### A Brief History of the Higgs Mechanism: The scientific work behind the Higgs boson

The electroweak theory, which unifies the electromagnetic and weak interactions of elementary particles, has, since 1970, received experimental support to a precision unprecedented in the history of science. This unification involves a close relationship between the massless photon, which carries the long-range electromagnetic force, and the W and Z vector bosons, which carry the short-range weak force and must therefore be very massive. Prior to the invention of the Higgs mechanism, it was not known how to formulate a consistent relativistic field theory with a local symmetry which could contain both massless and massive force carriers.

In 1962, Goldstone’s theorem had shown that spontaneous breaking of symmetry in a relativistic field theory results in massless spin-zero bosons, which are excluded experimentally. In a paper published in Physics Letters on 15 September 1964 (received on 27 July 1964), Peter Higgs showed that Goldstone bosons need not occur when a local symmetry is spontaneously broken in a relativistic theory (1). Instead, the Goldstone mode provides the third polarisation of a massive vector field. The other mode of the original scalar doublet remains as a massive spin-zero particle – the Higgs boson.

Higgs wrote a second short paper describing what came to be called “the Higgs model” and submitted it to Physics Letters, but it was rejected on the grounds that it did not warrant rapid publication. Higgs revised the paper and submitted it to Physical Review Letters, where it was accepted (2), but the referee, who turned out to be Yoichiro Nambu, asked Higgs to comment on the relation of his work to that of Francois Englert and Robert Brout, which was published in Physical Review Letters on 31 August 1964, the same day his paper was received. Higgs had been unaware of their work, because the Brussels group did not send preprints to Edinburgh. Higgs’ revised paper drew attention to the possibility of a massive spin-zero boson in its final paragraph. During October 1964, Higgs had discussions with Gerald Guralnik, Carl Hagen and Tom Kibble, who had discovered how the mass of non-interacting vector bosons can be generated by the Anderson mechanism (4).

The previous year, Philip Anderson had pointed out that, in a superconductor where the local gauge symmetry is broken spontaneously, the Goldstone (plasmon) mode becomes massive due to the gauge field interaction, whereas the electromagnetic modes are massive (Meissner effect) despite the gauge invariance (5). However, he did not discuss any relativistic model and so, since Lorentz invariance was a crucial ingredient of the Goldstone theorem, he did not demonstrate that it could be evaded. In Higgs’ second 1964 paper (2) he referred to Anderson’s work in a way which implied that Anderson knew about the non-relativistic counterpart of the Higgs boson. In fact, Anderson didn’t and it was not until 1981 that an unexpected feature of the Raman spectrum of NbSe2 was understood to be due to “a massive collective mode which exists in all superconductors – the oscillation of the amplitude of the superconducting gap” (6), the only Higgs boson to be discovered experimentally before 2012.

The search for the Higgs boson became a major objective of experimental particle physics. Although the best fit to all the electroweak precision measurements gave its mass between 52 and 110 GeV, it was excluded below 114 GeV. Its mass could not exceed 1 TeV if the electroweak theory itself is to remain valid up to this energy scale, precisely the range that is within reach CERN’s Large Hadron Collider. We know now that the ATLAS and CMS have found a Higgs-like boson at a mass of around 126 GeV which increasingly looks like having all the properties of the Standard Model Higgs boson.

Peter Higgs’ work was a crucial step on the road to a unified theory of the forces of Nature and is clearly basis for an experimental programme to look at further details of the discovered particle and its extensions beyond the Standard Model.

(1) P.W. Higgs, Phys. Lett. 12 (1964) 132

(2) P.W. Higgs, Phys. Rev. Lett. 13 (1964) 508

(3) F. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 321

(4) G.S. Guralnik, C.R. Hagen and T.W.B. Kibble, Phys. Rev. Lett. 13 (1964) 585

(5) P.W. Anderson, Phys. Rev. 130 (1963) 439

(6) P.B. Littlewood and C.M. Varma, Phys. Rev. Lett. 47 (1981) 811

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