Higgs boson

• 1. Introduction

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  The Higgs boson appears in roughly one collision out of every ten billion at the Large Hadron Collider, and it vanishes almost the instant it exists. This elementary particle belongs to the Standard Model of particle physics, and it is a quantum excitation of the Higgs field. Physicists searched for it for about 40 years before it turned up in 2012. Until then, the field behind it was the last unverified part of the Standard Model. Why would a theory of the universe need an invisible field that fills even empty space? Who proposed it, and why did almost nobody care at first? How do you find something this rare? And what does its discovery still leave unexplained? The particle also carries a nickname that its own namesake disliked.

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• 2. A Puzzle of Massless Bosons

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  Around 1960, theorists who had tamed the electromagnetic and strong forces with gauge invariant theories kept failing to do the same for the weak force. Gauge invariance means that certain quantities can be changed without altering any experimental outcome, and it reflects deep symmetries in nature. Philip Anderson put it this way: "It is only slightly overstating the case to say that physics is the study of symmetry." The trouble was that the symmetry requirements forced the weak force's carriers, the W and Z bosons, to have zero mass. Experiments showed they were massive. The fixes that looked promising seemed to demand extra particles called Goldstone bosons, and the evidence suggested those did not exist. Gauge theories began to fall into disrepute.

  Yoichiro Nambu had recognised in the late 1950s that spontaneous symmetry breaking could occur under certain conditions. In this process, a symmetric system ends up in an asymmetric state. In 1962, Philip Anderson, an expert in condensed matter physics, saw a connection through superconductivity. A superconductor pushes out external magnetic fields, a behaviour called the Meissner effect. That implies the electromagnetic field becomes short ranged inside it. In particle physics, a short ranged force goes together with massive carriers. Anderson suggested that the Goldstone bosons produced by symmetry breaking might be absorbed by the massless W and Z bosons. That would give the W and Z their mass and remove the unwanted Goldstone bosons in a single stroke.

  In 1964, Abraham Klein and Benjamin Lee showed that the idea could work in some limited, non-relativistic cases. Whether it would survive in a fully relativistic theory was still an open question.

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• 3. Three Papers in 1964

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  Between August and November 1964, three groups of physicists independently turned Anderson's hint into a complete relativistic theory. François Englert and Robert Brout published first, in August. Peter Higgs followed in October, and Gerald Guralnik, Carl Hagen and Tom Kibble completed the trio in November. Higgs had also published a short reply in September to an objection raised by Gilbert. It showed that, when calculating in the radiation gauge, both Goldstone's theorem and Gilbert's objection become inapplicable. Higgs later said that this objection prompted his own paper.

  The three teams used very different tools. Higgs relied on classical techniques. Englert and Brout calculated vacuum polarisation around an assumed symmetry-breaking vacuum state. Guralnik, Hagen and Kibble used operator formalism and conservation laws to study how Goldstone's theorem is avoided. All three reached similar conclusions. If an unusual field existed throughout the universe, there would be no Goldstone bosons, and some bosons would acquire mass. The field's oddest feature is that it holds less energy when it is nonzero, unlike every other known field.

  Only two of the papers wrote down equations for the field's quantum. In the paper by Higgs, the boson is massive, and a closing sentence calls the prediction of incomplete multiplets of scalar and vector bosons an essential feature. The physicist Frank Close notes that 1960s gauge theorists were fixated on massless vector bosons, so a massive scalar seemed unimportant, and only Higgs addressed it directly. In the paper by Guralnik, Hagen and Kibble, the boson is massless and decoupled from the massive states. Guralnik later argued that their paper alone showed there are no massless Goldstone bosons in the model and gave a complete analysis of the general mechanism. Higgs's name became attached to the whole theory, even though several researchers between about 1960 and 1972 developed different parts of it independently.

  Physical Review Letters honoured all three papers at its 50th anniversary celebration. In 2010, the six authors shared the J. J. Sakurai Prize for Theoretical Particle Physics. A controversy arose the same year, because a Nobel Prize can recognise at most three scientists and six were credited. In 1966, Higgs wrote a further paper showing how the boson would decay. Only a massive boson can decay, so its decays could prove the mechanism.

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• 4. Ignored, Then Embraced

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  In 1967, Steven Weinberg and Abdus Salam independently showed how this mechanism could break the electroweak symmetry in Sheldon Glashow's unified model of the weak and electromagnetic interactions. The result became the Standard Model of particle physics. Weinberg was the first to see that the mechanism would also supply mass terms for the fermions. Almost nobody noticed. Most physicists believed the non-Abelian gauge theories involved were a dead end, partly because they could not be renormalised.

  A study by Coleman found that "essentially no-one paid any attention" to Weinberg's paper before 1971. That paper is now the most cited in particle physics. David Politzer recalled in his 2004 Nobel speech that in 1970, Glashow's own teaching of the weak interaction made no mention of the work of Weinberg, Salam or Glashow himself.

  Then, in 1971-72, Martinus Veltman and Gerard 't Hooft proved in two papers that Yang-Mills theory could be renormalised, first for massless fields and then for massive ones. Politzer states that almost everyone learned of the theory through Benjamin Lee, who combined that work with insights from others and popularised the completed theory. From 1971, interest and acceptance "exploded". The electroweak theory went on to predict weak neutral currents, three bosons, and the top and charm quarks. Many of those involved eventually won Nobel Prizes or other major awards.

  A 1974 review in Reviews of Modern Physics captured the mood. It said that while no one doubted the mathematical correctness of the arguments, no one quite believed that nature was "diabolically clever enough to take advantage of them". The theory's answers matched experiment, but nobody yet knew whether it was fundamentally correct.

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• 5. The Long Hunt

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  Catching a Higgs boson means accelerating two beams of particles to very high energies and colliding them inside a detector. Only occasionally does a collision create one, and only fleetingly. Detectors cannot see the boson itself. They record its decay products and reconstruct the process. Many other processes leave similar signatures, but the Standard Model predicts how often each should occur. A consistent surplus of Higgs-like signatures over that expectation would be strong evidence.

  The demands were enormous. The data of hundreds of trillions of collisions had to be analysed. Physicists also require two independent detectors to each show less than a one-in-a-million chance that background events alone explain the result. That threshold is five standard deviations, or five sigma. As of 2012, the collisions produced 25 petabytes of data per year. The LHC Computing Grid handled it, with over 170 computing facilities across 36 countries.

  The first extensive search ran at CERN's Large Electron-Positron Collider, known as LEP, in the 1990s. When it closed in 2000, it had found no conclusive evidence. That implied any Higgs boson would have to be heavier than 114.4 GeV. The search moved to the Tevatron at Fermilab in the United States, the collider that discovered the top quark in 1995. It had been upgraded for the task. It was the only operational supercollider, because the LHC was unfinished and the Superconducting Super Collider had been cancelled in 1993. The Tevatron shut down on the 30th of September 2011, since it could no longer keep up with the LHC. Its final analysis excluded a Higgs mass between 147 and 180 GeV and showed a small, insignificant excess between 115 and 140 GeV.

  The Large Hadron Collider sits in a 27 km tunnel under the ground near Geneva, the same tunnel that once held LEP. It was designed to either confirm or exclude the Higgs boson. Its first beams carried 3.5 TeV each, for 7 TeV in total, almost 3.6 times the Tevatron. Plans called for 14 TeV later, over seven times any previous collider. Nine days after its inaugural tests, a magnet quench caused by a faulty electrical connection damaged over 50 superconducting magnets and contaminated the vacuum system. That delayed operations by 14 months. Data collection began in March 2010. Several promising excesses "evaporated" and proved to be random fluctuations. From around May 2011, though, both ATLAS and CMS saw a small, consistent excess in gamma and four-lepton decay signatures near a mass of 125 GeV.

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• 6. Announcement and Proof

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  On the 28th of November 2011, the leaders of ATLAS and CMS met the director general of CERN and discussed their latest analyses outside their own teams for the first time. Both suspected they were converging on a shared result near 125 GeV, and initial preparations began in case it held. The anomalous data had become "too large to ignore", though it was still far from conclusive. Publicly, the "tantalising hints" of around 2-3 sigma had many people expecting the 2012 data to settle the question.

  On the 22nd of June 2012, CERN announced an upcoming seminar. From around the 1st of July, rumours of a major announcement spread through social media. Speculation reached a "fevered" pitch when reports emerged that Peter Higgs would attend and that "five leading physicists" had been invited. These were generally believed to be the five living 1964 authors. Higgs, Englert, Guralnik and Hagen attended, and Kibble confirmed his invitation. Brout had died in 2011.

  On the 4th of July 2012, both experiments announced the same discovery independently. CMS reported a previously unknown boson with a mass of 125.3 GeV, and ATLAS reported one at 126.0 GeV. Each reached a local significance of five sigma, which means less than one chance in three million of a result this strong arising by chance. When more channels were included, the CMS figure fell to 4.9 sigma. The teams had worked blinded from each other since late 2011 or early 2012, so they never compared results. That made a shared finding more convincing. On the 31st of July, ATLAS added a third channel and reached 5.9 sigma, a one in 588 million chance.

  The particle was not yet declared a Higgs boson. Production rates and decays broadly matched the Standard Model, but the experimental uncertainties left room for alternatives. In November 2012, at a conference in Kyoto, researchers reported that new evidence was falling into line with the Standard Model more than with its rivals. As of December 2012, CERN still said only that the particle was "consistent with" the Higgs boson, even though media reports in late 2012 wrongly announced a confirmation. The LHC's planned shutdown and 2013-14 upgrade were postponed by seven weeks into 2013 to collect more data.

  On the 14th of March 2013, CERN confirmed that CMS and ATLAS had compared several options for the particle's spin and parity, and all preferred no spin and even parity. Spin-1 had already been ruled out by the decay into two photons. The spin-2 hypothesis was excluded with a confidence level above 99.9%. The particle became the first elementary scalar particle discovered in nature. Decays into photon pairs, W and Z pairs and tau leptons were observed at rates consistent with the Standard Model. In July 2017, CERN began calling it simply the Higgs boson. In July 2018, ATLAS and CMS reported its decay into a pair of bottom quarks, which makes up approximately 60% of all of its decays.

  The media had long called it the "God particle", after the 1993 book The God Particle by Nobel laureate Leon M. Lederman. Physicists criticised the name, and Peter Higgs was among them. In 2013, Higgs and François Englert were awarded the Nobel Prize in Physics for their theoretical predictions.

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• 7. The Field Everywhere

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  Imagine a sombrero. The Higgs field has a potential energy shaped like one, with its lowest points in the brim rather than at the centre. Unlike any other known field, it holds less energy when it is nonzero, so it takes a nonzero value everywhere, including otherwise empty space. This breaks the weak isospin symmetry of the electroweak interaction. Three components of the field are absorbed by the W and Z bosons and give them mass. The remaining neutral component shows up as the Higgs boson. Because the W and Z are massive, the weak force reaches only a very short distance.

  About one picosecond after the Big Bang, the universe cooled below the crossover temperature at which this symmetry breaking occurred. Atoms and other structures could not form without it. Neither could the nuclear reactions in stars such as the Sun.

  Popular accounts often overstate the field's role. It does not create mass out of nothing, and it is not responsible for the mass of every particle. Approximately 99% of the mass of baryons, the composite particles such as the proton and neutron, comes instead from quantum chromodynamic binding energy. That energy is the sum of the kinetic energies of the quarks and the energies of the massless gluons that mediate the strong interaction inside them. For the fermions, the masses must be entered by hand, since each sets how strongly that particle couples to the field.

  Teachers have reached for analogies including the rainbow and the prism, electric fields, and ripples on the surface of water. Pictures of people pushing through a crowd, or objects moving through syrup or molasses, are popular but misleading. The Higgs field does not actually resist particles, and mass is not caused by resistance.

  The Standard Model does not predict the boson's own mass, so it had to be measured. It is also the only particle that stays massive even at very high energies. CMS reported a mass of 125.35 GeV in 2022, and ATLAS reported 125.11 GeV in 2023.

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• 8. Open Questions

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  Rolf-Dieter Heuer, director general of CERN when the boson was found, argued that proving a scalar field exists is almost as important as the field's role in giving mass. Every other fundamental field in the Standard Model belongs to fermions or spin-1 bosons. So the Higgs field suggests that other hypothetical scalar fields, from the inflaton to quintessence, might exist too. The inflaton is a proposed field behind the expansion of space in the first fraction of a second of the universe. Papers have asked whether the Higgs field could be that field. Such theories are highly tentative and face significant problems related to unitarity.

  The Standard Model also allows our universe's vacuum to be long-lived but not completely stable. A Higgs mass near 125 GeV sits extremely close to the boundary for stability. Settling which side it falls on needs a far more precise measurement of the top quark's mass, which a future electron-positron collider could supply. Reports that the Higgs boson might "end" the universe misrepresent this. Even in the unstable case, the change would more than likely lie many billions of years away.

  The Standard Model treats the Higgs boson's mass as a number to be measured, not calculated. Quantum corrections should apparently push it far higher than observed, yet the model also needs a mass of the order of 100 GeV. Explaining the near-perfect cancellation between these is called the hierarchy problem. The weak force is roughly 10 to the 32nd power times stronger than gravity, which is linked to the same puzzle. Proposed answers include supersymmetry, conformal solutions and extra dimensions such as braneworld models. Other models make the Higgs a composite particle, as in technicolour, where strongly bound pairs of fermions called techniquarks play its role. Two-Higgs-doublet models predict a quintet of scalar particles.

  A related mismatch involves the vacuum energy. Observed vacuum energy density is extremely close to zero, while the densities predicted from the Higgs field and supersymmetry are many orders of magnitude larger. This cosmological constant problem remains a major unanswered problem in physics.

  One property of the Higgs boson is still unmeasured: its self-coupling. Higgs boson pair production offers a direct probe, and the result would reveal the full shape of the sombrero potential.

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