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Theorisation

Particle physicists study matter made from fundamental particles whose interactions are mediated by exchange particles – gauge bosons – acting as force carriers. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as field theories in which the objects of study are not particles and forces, but quantum fields and their symmetries. However, attempts to produce quantum field models for two of the four known fundamental forces – the electromagnetic force and the weak nuclear force – and then to unify these interactions, were still unsuccessful.

One known problem was that gauge invariant approaches, including non-abelian models such as Yang–Mills theory (1954), which held great promise for unified theories, also seemed to predict known massive particles as massless. Goldstone's theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions, since it appeared to show that zero-mass particles known as Goldstone bosons would also have to exist that simply were "not seen". According to Guralnik, physicists had "no understanding" how these problems could be overcome.

Particle physicist and mathematician Peter Woit summarised the state of research at the time:

Yang and Mills work on non-abelian gauge theory had one huge problem: in perturbation theory it has massless particles which don't correspond to anything we see. One way of getting rid of this problem is now fairly well understood, the phenomenon of confinement realized in QCD, where the strong interactions get rid of the massless "gluon" states at long distances. By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry. What Philip Anderson realized and worked out in the summer of 1962 was that, when you have both gauge symmetry and spontaneous symmetry breaking, the massless Nambu–Goldstone mode can combine with the massless gauge field modes to produce a physical massive vector field. This is what happens in superconductivity, a subject about which Anderson was (and is) one of the leading experts.

The Higgs mechanism is a process by which vector bosons can acquire rest mass without explicitly breaking gauge invariance, as a byproduct of spontaneous symmetry breaking. Initially, the mathematical theory behind spontaneous symmetry breaking was conceived and published within particle physics by Yoichiro Nambu in 1960 (and somewhat anticipated by Ernst Stueckelberg in 1938), and the concept that such a mechanism could offer a possible solution for the "mass problem" was originally suggested in 1962 by Philip Anderson, who had previously written papers on broken symmetry and its outcomes in superconductivity. Anderson concluded in his 1963 paper on the Yang–Mills theory, that "considering the superconducting analog... hese two types of bosons seem capable of canceling each other out... leaving finite mass bosons"), and in March 1964, Abraham Klein and Benjamin Lee showed that Goldstone's theorem could be avoided this way in at least some non-relativistic cases, and speculated it might be possible in truly relativistic cases.

These approaches were quickly developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by François Englert and Robert Brout in August 1964; by Peter Higgs in October 1964; and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964. Higgs also wrote a short, but important, response published in September 1964 to an objection by Gilbert, which showed that if calculating within the radiation gauge, Goldstone's theorem and Gilbert's objection would become inapplicable. Higgs later described Gilbert's objection as prompting his own paper. Properties of the model were further considered by Guralnik in 1965, by Higgs in 1966, by Kibble in 1967, and further by GHK in 1967. The original three 1964 papers demonstrated that when a gauge theory is combined with an additional charged scalar field that spontaneously breaks the symmetry, the gauge bosons may consistently acquire a finite mass. In 1967, Steven Weinberg and Abdus Salam independently showed how a Higgs mechanism could be used to break the electroweak symmetry of Sheldon Glashow 's unified model for the weak and electromagnetic interactions, (itself an extension of work by Schwinger), forming what became the Standard Model of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions.

At first, these seminal papers on spontaneous breaking of gauge symmetries were largely ignored, because it was widely believed that the (non-Abelian gauge) theories in question were a dead-end, and in particular that they could not be renormalised. In 1971–72, Martinus Veltman and Gerard 't Hooft proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields. Their contribution, and the work of others on the renormalisation group – including "substantial" theoretical work by Russian physicists Ludvig Faddeev, Andrei Slavnov, Efim Fradkin, and Igor Tyutin – was eventually "enormously profound and influential", but even with all key elements of the eventual theory published there was still almost no wider interest. For example, Coleman found in a study that "essentially no-one paid any attention" to Weinberg's paper prior to 1971 and discussed by David Politzer in his 2004 Nobel speech. – now the most cited in particle physics – and even in 1970 according to Politzer, Glashow's teaching of the weak interaction contained no mention of Weinberg's, Salam's, or Glashow's own work. In practice, Politzer states, almost everyone learned of the theory due to physicist Benjamin Lee, who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory. In this way, from 1971, interest and acceptance "exploded" and the ideas were quickly absorbed in the mainstream.

The resulting electroweak theory and Standard Model have accurately predicted (among other things) weak neutral currents, three bosons, the top and charm quarks, and with great precision, the mass and other properties of some of these. Many of those involved eventually won Nobel Prizes or other renowned awards. A 1974 paper and comprehensive review in Reviews of Modern Physics commented that "while no one doubted the correctness of these arguments, no one quite believed that nature was diabolically clever enough to take advantage of them", adding that the theory had so far produced accurate answers that accorded with experiment, but it was unknown whether the theory was fundamentally correct. By 1986 and again in the 1990s it became possible to write that understanding and proving the Higgs sector of the Standard Model was "the central problem today in particle physics".