712],"height:0.1514em;",[507,2369,2370,2373],{"style":1918},[507,2371],{"className":2372,"style":721},[720],[507,2374,2376],{"className":2375},[725,726,727,728],[507,2377,1878],{"className":2378,"style":2379},[551,552,728],"margin-right:0.0556em;",[507,2381,1398],{"className":2382},[1397],[507,2384,2386],{"className":2385},[708],[507,2387,2390],{"className":2388,"style":2389},[712],"height:0.2861em;",[507,2391],{},[507,2393],{"className":2394,"style":673},[672],[507,2396,590],{"className":2397},[677],[507,2399],{"className":2400,"style":673},[672],[507,2402,2404,2407],{"className":2403},[542],[507,2405],{"className":2406,"style":1015},[546],[507,2408,1883],{"className":2409},[551],[324,2411,2412,2413,2417,2418,2422],{},"One combination of the gauge fields gets no mass: that is the photon. This is the structure of the electroweak theory built by Sheldon Glashow, Steven Weinberg and Abdus Salam ",[341,2414,2416],{"className":2415},[344],"[9,10]",". In 1971 Gerard 't Hooft showed that such theories remain mathematically consistent (renormalisable) at all energies ",[341,2419,2421],{"className":2420},[344],"[11]",", which transformed the idea from an elegant model into a serious candidate.",[324,2424,2425,2426,2430],{},"The theory made a striking prediction: the ratio of the W and Z masses is fixed by the same angle that controls how the weak and electromagnetic forces mix. When the W and then the Z were discovered at CERN in 1983 ",[341,2427,2429],{"className":2428},[344],"[12]",", their masses matched. That was strong evidence that the electroweak symmetry is broken in roughly the way the Higgs mechanism describes, decades before the Higgs boson itself was seen.",[389,2432,2434],{"id":2433},"the-higgs-boson","The Higgs Boson",[324,2436,2437,2438,2440],{},"Of the four real components of the Higgs doublet, three are eaten by the W⁺, W⁻ and Z. The fourth remains as a physical particle: a ripple in the field about its minimum, moving up and down the walls of the trough. That ripple is the ",[331,2439,125],{},". Its mass is",[507,2442,2444],{"className":2443},[561],[507,2445,2447,2482],{"className":2446},[510],[507,2448,2450],{"className":2449},[514],[516,2451,2452],{"xmlns":518,"display":570},[520,2453,2454,2479],{},[523,2455,2456,2463,2465,2473,2475,2477],{},[1787,2457,2458,2460],{},[526,2459,1791],{},[526,2461,2462],{},"H",[579,2464,590],{},[1228,2466,2467],{},[523,2468,2469,2471],{},[601,2470,603],{},[526,2472,622],{},[605,2474,607],{},[526,2476,1208],{},[526,2478,488],{"mathvariant":1243},[530,2480,2481],{"encoding":532},"m_H = \\sqrt{2\\lambda}\\,v.",[507,2483,2485,2541],{"className":2484,"ariaHidden":538},[537],[507,2486,2488,2491,2532,2535,2538],{"className":2487},[542],[507,2489],{"className":2490,"style":1896},[546],[507,2492,2494,2497],{"className":2493},[551],[507,2495,1791],{"className":2496},[551,552],[507,2498,2500],{"className":2499},[700],[507,2501,2503,2524],{"className":2502},[704,1323],[507,2504,2506,2521],{"className":2505},[708],[507,2507,2509],{"className":2508,"style":1915},[712],[507,2510,2511,2514],{"style":1918},[507,2512],{"className":2513,"style":721},[720],[507,2515,2517],{"className":2516},[725,726,727,728],[507,2518,2462],{"className":2519,"style":2520},[551,552,728],"margin-right:0.0813em;",[507,2522,1398],{"className":2523},[1397],[507,2525,2527],{"className":2526},[708],[507,2528,2530],{"className":2529,"style":1938},[712],[507,2531],{},[507,2533],{"className":2534,"style":673},[672],[507,2536,590],{"className":2537},[677],[507,2539],{"className":2540,"style":673},[672],[507,2542,2544,2548,2601,2604,2607],{"className":2543},[542],[507,2545],{"className":2546,"style":2547},[546],"height:1.04em;vertical-align:-0.0589em;",[507,2549,2551],{"className":2550},[551,1472],[507,2552,2554,2592],{"className":2553},[704,1323],[507,2555,2557,2589],{"className":2556},[708],[507,2558,2561,2576],{"className":2559,"style":2560},[712],"height:0.9811em;",[507,2562,2564,2567],{"className":2563,"style":1487},[1486],[507,2565],{"className":2566,"style":1337},[720],[507,2568,2570,2573],{"className":2569,"style":1494},[551],[507,2571,603],{"className":2572},[551],[507,2574,622],{"className":2575},[551,552],[507,2577,2579,2582],{"style":2578},"top:-2.9411em;",[507,2580],{"className":2581,"style":1337},[720],[507,2583,2585],{"className":2584,"style":1508},[1507],[1510,2586,2587],{"xmlns":1512,"width":1513,"height":1514,"viewBox":1515,"preserveAspectRatio":1516},[1518,2588],{"d":1520},[507,2590,1398],{"className":2591},[1397],[507,2593,2595],{"className":2594},[708],[507,2596,2599],{"className":2597,"style":2598},[712],"height:0.0589em;",[507,2600],{},[507,2602],{"className":2603,"style":735},[672],[507,2605,1208],{"className":2606,"style":1370},[551,552],[507,2608,488],{"className":2609},[551],[324,2611,2612,2613,2616,2617,2647,2648,488],{},"This is an important point about prediction versus fitting. The theory predicted that the Higgs boson should exist, that it should have spin zero, and exactly how strongly it should couple to every other particle once its mass was known. It did ",[331,2614,2615],{},"not"," predict the mass itself, because ",[507,2618,2620,2634],{"className":2619},[510],[507,2621,2623],{"className":2622},[514],[516,2624,2625],{"xmlns":518},[520,2626,2627,2631],{},[523,2628,2629],{},[526,2630,622],{},[530,2632,2633],{"encoding":532},"\\lambda",[507,2635,2637],{"className":2636,"ariaHidden":538},[537],[507,2638,2640,2644],{"className":2639},[542],[507,2641],{"className":2642,"style":2643},[546],"height:0.6944em;",[507,2645,622],{"className":2646},[551,552]," was a free parameter. The measured value, about 125 GeV, implies ",[507,2649,2651,2670],{"className":2650},[510],[507,2652,2654],{"className":2653},[514],[516,2655,2656],{"xmlns":518},[520,2657,2658,2667],{},[523,2659,2660,2662,2664],{},[526,2661,622],{},[579,2663,1234],{},[601,2665,2666],{},"0.13",[530,2668,2669],{"encoding":532},"\\lambda \\approx 0.13",[507,2671,2673,2691],{"className":2672,"ariaHidden":538},[537],[507,2674,2676,2679,2682,2685,2688],{"className":2675},[542],[507,2677],{"className":2678,"style":2643},[546],[507,2680,622],{"className":2681},[551,552],[507,2683],{"className":2684,"style":673},[672],[507,2686,1234],{"className":2687},[677],[507,2689],{"className":2690,"style":673},[672],[507,2692,2694,2697],{"className":2693},[542],[507,2695],{"className":2696,"style":1015},[546],[507,2698,2666],{"className":2699},[551],[389,2701,2703],{"id":2702},"how-fermions-get-mass-yukawa-couplings","How Fermions Get Mass: Yukawa Couplings",[324,2705,2706],{},"The Higgs field also explains the masses of electrons, muons and quarks, for a separate reason. In the Standard Model, left-handed and right-handed versions of these particles transform differently under the electroweak symmetry, so an ordinary mass term, which links the two, is forbidden. A coupling to the Higgs field is allowed. When the field takes its vacuum value, that coupling turns into a mass:",[507,2708,2710],{"className":2709},[561],[507,2711,2713,2755],{"className":2712},[510],[507,2714,2716],{"className":2715},[514],[516,2717,2718],{"xmlns":518,"display":570},[520,2719,2720,2752],{},[523,2721,2722,2729,2731,2750],{},[1787,2723,2724,2726],{},[526,2725,1791],{},[526,2727,2728],{},"f",[579,2730,590],{},[1202,2732,2733,2746],{},[523,2734,2735,2742,2744],{},[1787,2736,2737,2740],{},[526,2738,2739],{},"y",[526,2741,2728],{},[605,2743,607],{},[526,2745,1208],{},[1228,2747,2748],{},[601,2749,603],{},[579,2751,1215],{"separator":538},[530,2753,2754],{"encoding":532},"m_f = \\frac{y_f\\, v}{\\sqrt{2}},",[507,2756,2758,2816],{"className":2757,"ariaHidden":538},[537],[507,2759,2761,2765,2807,2810,2813],{"className":2760},[542],[507,2762],{"className":2763,"style":2764},[546],"height:0.7167em;vertical-align:-0.2861em;",[507,2766,2768,2771],{"className":2767},[551],[507,2769,1791],{"className":2770},[551,552],[507,2772,2774],{"className":2773},[700],[507,2775,2777,2799],{"className":2776},[704,1323],[507,2778,2780,2796],{"className":2779},[708],[507,2781,2784],{"className":2782,"style":2783},[712],"height:0.3361em;",[507,2785,2786,2789],{"style":1918},[507,2787],{"className":2788,"style":721},[720],[507,2790,2792],{"className":2791},[725,726,727,728],[507,2793,2728],{"className":2794,"style":2795},[551,552,728],"margin-right:0.1076em;",[507,2797,1398],{"className":2798},[1397],[507,2800,2802],{"className":2801},[708],[507,2803,2805],{"className":2804,"style":2389},[712],[507,2806],{},[507,2808],{"className":2809,"style":673},[672],[507,2811,590],{"className":2812},[677],[507,2814],{"className":2815,"style":673},[672],[507,2817,2819,2822,2976],{"className":2818},[542],[507,2820],{"className":2821,"style":1440},[546],[507,2823,2825,2828,2973],{"className":2824},[551],[507,2826],{"className":2827},[661,1316],[507,2829,2831],{"className":2830},[1202],[507,2832,2834,2965],{"className":2833},[704,1323],[507,2835,2837,2962],{"className":2836},[708],[507,2838,2840,2899,2907],{"className":2839,"style":1459},[712],[507,2841,2843,2846],{"style":2842},"top:-2.2028em;",[507,2844],{"className":2845,"style":1337},[720],[507,2847,2849],{"className":2848},[551],[507,2850,2852],{"className":2851},[551,1472],[507,2853,2855,2890],{"className":2854},[704,1323],[507,2856,2858,2887],{"className":2857},[708],[507,2859,2862,2874],{"className":2860,"style":2861},[712],"height:0.9072em;",[507,2863,2865,2868],{"className":2864,"style":1487},[1486],[507,2866],{"className":2867,"style":1337},[720],[507,2869,2871],{"className":2870,"style":1494},[551],[507,2872,603],{"className":2873},[551],[507,2875,2877,2880],{"style":2876},"top:-2.8672em;",[507,2878],{"className":2879,"style":1337},[720],[507,2881,2883],{"className":2882,"style":1508},[1507],[1510,2884,2885],{"xmlns":1512,"width":1513,"height":1514,"viewBox":1515,"preserveAspectRatio":1516},[1518,2886],{"d":1520},[507,2888,1398],{"className":2889},[1397],[507,2891,2893],{"className":2892},[708],[507,2894,2897],{"className":2895,"style":2896},[712],"height:0.1328em;",[507,2898],{},[507,2900,2901,2904],{"style":1346},[507,2902],{"className":2903,"style":1337},[720],[507,2905],{"className":2906,"style":1354},[1353],[507,2908,2909,2912],{"style":1357},[507,2910],{"className":2911,"style":1337},[720],[507,2913,2915,2956,2959],{"className":2914},[551],[507,2916,2918,2921],{"className":2917},[551],[507,2919,2739],{"className":2920,"style":1370},[551,552],[507,2922,2924],{"className":2923},[700],[507,2925,2927,2948],{"className":2926},[704,1323],[507,2928,2930,2945],{"className":2929},[708],[507,2931,2933],{"className":2932,"style":2783},[712],[507,2934,2936,2939],{"style":2935},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[507,2937],{"className":2938,"style":721},[720],[507,2940,2942],{"className":2941},[725,726,727,728],[507,2943,2728],{"className":2944,"style":2795},[551,552,728],[507,2946,1398],{"className":2947},[1397],[507,2949,2951],{"className":2950},[708],[507,2952,2954],{"className":2953,"style":2389},[712],[507,2955],{},[507,2957],{"className":2958,"style":735},[672],[507,2960,1208],{"className":2961,"style":1370},[551,552],[507,2963,1398],{"className":2964},[1397],[507,2966,2968],{"className":2967},[708],[507,2969,2971],{"className":2970,"style":1561},[712],[507,2972],{},[507,2974],{"className":2975},[668,1316],[507,2977,1215],{"className":2978},[1414],[324,2980,2981,2982,1632,3052,3055,3056,3084,3085,3181,3182,488],{},"where ",[507,2983,2985,3003],{"className":2984},[510],[507,2986,2988],{"className":2987},[514],[516,2989,2990],{"xmlns":518},[520,2991,2992,3000],{},[523,2993,2994],{},[1787,2995,2996,2998],{},[526,2997,2739],{},[526,2999,2728],{},[530,3001,3002],{"encoding":532},"y_f",[507,3004,3006],{"className":3005,"ariaHidden":538},[537],[507,3007,3009,3012],{"className":3008},[542],[507,3010],{"className":3011,"style":2764},[546],[507,3013,3015,3018],{"className":3014},[551],[507,3016,2739],{"className":3017,"style":1370},[551,552],[507,3019,3021],{"className":3020},[700],[507,3022,3024,3044],{"className":3023},[704,1323],[507,3025,3027,3041],{"className":3026},[708],[507,3028,3030],{"className":3029,"style":2783},[712],[507,3031,3032,3035],{"style":2935},[507,3033],{"className":3034,"style":721},[720],[507,3036,3038],{"className":3037},[725,726,727,728],[507,3039,2728],{"className":3040,"style":2795},[551,552,728],[507,3042,1398],{"className":3043},[1397],[507,3045,3047],{"className":3046},[708],[507,3048,3050],{"className":3049,"style":2389},[712],[507,3051],{},[331,3053,3054],{},"Yukawa coupling"," of fermion ",[507,3057,3059,3072],{"className":3058},[510],[507,3060,3062],{"className":3061},[514],[516,3063,3064],{"xmlns":518},[520,3065,3066,3070],{},[523,3067,3068],{},[526,3069,2728],{},[530,3071,2728],{"encoding":532},[507,3073,3075],{"className":3074,"ariaHidden":538},[537],[507,3076,3078,3081],{"className":3077},[542],[507,3079],{"className":3080,"style":547},[546],[507,3082,2728],{"className":3083,"style":2795},[551,552],". The top quark has ",[507,3086,3088,3112],{"className":3087},[510],[507,3089,3091],{"className":3090},[514],[516,3092,3093],{"xmlns":518},[520,3094,3095,3109],{},[523,3096,3097,3104,3106],{},[1787,3098,3099,3101],{},[526,3100,2739],{},[526,3102,3103],{},"t",[579,3105,1234],{},[601,3107,3108],{},"1",[530,3110,3111],{"encoding":532},"y_t \\approx 1",[507,3113,3115,3172],{"className":3114,"ariaHidden":538},[537],[507,3116,3118,3122,3163,3166,3169],{"className":3117},[542],[507,3119],{"className":3120,"style":3121},[546],"height:0.6776em;vertical-align:-0.1944em;",[507,3123,3125,3128],{"className":3124},[551],[507,3126,2739],{"className":3127,"style":1370},[551,552],[507,3129,3131],{"className":3130},[700],[507,3132,3134,3155],{"className":3133},[704,1323],[507,3135,3137,3152],{"className":3136},[708],[507,3138,3141],{"className":3139,"style":3140},[712],"height:0.2806em;",[507,3142,3143,3146],{"style":2935},[507,3144],{"className":3145,"style":721},[720],[507,3147,3149],{"className":3148},[725,726,727,728],[507,3150,3103],{"className":3151},[551,552,728],[507,3153,1398],{"className":3154},[1397],[507,3156,3158],{"className":3157},[708],[507,3159,3161],{"className":3160,"style":1938},[712],[507,3162],{},[507,3164],{"className":3165,"style":673},[672],[507,3167,1234],{"className":3168},[677],[507,3170],{"className":3171,"style":673},[672],[507,3173,3175,3178],{"className":3174},[542],[507,3176],{"className":3177,"style":1015},[546],[507,3179,3108],{"className":3180},[551]," and a mass near 173 GeV; the electron has ",[507,3183,3185,3224],{"className":3184},[510],[507,3186,3188],{"className":3187},[514],[516,3189,3190],{"xmlns":518},[520,3191,3192,3221],{},[523,3193,3194,3201,3203,3206,3209],{},[1787,3195,3196,3198],{},[526,3197,2739],{},[526,3199,3200],{},"e",[579,3202,1234],{},[601,3204,3205],{},"3",[579,3207,3208],{},"×",[595,3210,3211,3214],{},[601,3212,3213],{},"10",[523,3215,3216,3218],{},[579,3217,593],{},[601,3219,3220],{},"6",[530,3222,3223],{"encoding":532},"y_e \\approx 3\\times10^{-6}",[507,3225,3227,3282,3301],{"className":3226,"ariaHidden":538},[537],[507,3228,3230,3233,3273,3276,3279],{"className":3229},[542],[507,3231],{"className":3232,"style":3121},[546],[507,3234,3236,3239],{"className":3235},[551],[507,3237,2739],{"className":3238,"style":1370},[551,552],[507,3240,3242],{"className":3241},[700],[507,3243,3245,3265],{"className":3244},[704,1323],[507,3246,3248,3262],{"className":3247},[708],[507,3249,3251],{"className":3250,"style":2367},[712],[507,3252,3253,3256],{"style":2935},[507,3254],{"className":3255,"style":721},[720],[507,3257,3259],{"className":3258},[725,726,727,728],[507,3260,3200],{"className":3261},[551,552,728],[507,3263,1398],{"className":3264},[1397],[507,3266,3268],{"className":3267},[708],[507,3269,3271],{"className":3270,"style":1938},[712],[507,3272],{},[507,3274],{"className":3275,"style":673},[672],[507,3277,1234],{"className":3278},[677],[507,3280],{"className":3281,"style":673},[672],[507,3283,3285,3289,3292,3295,3298],{"className":3284},[542],[507,3286],{"className":3287,"style":3288},[546],"height:0.7278em;vertical-align:-0.0833em;",[507,3290,3205],{"className":3291},[551],[507,3293],{"className":3294,"style":657},[672],[507,3296,3208],{"className":3297},[766],[507,3299],{"className":3300,"style":657},[672],[507,3302,3304,3307,3310],{"className":3303},[542],[507,3305],{"className":3306,"style":988},[546],[507,3308,3108],{"className":3309},[551],[507,3311,3313,3316],{"className":3312},[551],[507,3314,956],{"className":3315},[551],[507,3317,3319],{"className":3318},[700],[507,3320,3322],{"className":3321},[704],[507,3323,3325],{"className":3324},[708],[507,3326,3328],{"className":3327,"style":988},[712],[507,3329,3330,3333],{"style":917},[507,3331],{"className":3332,"style":721},[720],[507,3334,3336],{"className":3335},[725,726,727,728],[507,3337,3339,3342],{"className":3338},[551,728],[507,3340,593],{"className":3341},[551,728],[507,3343,3220],{"className":3344},[551,728],[324,3346,3347,3348,3351,3352,3355],{},"Here the prediction-versus-fitting distinction matters again. The Higgs mechanism explains ",[380,3349,3350],{},"how"," fermions can have mass consistently. It does not explain ",[380,3353,3354],{},"why"," each mass has the value it has. Each Yukawa coupling is measured and inserted by hand. Why they span more than five orders of magnitude remains unknown.",[362,3357,3359],{"id":3358},"most-of-your-mass-is-not-from-the-higgs","Most of Your Mass Is Not From the Higgs",[324,3361,3362],{},"A frequent misconception is that the Higgs field is responsible for the mass of everything. It is not.",[324,3364,3365,3366,3455,3456,488],{},"A proton is made of two up quarks and a down quark, whose rest masses, which do come from the Higgs field, add up to roughly 1% of the proton's mass. The rest is energy: the motion of quarks and the energy of the gluon field that binds them, described by quantum chromodynamics (QCD). Through ",[507,3367,3369,3395],{"className":3368},[510],[507,3370,3372],{"className":3371},[514],[516,3373,3374],{"xmlns":518},[520,3375,3376,3392],{},[523,3377,3378,3381,3383,3385],{},[526,3379,3380],{},"E",[579,3382,590],{},[526,3384,1791],{},[595,3386,3387,3390],{},[526,3388,3389],{},"c",[601,3391,603],{},[530,3393,3394],{"encoding":532},"E = mc^2",[507,3396,3398,3417],{"className":3397,"ariaHidden":538},[537],[507,3399,3401,3404,3408,3411,3414],{"className":3400},[542],[507,3402],{"className":3403,"style":1165},[546],[507,3405,3380],{"className":3406,"style":3407},[551,552],"margin-right:0.0576em;",[507,3409],{"className":3410,"style":673},[672],[507,3412,590],{"className":3413},[677],[507,3415],{"className":3416,"style":673},[672],[507,3418,3420,3423,3426],{"className":3419},[542],[507,3421],{"className":3422,"style":988},[546],[507,3424,1791],{"className":3425},[551,552],[507,3427,3429,3432],{"className":3428},[551],[507,3430,3389],{"className":3431},[551,552],[507,3433,3435],{"className":3434},[700],[507,3436,3438],{"className":3437},[704],[507,3439,3441],{"className":3440},[708],[507,3442,3444],{"className":3443,"style":988},[712],[507,3445,3446,3449],{"style":917},[507,3447],{"className":3448,"style":721},[720],[507,3450,3452],{"className":3451},[725,726,727,728],[507,3453,603],{"className":3454},[551,728],", that energy appears as mass. Lattice QCD calculations have reproduced the masses of the proton, neutron and other light hadrons from first principles, confirming that the strong interaction accounts for them ",[341,3457,3459],{"className":3458},[344],"[13]",[324,3461,3462,3463,3466],{},"Since protons and neutrons make up more than 99% of the mass of ordinary matter ",[341,3464,3459],{"className":3465},[344],", most of the mass of a human body, a planet or a star comes from QCD binding energy, not directly from the Higgs field.",[324,3468,3469],{},"The Higgs field still matters enormously for ordinary matter. It sets the electron's mass, and the electron's mass sets the size of atoms and the energies of chemistry. It sets the masses of the up and down quarks, whose small difference makes the neutron slightly heavier than the proton and therefore allows hydrogen atoms to be stable. And it gives the W and Z their mass, which keeps the weak force weak and lets the Sun burn slowly for billions of years.",[362,3471,3473],{"id":3472},"evidence-the-2012-discovery","Evidence: The 2012 Discovery",[389,3475,3477],{"id":3476},"the-search","The Search",[324,3479,3480],{},"A Higgs boson is extremely short-lived. It cannot be seen directly, only inferred from the particles it decays into. And it is produced rarely: at the Large Hadron Collider (LHC), only about one proton collision in a billion or more creates one. Physicists had to collide protons at unprecedented rates and search through the debris for a small excess of events at one particular mass.",[324,3482,3483,3484,1703,3487,3490],{},"The two general-purpose detectors, ",[331,3485,3486],{},"ATLAS",[331,3488,3489],{},"CMS",", were built partly for this purpose by independent collaborations of thousands of physicists, using different technologies so that each could check the other.",[389,3492,3494],{"id":3493},"the-observation","The Observation",[324,3496,3497,3498,3501],{},"On 4 July 2012, both collaborations announced the observation of a new particle. The papers were published that year in ",[380,3499,3500],{},"Physics Letters B",":",[418,3503,3504,3638],{},[421,3505,3506,3508,3509,3633,3634,488],{},[331,3507,3486],{}," reported a new neutral boson with a mass of ",[507,3510,3512,3555],{"className":3511},[510],[507,3513,3515],{"className":3514},[514],[516,3516,3517],{"xmlns":518},[520,3518,3519,3552],{},[523,3520,3521,3524,3527,3530,3532,3534,3537,3539,3541,3543,3545,3547,3550],{},[601,3522,3523],{},"126.0",[579,3525,3526],{},"±",[601,3528,3529],{},"0.4",[605,3531,607],{},[579,3533,582],{"stretchy":581},[605,3535,3536],{},"stat",[579,3538,587],{"stretchy":581},[579,3540,3526],{},[601,3542,3529],{},[605,3544,607],{},[579,3546,582],{"stretchy":581},[605,3548,3549],{},"sys",[579,3551,587],{"stretchy":581},[530,3553,3554],{"encoding":532},"126.0 \\pm 0.4\\,(\\text{stat}) \\pm 0.4\\,(\\text{sys})",[507,3556,3558,3576,3609],{"className":3557,"ariaHidden":538},[537],[507,3559,3561,3564,3567,3570,3573],{"className":3560},[542],[507,3562],{"className":3563,"style":3288},[546],[507,3565,3523],{"className":3566},[551],[507,3568],{"className":3569,"style":657},[672],[507,3571,3526],{"className":3572},[766],[507,3574],{"className":3575,"style":657},[672],[507,3577,3579,3582,3585,3588,3591,3597,3600,3603,3606],{"className":3578},[542],[507,3580],{"className":3581,"style":653},[546],[507,3583,3529],{"className":3584},[551],[507,3586],{"className":3587,"style":735},[672],[507,3589,582],{"className":3590},[661],[507,3592,3594],{"className":3593},[551,1592],[507,3595,3536],{"className":3596},[551],[507,3598,587],{"className":3599},[668],[507,3601],{"className":3602,"style":657},[672],[507,3604,3526],{"className":3605},[766],[507,3607],{"className":3608,"style":657},[672],[507,3610,3612,3615,3618,3621,3624,3630],{"className":3611},[542],[507,3613],{"className":3614,"style":653},[546],[507,3616,3529],{"className":3617},[551],[507,3619],{"className":3620,"style":735},[672],[507,3622,582],{"className":3623},[661],[507,3625,3627],{"className":3626},[551,1592],[507,3628,3549],{"className":3629},[551],[507,3631,587],{"className":3632},[668]," GeV, at a significance of 5.9 standard deviations ",[341,3635,3637],{"className":3636},[344],"[14]",[421,3639,3640,3642,3643,3764,3765,488],{},[331,3641,3489],{}," reported an excess at ",[507,3644,3646,3686],{"className":3645},[510],[507,3647,3649],{"className":3648},[514],[516,3650,3651],{"xmlns":518},[520,3652,3653,3683],{},[523,3654,3655,3658,3660,3662,3664,3666,3668,3670,3672,3675,3677,3679,3681],{},[601,3656,3657],{},"125.3",[579,3659,3526],{},[601,3661,3529],{},[605,3663,607],{},[579,3665,582],{"stretchy":581},[605,3667,3536],{},[579,3669,587],{"stretchy":581},[579,3671,3526],{},[601,3673,3674],{},"0.5",[605,3676,607],{},[579,3678,582],{"stretchy":581},[605,3680,3549],{},[579,3682,587],{"stretchy":581},[530,3684,3685],{"encoding":532},"125.3 \\pm 0.4\\,(\\text{stat}) \\pm 0.5\\,(\\text{sys})",[507,3687,3689,3707,3740],{"className":3688,"ariaHidden":538},[537],[507,3690,3692,3695,3698,3701,3704],{"className":3691},[542],[507,3693],{"className":3694,"style":3288},[546],[507,3696,3657],{"className":3697},[551],[507,3699],{"className":3700,"style":657},[672],[507,3702,3526],{"className":3703},[766],[507,3705],{"className":3706,"style":657},[672],[507,3708,3710,3713,3716,3719,3722,3728,3731,3734,3737],{"className":3709},[542],[507,3711],{"className":3712,"style":653},[546],[507,3714,3529],{"className":3715},[551],[507,3717],{"className":3718,"style":735},[672],[507,3720,582],{"className":3721},[661],[507,3723,3725],{"className":3724},[551,1592],[507,3726,3536],{"className":3727},[551],[507,3729,587],{"className":3730},[668],[507,3732],{"className":3733,"style":657},[672],[507,3735,3526],{"className":3736},[766],[507,3738],{"className":3739,"style":657},[672],[507,3741,3743,3746,3749,3752,3755,3761],{"className":3742},[542],[507,3744],{"className":3745,"style":653},[546],[507,3747,3674],{"className":3748},[551],[507,3750],{"className":3751,"style":735},[672],[507,3753,582],{"className":3754},[661],[507,3756,3758],{"className":3757},[551,1592],[507,3759,3549],{"className":3760},[551],[507,3762,587],{"className":3763},[668]," GeV, with a significance of 5.0 standard deviations ",[341,3766,3768],{"className":3767},[344],"[15]",[324,3770,3771],{},"In particle physics, 5 standard deviations (\"five sigma\") is the conventional threshold for claiming a discovery. It corresponds to a probability of roughly one in 3.5 million that background fluctuations alone would produce a signal at least as strong. The clearest signals came from two rare but clean decay channels: a Higgs boson decaying into two photons, and into two Z bosons that each decay into a pair of electrons or muons.",[324,3773,3774,3775,3778,3779,3783],{},"The observation of the decay into two photons also showed that the new particle could not have spin 1, consistent with the spin-0 prediction ",[341,3776,3768],{"className":3777},[344],". In 2013 François Englert and Peter Higgs received the Nobel Prize in Physics for the theoretical discovery of the mechanism ",[341,3780,3782],{"className":3781},[344],"[16]",". Robert Brout had died in 2011.",[389,3785,3787],{"id":3786},"what-has-been-measured-since","What Has Been Measured Since",[324,3789,3790,3793],{},[331,3791,3792],{},"Established fact:"," a boson with a mass near 125 GeV exists, and its properties so far match the Standard Model Higgs boson.",[418,3795,3796,3918,3927,4130,4141],{},[421,3797,3798,3801,3802,3855,3856,3860,3861,3855,3914,488],{},[331,3799,3800],{},"Mass."," The ATLAS and CMS combined Run 1 measurement gave ",[507,3803,3805,3825],{"className":3804},[510],[507,3806,3808],{"className":3807},[514],[516,3809,3810],{"xmlns":518},[520,3811,3812,3822],{},[523,3813,3814,3817,3819],{},[601,3815,3816],{},"125.09",[579,3818,3526],{},[601,3820,3821],{},"0.24",[530,3823,3824],{"encoding":532},"125.09 \\pm 0.24",[507,3826,3828,3846],{"className":3827,"ariaHidden":538},[537],[507,3829,3831,3834,3837,3840,3843],{"className":3830},[542],[507,3832],{"className":3833,"style":3288},[546],[507,3835,3816],{"className":3836},[551],[507,3838],{"className":3839,"style":657},[672],[507,3841,3526],{"className":3842},[766],[507,3844],{"className":3845,"style":657},[672],[507,3847,3849,3852],{"className":3848},[542],[507,3850],{"className":3851,"style":1015},[546],[507,3853,3821],{"className":3854},[551]," GeV ",[341,3857,3859],{"className":3858},[344],"[17]",". The Particle Data Group's 2024 world average is ",[507,3862,3864,3884],{"className":3863},[510],[507,3865,3867],{"className":3866},[514],[516,3868,3869],{"xmlns":518},[520,3870,3871,3881],{},[523,3872,3873,3876,3878],{},[601,3874,3875],{},"125.20",[579,3877,3526],{},[601,3879,3880],{},"0.11",[530,3882,3883],{"encoding":532},"125.20 \\pm 0.11",[507,3885,3887,3905],{"className":3886,"ariaHidden":538},[537],[507,3888,3890,3893,3896,3899,3902],{"className":3889},[542],[507,3891],{"className":3892,"style":3288},[546],[507,3894,3875],{"className":3895},[551],[507,3897],{"className":3898,"style":657},[672],[507,3900,3526],{"className":3901},[766],[507,3903],{"className":3904,"style":657},[672],[507,3906,3908,3911],{"className":3907},[542],[507,3909],{"className":3910,"style":1015},[546],[507,3912,3880],{"className":3913},[551],[341,3915,3917],{"className":3916},[344],"[18]",[421,3919,3920,3923,3924,488],{},[331,3921,3922],{},"Spin and parity."," The data are consistent with spin 0 and even parity; the pure odd-parity hypothesis is disfavoured ",[341,3925,3917],{"className":3926},[344],[421,3928,3929,3932,3933,4051,4052,4055,4056,4129],{},[331,3930,3931],{},"Width."," The total decay width, which sets its lifetime, is measured indirectly as ",[507,3934,3936,3971],{"className":3935},[510],[507,3937,3939],{"className":3938},[514],[516,3940,3941],{"xmlns":518},[520,3942,3943,3968],{},[523,3944,3945,3948],{},[601,3946,3947],{},"3.",[3949,3950,3951,3954,3961],"msubsup",{},[601,3952,3953],{},"7",[523,3955,3956,3958],{},[579,3957,593],{},[601,3959,3960],{},"1.4",[523,3962,3963,3965],{},[579,3964,619],{},[601,3966,3967],{},"1.9",[530,3969,3970],{"encoding":532},"3.7^{+1.9}_{-1.4}",[507,3972,3974],{"className":3973,"ariaHidden":538},[537],[507,3975,3977,3981,3984],{"className":3976},[542],[507,3978],{"className":3979,"style":3980},[546],"height:1.1789em;vertical-align:-0.3246em;",[507,3982,3947],{"className":3983},[551],[507,3985,3987,3990],{"className":3986},[551],[507,3988,3953],{"className":3989},[551],[507,3991,3993],{"className":3992},[700],[507,3994,3996,4042],{"className":3995},[704,1323],[507,3997,3999,4039],{"className":3998},[708],[507,4000,4003,4021],{"className":4001,"style":4002},[712],"height:0.8542em;",[507,4004,4006,4009],{"style":4005},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[507,4007],{"className":4008,"style":721},[720],[507,4010,4012],{"className":4011},[725,726,727,728],[507,4013,4015,4018],{"className":4014},[551,728],[507,4016,593],{"className":4017},[551,728],[507,4019,3960],{"className":4020},[551,728],[507,4022,4024,4027],{"style":4023},"top:-3.1031em;margin-right:0.05em;",[507,4025],{"className":4026,"style":721},[720],[507,4028,4030],{"className":4029},[725,726,727,728],[507,4031,4033,4036],{"className":4032},[551,728],[507,4034,619],{"className":4035},[551,728],[507,4037,3967],{"className":4038},[551,728],[507,4040,1398],{"className":4041},[1397],[507,4043,4045],{"className":4044},[708],[507,4046,4049],{"className":4047,"style":4048},[712],"height:0.3246em;",[507,4050],{}," MeV ",[341,4053,3917],{"className":4054},[344],", consistent with the Standard Model expectation of roughly 4 MeV. This corresponds to a lifetime around ",[507,4057,4059,4082],{"className":4058},[510],[507,4060,4062],{"className":4061},[514],[516,4063,4064],{"xmlns":518},[520,4065,4066,4079],{},[523,4067,4068],{},[595,4069,4070,4072],{},[601,4071,3213],{},[523,4073,4074,4076],{},[579,4075,593],{},[601,4077,4078],{},"22",[530,4080,4081],{"encoding":532},"10^{-22}",[507,4083,4085],{"className":4084,"ariaHidden":538},[537],[507,4086,4088,4091,4094],{"className":4087},[542],[507,4089],{"className":4090,"style":988},[546],[507,4092,3108],{"className":4093},[551],[507,4095,4097,4100],{"className":4096},[551],[507,4098,956],{"className":4099},[551],[507,4101,4103],{"className":4102},[700],[507,4104,4106],{"className":4105},[704],[507,4107,4109],{"className":4108},[708],[507,4110,4112],{"className":4111,"style":988},[712],[507,4113,4114,4117],{"style":917},[507,4115],{"className":4116,"style":721},[720],[507,4118,4120],{"className":4119},[725,726,727,728],[507,4121,4123,4126],{"className":4122},[551,728],[507,4124,593],{"className":4125},[551,728],[507,4127,4078],{"className":4128},[551,728]," seconds.",[421,4131,4132,4135,4136,4140],{},[331,4133,4134],{},"Couplings scale with mass."," Ten years after discovery, ATLAS and CMS published detailed maps of the Higgs boson's interactions with W and Z bosons, the top and bottom quarks, the tau lepton and the muon ",[341,4137,4139],{"className":4138},[344],"[19,20]",". Across these particles, spanning a wide range of masses, the coupling strength grows in proportion to the particle's mass, as the Yukawa picture requires.",[421,4142,4143,4146,4147,488],{},[331,4144,4145],{},"Direct coupling to the top quark."," In 2018 both experiments observed Higgs bosons produced together with a top quark–antiquark pair, a direct measurement of the largest Yukawa coupling ",[341,4148,4150],{"className":4149},[344],"[21,22]",[324,4152,4153],{},"These are demanding tests. A particle with the right mass but the wrong couplings would have signalled a different mechanism. So far, none of the measurements departs significantly from the Standard Model.",[362,4155,4157],{"id":4156},"limitations-and-open-problems","Limitations and Open Problems",[324,4159,4160],{},"The discovery confirmed the mechanism. It did not close the subject. Several questions remain, at different levels of certainty.",[389,4162,4164],{"id":4163},"the-shape-of-the-potential-is-not-yet-measured","The Shape of the Potential Is Not Yet Measured",[324,4166,4167,4170,4171,4199],{},[331,4168,4169],{},"Accepted theory, not yet directly tested:"," the Mexican-hat potential is inferred, not observed. Its shape is tested by the Higgs boson's interaction with itself, the self-coupling ",[507,4172,4174,4187],{"className":4173},[510],[507,4175,4177],{"className":4176},[514],[516,4178,4179],{"xmlns":518},[520,4180,4181,4185],{},[523,4182,4183],{},[526,4184,622],{},[530,4186,2633],{"encoding":532},[507,4188,4190],{"className":4189,"ariaHidden":538},[537],[507,4191,4193,4196],{"className":4192},[542],[507,4194],{"className":4195,"style":2643},[546],[507,4197,622],{"className":4198},[551,552],", which would show up in rare events producing two Higgs bosons at once. Current LHC data only constrain it loosely. Measuring it is a central goal of the High-Luminosity LHC and of proposed future colliders. Until then, the potential written above is the simplest form consistent with the data, not a measured curve.",[389,4201,4203],{"id":4202},"vacuum-metastability","Vacuum Metastability",[324,4205,4206,4209,4210,4238,4239,4267,4268,4333,4334,3855,4400,4404,4405,488],{},[331,4207,4208],{},"Theoretical calculation with significant uncertainty:"," the self-coupling ",[507,4211,4213,4226],{"className":4212},[510],[507,4214,4216],{"className":4215},[514],[516,4217,4218],{"xmlns":518},[520,4219,4220,4224],{},[523,4221,4222],{},[526,4223,622],{},[530,4225,2633],{"encoding":532},[507,4227,4229],{"className":4228,"ariaHidden":538},[537],[507,4230,4232,4235],{"className":4231},[542],[507,4233],{"className":4234,"style":2643},[546],[507,4236,622],{"className":4237},[551,552]," changes with energy because of quantum effects, most strongly from the heavy top quark. Extrapolating the Standard Model to very high energies, with the measured Higgs and top masses, ",[507,4240,4242,4255],{"className":4241},[510],[507,4243,4245],{"className":4244},[514],[516,4246,4247],{"xmlns":518},[520,4248,4249,4253],{},[523,4250,4251],{},[526,4252,622],{},[530,4254,2633],{"encoding":532},[507,4256,4258],{"className":4257,"ariaHidden":538},[537],[507,4259,4261,4264],{"className":4260},[542],[507,4262],{"className":4263,"style":2643},[546],[507,4265,622],{"className":4266},[551,552]," appears to turn slightly negative around ",[507,4269,4271,4289],{"className":4270},[510],[507,4272,4274],{"className":4273},[514],[516,4275,4276],{"xmlns":518},[520,4277,4278,4286],{},[523,4279,4280],{},[595,4281,4282,4284],{},[601,4283,3213],{},[601,4285,3213],{},[530,4287,4288],{"encoding":532},"10^{10}",[507,4290,4292],{"className":4291,"ariaHidden":538},[537],[507,4293,4295,4298,4301],{"className":4294},[542],[507,4296],{"className":4297,"style":988},[546],[507,4299,3108],{"className":4300},[551],[507,4302,4304,4307],{"className":4303},[551],[507,4305,956],{"className":4306},[551],[507,4308,4310],{"className":4309},[700],[507,4311,4313],{"className":4312},[704],[507,4314,4316],{"className":4315},[708],[507,4317,4319],{"className":4318,"style":988},[712],[507,4320,4321,4324],{"style":917},[507,4322],{"className":4323,"style":721},[720],[507,4325,4327],{"className":4326},[725,726,727,728],[507,4328,4330],{"className":4329},[551,728],[507,4331,3213],{"className":4332},[551,728]," to ",[507,4335,4337,4356],{"className":4336},[510],[507,4338,4340],{"className":4339},[514],[516,4341,4342],{"xmlns":518},[520,4343,4344,4353],{},[523,4345,4346],{},[595,4347,4348,4350],{},[601,4349,3213],{},[601,4351,4352],{},"11",[530,4354,4355],{"encoding":532},"10^{11}",[507,4357,4359],{"className":4358,"ariaHidden":538},[537],[507,4360,4362,4365,4368],{"className":4361},[542],[507,4363],{"className":4364,"style":988},[546],[507,4366,3108],{"className":4367},[551],[507,4369,4371,4374],{"className":4370},[551],[507,4372,956],{"className":4373},[551],[507,4375,4377],{"className":4376},[700],[507,4378,4380],{"className":4379},[704],[507,4381,4383],{"className":4382},[708],[507,4384,4386],{"className":4385,"style":988},[712],[507,4387,4388,4391],{"style":917},[507,4389],{"className":4390,"style":721},[720],[507,4392,4394],{"className":4393},[725,726,727,728],[507,4395,4397],{"className":4396},[551,728],[507,4398,4352],{"className":4399},[551,728],[341,4401,4403],{"className":4402},[344],"[23,24]",". If so, the valley we live in would not be the deepest one. There would be a lower-energy state elsewhere, and our vacuum would be ",[331,4406,4407],{},"metastable",[324,4409,4410,4411,4415,4416,488],{},"Two points keep this from being alarming. First, the calculated lifetime of our vacuum is vastly longer than the age of the universe ",[341,4412,4414],{"className":4413},[344],"[23]",". Second, the conclusion depends sensitively on the top-quark mass and assumes no new physics at any energy up to that scale, which is itself unlikely. What makes the result interesting is not danger but coincidence: the measured Higgs mass sits close to the boundary between stability and instability, a \"near-criticality\" whose meaning, if any, is unknown ",[341,4417,4419],{"className":4418},[344],"[24]",[389,4421,4423],{"id":4422},"the-hierarchy-problem","The Hierarchy Problem",[324,4425,4426,4429,4430,4496,4497,4563],{},[331,4427,4428],{},"Open problem:"," quantum effects shift the Higgs mass by amounts proportional to the energy scale of any heavier physics it interacts with. If the Standard Model is valid up to the Planck scale, around ",[507,4431,4433,4452],{"className":4432},[510],[507,4434,4436],{"className":4435},[514],[516,4437,4438],{"xmlns":518},[520,4439,4440,4449],{},[523,4441,4442],{},[595,4443,4444,4446],{},[601,4445,3213],{},[601,4447,4448],{},"19",[530,4450,4451],{"encoding":532},"10^{19}",[507,4453,4455],{"className":4454,"ariaHidden":538},[537],[507,4456,4458,4461,4464],{"className":4457},[542],[507,4459],{"className":4460,"style":988},[546],[507,4462,3108],{"className":4463},[551],[507,4465,4467,4470],{"className":4466},[551],[507,4468,956],{"className":4469},[551],[507,4471,4473],{"className":4472},[700],[507,4474,4476],{"className":4475},[704],[507,4477,4479],{"className":4478},[708],[507,4480,4482],{"className":4481,"style":988},[712],[507,4483,4484,4487],{"style":917},[507,4485],{"className":4486,"style":721},[720],[507,4488,4490],{"className":4489},[725,726,727,728],[507,4491,4493],{"className":4492},[551,728],[507,4494,4448],{"className":4495},[551,728]," GeV, those shifts would be about ",[507,4498,4500,4519],{"className":4499},[510],[507,4501,4503],{"className":4502},[514],[516,4504,4505],{"xmlns":518},[520,4506,4507,4516],{},[523,4508,4509],{},[595,4510,4511,4513],{},[601,4512,3213],{},[601,4514,4515],{},"17",[530,4517,4518],{"encoding":532},"10^{17}",[507,4520,4522],{"className":4521,"ariaHidden":538},[537],[507,4523,4525,4528,4531],{"className":4524},[542],[507,4526],{"className":4527,"style":988},[546],[507,4529,3108],{"className":4530},[551],[507,4532,4534,4537],{"className":4533},[551],[507,4535,956],{"className":4536},[551],[507,4538,4540],{"className":4539},[700],[507,4541,4543],{"className":4542},[704],[507,4544,4546],{"className":4545},[708],[507,4547,4549],{"className":4548,"style":988},[712],[507,4550,4551,4554],{"style":917},[507,4552],{"className":4553,"style":721},[720],[507,4555,4557],{"className":4556},[725,726,727,728],[507,4558,4560],{"className":4559},[551,728],[507,4561,4515],{"className":4562},[551,728]," times larger than the observed mass. The observed value can only come out small if large contributions cancel with extraordinary precision.",[324,4565,4566,4567,4570,4571,1588,4574,4578],{},"This is the ",[331,4568,4569],{},"hierarchy problem"," or ",[331,4572,4573],{},"naturalness problem",[341,4575,4577],{"className":4576},[344],"[25,26]",". It is not a contradiction; nothing forbids such a cancellation. It is a question of explanation: why is the Higgs mass so far below the scale of gravity?",[324,4580,4581,4584,4585,1703,4587,4589,4590,488],{},[331,4582,4583],{},"Speculation:"," proposed answers include supersymmetry, a composite Higgs made of more fundamental particles, extra spatial dimensions (see ",[336,4586,170],{"href":169},[336,4588,180],{"href":179},"), or anthropic selection among many possible universes. Many of these ideas predicted new particles at LHC energies. None has been found so far. That does not rule them out, but it has pushed them into less comfortable territory and reopened the question of whether naturalness is the right guide at all ",[341,4591,4593],{"className":4592},[344],"[26]",[389,4595,4597],{"id":4596},"other-unknowns","Other Unknowns",[418,4599,4600,4606,4612,4618],{},[421,4601,4602,4605],{},[331,4603,4604],{},"Is the Higgs elementary?"," Every measurement is so far consistent with a point-like particle, but a composite structure at higher energies is not excluded.",[421,4607,4608,4611],{},[331,4609,4610],{},"Is there only one?"," Many extensions of the Standard Model include several Higgs bosons. None beyond the 125 GeV particle has been observed.",[421,4613,4614,4617],{},[331,4615,4616],{},"Neutrino masses."," Neutrinos have mass, but whether it comes from Yukawa couplings to the Higgs field, from a different mechanism, or both, is unknown.",[421,4619,4620,4623],{},[331,4621,4622],{},"The early universe."," Electroweak symmetry is believed to have been unbroken in the hot early universe and broken as it cooled. Whether that transition was gradual or abrupt affects ideas about the origin of the matter–antimatter asymmetry and possible primordial gravitational waves. For the measured Higgs mass, the Standard Model predicts a smooth crossover; an abrupt transition would require new physics.",[362,4625,4627],{"id":4626},"what-the-discovery-settled","What the Discovery Settled",[324,4629,4630],{},"The Higgs field solved a specific problem. Gauge symmetry, the principle that explained electromagnetism, seemed incompatible with a short-range weak force and with the masses of ordinary particles. The Higgs mechanism reconciled them. The symmetry remains exact in the laws but is hidden in the state of the vacuum, and mass becomes a property of how particles interact with that vacuum.",[324,4632,4633],{},"A spin-0 boson of about 125 GeV exists. Its measured couplings grow with particle mass as predicted, and the W and Z masses fit electroweak theory. The discovery settled the existence of the field's excitation; it did not settle the exact shape of its potential, its self-interaction, or the fate of the vacuum at extreme energies.",[324,4635,4636],{},"Nor did it explain why fermions have their particular masses, why the Higgs is so light compared with the Planck scale, or whether this particle is the last piece of the Standard Model or the first sign of something deeper.",[324,4638,4639],{},"The Higgs boson was the final predicted particle of the Standard Model to be found. It completed a theory. In doing so it also turned the vacuum itself into an object of experimental physics, something with structure, a measurable value and possibly a history.",[320,4641,4643],{"id":4642},"references","References",[324,4645,4646,4649,4650,4653,4654,4657,4658,4661],{},[331,4647,345,4648],{}," Yang, C. N., & Mills, R. L. 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(1961)."," \"Field Theories with «Superconductor» Solutions.\" ",[380,4691,4692],{},"Il Nuovo Cimento",[331,4694,4448],{},"(1), 154–164.",[4659,4697],{},[336,4699,4700],{"href":4700,"rel":4701},"https:\u002F\u002Fdoi.org\u002F10.1007\u002FBF02812722",[4665],[324,4703,4704,4707,4708,4653,4710,4713,4714,4716],{},[331,4705,453,4706],{}," Anderson, P. W. (1963)."," \"Plasmons, Gauge Invariance, and Mass.\" ",[380,4709,4652],{},[331,4711,4712],{},"130","(1), 439–442.",[4659,4715],{},[336,4717,4718],{"href":4718,"rel":4719},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRev.130.439",[4665],[324,4721,4722,4725,4726,4653,4729,4732,4733,4735],{},[331,4723,466,4724],{}," Englert, F., & Brout, R. (1964)."," \"Broken Symmetry and the Mass of Gauge Vector Mesons.\" ",[380,4727,4728],{},"Physical Review Letters",[331,4730,4731],{},"13","(9), 321–323.",[4659,4734],{},[336,4736,4737],{"href":4737,"rel":4738},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevLett.13.321",[4665],[324,4740,4741,4745,4746,4653,4749,4752,4753,4755],{},[331,4742,4743,4744],{},"[6]"," Higgs, P. W. (1964)."," \"Broken Symmetries, Massless Particles and Gauge Fields.\" ",[380,4747,4748],{},"Physics Letters",[331,4750,4751],{},"12","(2), 132–133.",[4659,4754],{},[336,4756,4757],{"href":4757,"rel":4758},"https:\u002F\u002Fdoi.org\u002F10.1016\u002F0031-9163(64)91136-9",[4665],[324,4760,4761,4764,4765,4653,4767,4769,4770,4772],{},[331,4762,4763,4744],{},"[7]"," \"Broken Symmetries and the Masses of Gauge Bosons.\" ",[380,4766,4728],{},[331,4768,4731],{},"(16), 508–509.",[4659,4771],{},[336,4773,4774],{"href":4774,"rel":4775},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevLett.13.508",[4665],[324,4777,4778,4781,4782,4653,4784,4786,4787,4789],{},[331,4779,487,4780],{}," Guralnik, G. S., Hagen, C. R., & Kibble, T. W. B. (1964)."," \"Global Conservation Laws and Massless Particles.\" ",[380,4783,4728],{},[331,4785,4731],{},"(20), 585–587.",[4659,4788],{},[336,4790,4791],{"href":4791,"rel":4792},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevLett.13.585",[4665],[324,4794,4795,4799,4800,4653,4803,4805,4806,4808],{},[331,4796,4797,4798],{},"[9]"," Glashow, S. L. (1961)."," \"Partial-Symmetries of Weak Interactions.\" ",[380,4801,4802],{},"Nuclear Physics",[331,4804,4078],{},"(4), 579–588.",[4659,4807],{},[336,4809,4810],{"href":4810,"rel":4811},"https:\u002F\u002Fdoi.org\u002F10.1016\u002F0029-5582(61)90469-2",[4665],[324,4813,4814,4818,4819,4653,4821,4823,4824,4826],{},[331,4815,4816,4817],{},"[10]"," Weinberg, S. (1967)."," \"A Model of Leptons.\" ",[380,4820,4728],{},[331,4822,4448],{},"(21), 1264–1266.",[4659,4825],{},[336,4827,4828],{"href":4828,"rel":4829},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevLett.19.1264",[4665],[324,4831,4832,4835,4836,4653,4839,4842,4843,4845],{},[331,4833,2421,4834],{}," 't Hooft, G. (1971)."," \"Renormalizable Lagrangians for Massive Yang-Mills Fields.\" ",[380,4837,4838],{},"Nuclear Physics B",[331,4840,4841],{},"35","(1), 167–188.",[4659,4844],{},[336,4846,4847],{"href":4847,"rel":4848},"https:\u002F\u002Fdoi.org\u002F10.1016\u002F0550-3213(71)90139-8",[4665],[324,4850,4851,4854,4855,4653,4857,4860,4861,4863],{},[331,4852,2429,4853],{}," UA1 Collaboration, Arnison, G., et al. (1983)."," \"Experimental Observation of Isolated Large Transverse Energy Electrons with Associated Missing Energy at √s = 540 GeV.\" ",[380,4856,3500],{},[331,4858,4859],{},"122","(1), 103–116.",[4659,4862],{},[336,4864,4865],{"href":4865,"rel":4866},"https:\u002F\u002Fdoi.org\u002F10.1016\u002F0370-2693(83)91177-2",[4665],[324,4868,4869,4872,4873,4653,4876,4879,4880,4882],{},[331,4870,3459,4871],{}," Dürr, S., Fodor, Z., Frison, J., et al. (2008)."," \"Ab Initio Determination of Light Hadron Masses.\" ",[380,4874,4875],{},"Science",[331,4877,4878],{},"322","(5905), 1224–1227.",[4659,4881],{},[336,4883,4884],{"href":4884,"rel":4885},"https:\u002F\u002Fdoi.org\u002F10.1126\u002Fscience.1163233",[4665],[324,4887,4888,4891,4892,4653,4894,4897,4898,4900],{},[331,4889,3637,4890],{}," ATLAS Collaboration. (2012)."," \"Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC.\" ",[380,4893,3500],{},[331,4895,4896],{},"716","(1), 1–29.",[4659,4899],{},[336,4901,4902],{"href":4902,"rel":4903},"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.physletb.2012.08.020",[4665],[324,4905,4906,4909,4910,4653,4912,4914,4915,4917],{},[331,4907,3768,4908],{}," CMS Collaboration. (2012)."," \"Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC.\" ",[380,4911,3500],{},[331,4913,4896],{},"(1), 30–61.",[4659,4916],{},[336,4918,4919],{"href":4919,"rel":4920},"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.physletb.2012.08.021",[4665],[324,4922,4923,4926,4927,488,4930,4932],{},[331,4924,3782,4925],{}," The Royal Swedish Academy of Sciences. (2013)."," \"The Nobel Prize in Physics 2013.\" Press release, ",[380,4928,4929],{},"NobelPrize.org",[4659,4931],{},[336,4933,4934],{"href":4934,"rel":4935},"https:\u002F\u002Fwww.nobelprize.org\u002Fprizes\u002Fphysics\u002F2013\u002Fpress-release\u002F",[4665],[324,4937,4938,4941,4942,4653,4944,4947,4948,4950],{},[331,4939,3859,4940],{}," ATLAS and CMS Collaborations. (2015)."," \"Combined Measurement of the Higgs Boson Mass in pp Collisions at √s = 7 and 8 TeV with the ATLAS and CMS Experiments.\" ",[380,4943,4728],{},[331,4945,4946],{},"114","(19), 191803.",[4659,4949],{},[336,4951,4952],{"href":4952,"rel":4953},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevLett.114.191803",[4665],[324,4955,4956,4959,4960,4653,4963,4966,4967,4969,4973,4974],{},[331,4957,3917,4958],{}," Navas, S., et al. (Particle Data Group). (2024)."," \"Review of Particle Physics: Higgs Boson Listings.\" ",[380,4961,4962],{},"Physical Review D",[331,4964,4965],{},"110",", 030001.",[4659,4968],{},[336,4970,4971],{"href":4971,"rel":4972},"https:\u002F\u002Fpdg.lbl.gov\u002F2024\u002Flistings\u002Frpp2024-list-higgs-boson.pdf",[4665]," · ",[336,4975,4976],{"href":4976,"rel":4977},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevD.110.030001",[4665],[324,4979,4980,4984,4985,4653,4988,4991,4992,4994],{},[331,4981,4982,4983],{},"[19]"," ATLAS Collaboration. (2022)."," \"A Detailed Map of Higgs Boson Interactions by the ATLAS Experiment Ten Years After the Discovery.\" ",[380,4986,4987],{},"Nature",[331,4989,4990],{},"607",", 52–59.",[4659,4993],{},[336,4995,4996],{"href":4996,"rel":4997},"https:\u002F\u002Fdoi.org\u002F10.1038\u002Fs41586-022-04893-w",[4665],[324,4999,5000,5004,5005,4653,5007,5009,5010,5012],{},[331,5001,5002,5003],{},"[20]"," CMS Collaboration. (2022)."," \"A Portrait of the Higgs Boson by the CMS Experiment Ten Years After the Discovery.\" ",[380,5006,4987],{},[331,5008,4990],{},", 60–68.",[4659,5011],{},[336,5013,5014],{"href":5014,"rel":5015},"https:\u002F\u002Fdoi.org\u002F10.1038\u002Fs41586-022-04892-x",[4665],[324,5017,5018,5022,5023,4653,5025,5028,5029,5031],{},[331,5019,5020,5021],{},"[21]"," CMS Collaboration. (2018)."," \"Observation of ttH Production.\" ",[380,5024,4728],{},[331,5026,5027],{},"120","(23), 231801.",[4659,5030],{},[336,5032,5033],{"href":5033,"rel":5034},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevLett.120.231801",[4665],[324,5036,5037,5041,5042,4653,5044,5047,5048,5050],{},[331,5038,5039,5040],{},"[22]"," ATLAS Collaboration. (2018)."," \"Observation of Higgs Boson Production in Association with a Top Quark Pair at the LHC with the ATLAS Detector.\" ",[380,5043,3500],{},[331,5045,5046],{},"784",", 173–191.",[4659,5049],{},[336,5051,5052],{"href":5052,"rel":5053},"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.physletb.2018.07.035",[4665],[324,5055,5056,5059,5060,4653,5063,5066,5067,5069],{},[331,5057,4414,5058],{}," Degrassi, G., Di Vita, S., Elias-Miró, J., Espinosa, J. R., Giudice, G. F., Isidori, G., & Strumia, A. (2012)."," \"Higgs Mass and Vacuum Stability in the Standard Model at NNLO.\" ",[380,5061,5062],{},"Journal of High Energy Physics",[331,5064,5065],{},"2012","(8), 098.",[4659,5068],{},[336,5070,5071],{"href":5071,"rel":5072},"https:\u002F\u002Fdoi.org\u002F10.1007\u002FJHEP08(2012)098",[4665],[324,5074,5075,5078,5079,4653,5081,5084,5085,5087],{},[331,5076,4419,5077],{}," Buttazzo, D., Degrassi, G., Giardino, P. P., Giudice, G. F., Sala, F., Salvio, A., & Strumia, A. (2013)."," \"Investigating the Near-Criticality of the Higgs Boson.\" ",[380,5080,5062],{},[331,5082,5083],{},"2013","(12), 089.",[4659,5086],{},[336,5088,5089],{"href":5089,"rel":5090},"https:\u002F\u002Fdoi.org\u002F10.1007\u002FJHEP12(2013)089",[4665],[324,5092,5093,5097,5098,4653,5100,5103,5104,5106],{},[331,5094,5095,5096],{},"[25]"," Susskind, L. (1979)."," \"Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory.\" ",[380,5099,4962],{},[331,5101,5102],{},"20","(10), 2619–2625.",[4659,5105],{},[336,5107,5108],{"href":5108,"rel":5109},"https:\u002F\u002Fdoi.org\u002F10.1103\u002FPhysRevD.20.2619",[4665],[324,5111,5112,5115,5116,5119,5120,5122],{},[331,5113,4593,5114],{}," Giudice, G. F. (2008)."," \"Naturally Speaking: The Naturalness Criterion and Physics at the LHC.\" ",[380,5117,5118],{},"arXiv preprint",", arXiv:0801.2562.",[4659,5121],{},[336,5123,5124],{"href":5124,"rel":5125},"https:\u002F\u002Farxiv.org\u002Fabs\u002F0801.2562",[4665],{"title":5127,"searchDepth":83,"depth":83,"links":5128},"",[5129,5130,5135,5141,5142,5147,5153],{"id":364,"depth":83,"text":365},{"id":386,"depth":83,"text":387,"children":5131},[5132,5133,5134],{"id":391,"depth":131,"text":392},{"id":412,"depth":131,"text":413},{"id":432,"depth":131,"text":433},{"id":497,"depth":83,"text":498,"children":5136},[5137,5138,5139,5140],{"id":501,"depth":131,"text":502},{"id":1639,"depth":131,"text":1640},{"id":2433,"depth":131,"text":2434},{"id":2702,"depth":131,"text":2703},{"id":3358,"depth":83,"text":3359},{"id":3472,"depth":83,"text":3473,"children":5143},[5144,5145,5146],{"id":3476,"depth":131,"text":3477},{"id":3493,"depth":131,"text":3494},{"id":3786,"depth":131,"text":3787},{"id":4156,"depth":83,"text":4157,"children":5148},[5149,5150,5151,5152],{"id":4163,"depth":131,"text":4164},{"id":4202,"depth":131,"text":4203},{"id":4422,"depth":131,"text":4423},{"id":4596,"depth":131,"text":4597},{"id":4626,"depth":83,"text":4627},"md",[125,126,127,128,129,130],{},true,{"title":122,"description":123},"evidence\u002Fhiggs-field","Fv_wrn-H3rsNQ65zp7EgrIOe7jOz7fTVjYptF4ogndU",1789530370339]