# The Inside Story of a Higgs Boson Theory

Physicists at CERN reported Aug. 1 that they are even more certain than they were at the historic July 4 announcement that the particle they recently observed is the "Higgs boson." I was fortunate to attend CERN's initial announcement of results from the two incredible and very beautiful sets of experiments suggesting that after nearly 50 years, the search for this elusive particle was successful.

The particle was hypothesized in a radical theory in 1964, and as I marveled at the precision of the experimental results, I reflected on my part in constructing that theory. The adventure had some wonderful, scary and even embarrassing moments.

In 1962 my Ph.D. thesis adviser, Walter Gilbert, suggested that I think about some new theoretical ideas of Yoichiro Nambu and collaborators. Nambu demonstrated that one could find unsuspected solutions to equations believed to be useful in explaining elementary particle phenomena. These solutions are called "spontaneous symmetry breaking" solutions because they show less symmetry than the original equations. Nambu's solutions include a zero mass particle, which are always required in the case of spontaneous symmetry breaking. This result, called the Nambu Goldstone theorem, was startling! It had been impossible to calculate an absolute mass as an exact result of a non-trivial theory.

The theorem posed a problem because one massless particle, the photon, has been experimentally observed Shortly after I started studying Nambu's papers, J.D. Bjorken proposed a modified version of Nambu's original theory where the massless particle could be identified with the photon. His equations differed from the conventional ones that describe how matter and light interact but I was able to show after some minor modifications that Bjorken's were correct.

This is where life started getting interesting. Bjorken's new theory agreed with conventional theory and rightly required that the photon have zero mass. No one had yet proved that the usual theory of electromagnetism exactly required zero mass photons. In fact, Julian Schwinger had found a case where an electromagnetic-like theory did not have a massless particle. This bothered me immensely. Something was very wrong if an "ersatz" electromagnetic theory required that the photon be massless but the generally used theory did not.

There must be an equivalent to the Nambu Goldstone theorem for normal electromagnetism that guaranteed that a massless photon, I thought. I searched for it and, thinking that I found it, proceeded to add an embarrassingly wrong chapter to my Ph.D. thesis. Sidney Coleman who was famous for his rapid mind and biting wit caught the error in my final exam. We removed the chapter and I passed the exam.

In the fateful year of 1964 I received a National Science Foundation postdoctoral fellowship and traveled with my new wife, Susan, to Imperial College in London. It turned out to be a magnificent social and physics experience.

Imperial was probably the best place to work on high energy theoretical physics then. It was filled with brilliant physicists and had a continuous stream of famous physics visitors. Paul Matthews and Abdus Salam led the high energy theory group. I soon began discussing physics with many younger people including Tom Kibble and Raymond Streater. Kibble and I became constant lunch companions often discussing topics related to my thesis. We were sure that I had only touched the surface.

I remained obsessed with finding a proof that the photon of traditional electromagnetic theory must have zero mass. In April I submitted a paper to *Physical Review Letters* that contained many new insights into the phenomena of spontaneous symmetry breaking and a new proof showing that the photon has zero mass. I realized a few days later that the paper had an extremely subtle error. Recognizing it was profound because it clarified that for broken symmetry quantum theories related to electromagnetism, the assumptions needed to prove the Nambu Goldstone theorem were wrong. These theories did not always require massless particles! I intended to revise the paper when the journal returned it, but because of unlikely events including postal strikes I never saw the manuscript again. PRL published it August 24. The paper was the first of the series of papers that laid the cornerstone of the "Standard Model" by leading to the unified theory of electromagnetic and weak interactions and the prediction of the Higgs Boson.

Almost immediately after understanding how to escape the Nambu Goldstone theorem, I realized how to construct a specific new example by finding a symmetry breaking solution of electromagnetism interacting with charged scalar (spinless) matter. This solution described an entirely new phase (just as steam, liquid and ice are phases of water) of the normal electromagnetic equations. This work was done in collaboration with Kibble and Carl Hagen from the University of Rochester who had been my friend and collaborator since our undergraduate days at MIT.

The results that we found were unprecedented. While the familiar solution had a massless photon and a charged massive scalar particle, this new broken symmetric solution had a massive unit spin particle and a single scalar particle of ultimately undetermined mass which is now called the Higgs boson. Gone was the pesky Nambu Goldstone massless scalar particle but given my previous errors, we were in no hurry to publish our results. This time we worked out every minute detail and applied every internal consistency check. I even traveled to Italy's Lake Como to consult my thesis advisor Walter Gilbert, who was giving summer school lectures there. We finally submitted our paper to PRL with the proof of the general mechanism to avoid the Nambu Goldstone theorem (the only work to have this) and the special example. We were surprised to discover that two very different but related papers, with parts of the example, one by Englert and Brout and the other by Higgs also existed. All three papers appeared in the same volume of PRL in 1964.

Initially, to the extent that these papers were noticed at all, they were not well received. An essential tool used in particle physics is symmetry. The alphabet soup of observed elementary particles is simplified by the experimental observation of a high degree of symmetry in the behavior of groups of particles. To explain this, the basic equations of most physical theories incorporate large amounts of symmetry. The solutions we proposed had less symmetry and violated a special symmetry called "gauge symmetry." This was new and made other physicists profoundly uncomfortable. Werner Heisenberg (Nobel Prize, Physics, 1932), one of the most important physicists of the 20th century made it clear to me in the summer of 1965, at a conference in his honor, that he thought these ideas were junk.

I thought that this was probably the end of my nascent career as a theoretical physicist, but thankfully I took a postdoctoral job at the University of Rochester where Hagen was about to become a professor. There, another great 20th century physicist Robert Marshak told me that if I wished to survive in physics that I must stop thinking about this sort of problem and move on. I wisely obeyed, but I was thrilled a few years later when Steve Weinberg and then Abdus Salam used our mechanism and a generalization of our simple example to build the unified model of weak and electromagnetic interactions and later, with Sheldon Glashow, received Nobel prizes.

I have worked on many different problems, all of them fascinating and deeply involving, but none, so far, have evolved to acquire the fundamental importance of my early adventures with symmetry breaking and mass.

We have many more questions to answer, particularly many currently pressing ones like how gravity fits together with all of this. We need to identify and characterize the "dark matter" and "dark energy" that makes up a majority of our universe. We have hopes that an idea called Supersymmetry will be confirmed. The apparent discovery of the boson opens up new doors for those inquiries.

My hope is that as the puzzle continues to be unraveled that some of the wonder and excitement that we physicists have felt for decades will continue to be felt across the world the way it was on July 4.