The 1964 PRL symmetry breaking papers were written by three teams who proposed related but different approaches to explain how mass could arise in local gauge theories.
These three papers were written by: Robert Brout and François Englert;[1][2] Peter Higgs;[3] and Gerald Guralnik, C. Richard Hagen, and Tom Kibble (GHK).
Together, these provide a theoretical means by which Goldstone's theorem (a problematic limitation affecting early modern particle physics theories) can be avoided.
A significant difficulty which one encounters, however, is Goldstone's theorem, which states that in any quantum field theory which has a spontaneously broken symmetry there must occur a zero-mass particle.
[14] In 2014, Guralnik and Carl Hagen wrote a paper that contended that even after 50 years there is still widespread misunderstanding, by physicists and the Nobel Committee, of the Goldstone boson role.
[6][17] The mathematical theory behind spontaneous symmetry breaking was initially conceived and published within particle physics by Yoichiro Nambu in 1960,[18] the concept that such a mechanism could offer a possible solution for the "mass problem" was originally suggested in 1962 by Philip Anderson,[19]: 4–5 [20] and Abraham Klein and Benjamin Lee showed in March 1964 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.
[21] 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;[1] by Peter Higgs in October 1964;[3] and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964.
[citation needed] Each of these papers is unique and demonstrates different approaches to showing how mass arise in gauge particles.
Over the years, the differences between these papers are no longer widely understood, due to the passage of time and acceptance of end-results by the particle physics community.
A study of citation indices is interesting—more than 40 years after the 1964 publication in Physical Review Letters there is little noticeable pattern of preference among them, with the vast majority of researchers in the field mentioning all three milestone papers.
[4] In reviews dated 2009 and 2011, Guralnik states that in the GHK model the boson is massless only in a lowest-order approximation, but it is not subject to any constraint and acquires mass at higher orders, and adds that the GHK paper was the only one to show that there are no massless Goldstone bosons in the model and to give a complete analysis of the general Higgs mechanism.
[14][5][15] All three reached similar conclusions, despite their very different approaches: Higgs' paper essentially used classical techniques, Englert and Brout's involved calculating vacuum polarization in perturbation theory around an assumed symmetry-breaking vacuum state, and GHK used operator formalism and conservation laws to explore in depth the ways in which Goldstone's theorem explicitly fails.
[citation needed] The resulting electroweak theory and Standard Model have correctly predicted (among other discoveries) weak neutral currents, three bosons, the top and charm quarks, and with great precision, the mass and other properties of some of these.
A 1974 paper in Reviews of Modern Physics commented that "while no one doubted the [mathematical] correctness of these arguments, no one quite believed that nature was diabolically clever enough to take advantage of them".