- Comments on the much anticipated December 13 CERN seminar on the status of the ATLAS and CMS searches for THE BOSON.
Headlines have been buzzing for the past week or so about a possible glimpse of a certain long-sought particle at the LHC--with phrases such as "the biggest scientific breakthrough of the century so far" being bandied about. As Tuesday's announcement approaches, I am reminded of the role that I played in predicting that now notorious particle's existence.
I have been thinking about the solutions to quantum field theory and particularly spontaneous symmetry breaking for fifty years starting with the build up to my PhD thesis at Harvard. At that time, the concept that there could be solutions to field equations that have lesser symmetry than the actions that generated them was very surprising if not heretical. Now the idea is so accepted that last week I ended my lectures in my advanced quantum mechanics course at Brown with the Goldstone solution of spontaneous broken quartic scalar field theory. The ideas I explained in that course are an important part of the subsequent quantum field theory, string theory and phenomenology courses that these students will take on the way to their degrees.
Initially, what impressed me most about these new solutions was that the price paid for breaking a continuous symmetry was the necessity of a zero mass excitation demonstrated clearly in the leading order approximations that existed at the time and eventually confirmed generally by Goldstone, Salam and Weinberg. My thesis advisor, Walter Gilbert, suggested that I study a model proposed by Bjorken which was very interesting because it started with a four fermion vector-vector interaction, a theory that is not renormalizable in coupling constant perturbation theory. If the current is forced to have a non-vanishing vacuum value, Bjorken claimed that the result, at least in lowest order, is a theory identical to ordinary quantized electrodynamics (QED). This was a highly suspect result because the symmetry that is broken is Lorentz invariance. It turns out that this breaking is innocuous to all orders and that one sector of the solution space of this theory does yield normal electrodynamics complete with a massless unit spin photon. This intrigued me and I could not help but wonder if there was not a similar way to argue that the photon of normal QED is required to be massless. Indeed, I produced a proof which Sidney Coleman showed to be wrong (to my great embarrassment) in my thesis exam. This was, in retrospect, an obviously reckless thing to claim since Schwinger had recently argued that there was no dynamical reason for the photon to be massless and had illustrated his point by a toy model of QED in two space time dimensions. Indeed, it is now very clear that the structure of coupling constant perturbation theory, not a general dynamics argument, imposes the massless condition order by order on the photon.
Fortunately, despite the error, I still passed my thesis exam and moved from Harvard to Imperial College, London on a NSF postdoctoral fellowship. I was still obsessed with finding a general proof showing normal QED dynamically required a massless photon and wrote a paper in April of 1964 claiming to have found this argument and published it in Physical Review Letters. Almost immediately, I realized that I had only succeeded in producing a statement about massless gauge modes in manifestly covariant theories. A careful analysis of these results allowed Hagen, Kibble and I to make a general exact statement of the mass mechanism that shows that the Goldstone theorem only applies to unphysical modes of gauge theories. We then wrote the now well known GHK paper which states this mass mechanism and give a particular example - charge symmetry broken scalar electrodynamics. We were very slow in sending the results off for publication because my experiences showed how careful one needed to be with this problem and also because we hoped to further extend our conclusions with additional examples. We eventually decided it was time to publish and literally were putting the finished paper in the envelope when Kibble discovered new papers by Englert and Brout and Higgs. We glanced at these, recognized they addressed the same issue, but felt they were deficient. Neither group had the general mechanism but only the example. Further, neither group dealt correctly with the Goldstone boson which is definitely present in both of their manifestly covariant models. Englert and Brout state there is a massless excitation but do not recognize it as being pure gauge and Higgs fails to recognize that the solutions to his equations have a massless pure gauge excitation. Englert and Brout entirely miss the Scalar boson (Higgs) while Higgs and GHK explicitly show it.
We decided to cite these works but only altered our manuscript by adding, in several places, references to these just-revealed papers. Not a single thought or calculation was removed or added, nor was any change made but to the referencing in our manuscript as the result of Kibble's having pointed out the existence of these new papers.
Any careful reading will show that our approach is very different from that of E, B or H. We further state emphatically that beyond seeing the papers at the final moment, we had no previous contact with E, B or H or previous knowledge of their work which is also clearly independent. I add that I had been talking freely about our results for months before the actual submission of the GHK paper.
Returning to the present, I am looking forward to Tuesday's announcements, although I will be amazed if there are any definitive results. The verification of a particle, particularly this one, requires a large amount of data and a tremendous amount of care. I have been very impressed with how the experimentalists in general have been handling this and watching the Brown experimentalists (who I know well) at work - David Cutts, Ulrich Heintz, Greg Landsberg (Physics coordinator for CMS), Meenakshi Narain, and their army of eager postdocs and students, I have no doubt that if the Boson exists, it will be found and it will stay found. While my personal interest undoubtedly biases my opinion, I think it is highly likely that an elementary scalar boson exists. While beautiful theories have often been wrong, the evidence so far seems to make this almost a sure thing. Of course, the chaos that follows a non-discovery would be exciting as well, but I think it very unlikely.
[youtube:mmVNIMUqXRg, 560, 340]
[youtube:AzL56nF0lIw, 560, 340]
[youtube:2Jy3SpOeHH4, 560, 340]
[youtube:VbVlBe05cfE, 560, 340]
Videos courtesy of Daniel Ferrante.
-----------
Gerald Guralnik is a professor of physics at Brown University, Providence, RI.
Edited on Dec 20, in response to requests for links to papers and for more information.
Video of the 2010 JJ Sakurai Prize for Theoretical Particle Physics Talks for Higgs Brout Englert Guralnik Hagen Kibble.
The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles.
A recent APS talk: The Beginnings of Spontaneous Symmetry Breaking in Particle Physics-- Derived From My on the Spot "Intellectual Battlefield Impressions".
A new posting of a 1965 conference talk with considerable addition to the original GHK paper: Gauge Invariance and the Goldstone Theorem.