THE most dramatic breakthrough that occurred in the recent past in physics is, undoubtedly, the experimental discovery in July 2012 of the elusive particle sought by physicists for over four decades, known as the Higgs boson. This was the crucial missing element in the Standard Model, the otherwise highly successful theory of elementary particles and fundamental forces of nature formulated in the 1960s by physicists attempting to understand the universe from a reductionist perspective. In this picture, without the Higgs boson, nothing in the universe—atoms, molecules, plants, animals, planets and stars—would have mass, which, one knows, is not the reality.

**Higgs boson**

The discovery of the Higgs boson was made by two independent experimental groups, CMS (Compact Muon Solenoid) and ATLAS (A Toroidal LHC Apparatus), at the world’s most powerful particle accelerator, the Large Hadron Collider (LHC), at the European Organisation for Nuclear Research (CERN) in Geneva (
*Frontline*, July 27, 2012). And yet, the year’s Nobel Prize in Physics fails to honour in any way the important contribution of the over 6,500 scientists from all over the world who are involved in these experiments even as it awards two (of the several) physicists whose work led to the formulation of the underlying mechanism in a quantum field theoretic framework of how this particle gave rise to mass in the early universe.

The 81-year-old Belgian physicist Francois Englert of the Université libre de Bruxelles, Brussels, and the 84-year-old British physicist Peter W. Higgs of the University of Edinburgh (after whom the newly discovered particle was named) have been jointly awarded the coveted prize. “The Nobel Prize,” says the announcement of the Royal Swedish Academy of Sciences, “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, *and which recently was confirmed through the discovery of the predicted fundamental particle by the ATLAS and CMS experiments at CERN’s Large Hadron Collider*” (emphasis added throughout).

Clearly, the importance of the LHC experiments was not lost on the six-member Nobel Committee. Not just the announcement, even the documents, both the popular and the advanced, providing the scientific background to the subject rightly emphasise the experimental part and devote significant space to describing the details of the painstaking search for the Higgs boson. Therefore, ignoring the significant contributions of the experimenters and other theorists has perhaps something to do with the anachronistic statutes of the Nobel Foundation. These have not changed with the times and do not recognise the manner in which present-day high-energy physics experiments are done: as one probes deeper and deeper into the structure of matter, one requires massive machines and mammoth detectors, and this involves the collaborative efforts of thousands of scientists. The LHC is the biggest apparatus ever built, requiring the largest ever collaborative research undertaken in experimental science.

**Nobel Foundation statutes**

The statutes of the Nobel Foundation currently allow science prizes to be awarded to a maximum of three people, and only the Peace Prize can be awarded to organisations too. There is, however, no such restriction in Alfred Nobel’s will, contrary to what is widely believed, which states that the prizes are for “those who, during the preceding year, shall have conferred the greatest benefit to mankind”. The will only restricts the award to work carried out in the previous year, which, however, has been violated in many past Nobel awards, and this year too, the awardees’ work was done nearly half a century ago. While whether the pursuit of high-energy physics confers any benefit to mankind is something very much debatable, the experimental discovery in the present case was made last year. The restriction on the science prizes to three individuals is, in that sense, an arbitrary one.

The mathematician Peter Woit wrote in his blog “Not Even Wrong”: “I don’t see how allowing a prize for a collaboration of scientists is any more a violation of Nobel’s intent than the current rules…. The problem with not allowing prizes to collaborations is that it rules out many parts of experimental science, only allowing prizes when experimental collaborations are organised by having an identifiable ‘leader’ (or, up to three of them)…. There’s also no reason to believe that he [Nobel] felt that experiments needed to have a ‘leader’ who would be the one to get prize recognition…. As far as the Nobel goes they [CMS and ATLAS groups] make the mistake of running their collaborations relatively democratically, without a ‘great man’ (or ‘great woman’) who could stand out and be awarded a prize.”

Jon Butterworth, an experimentalist with the ATLAS group, wrote along the same lines on *The Guardian*’s website in his column titled “Well done Higgs theorists but what about the experimenters?”:

“The discovery of a Higgs boson, showing that the theoretical ideas are manifested in the real world, was thanks to the work of many thousands. There are 3,000 or so people on ATLAS, a similar number on CMS, and hundreds who worked on the LHC. While the citation gives handsome credit for all this, part of me still wishes the prizes could have acknowledged it too….

“[The Nobel] prizes only give one view of how science is done. They encourage the idea that the typical manner of progress in science is the breakthrough of a lone genius. In reality, while lone geniuses and breakthroughs do occur, incremental progress and collaboration are more important in increasing our understanding of nature. *Even the theory breakthrough behind this prize required a body of incrementally acquired knowledge to which many contributed.”*

Another post said: “The Nobel Prize has long since lost touch with reality, specifically in physics. Science is an increasingly collaborative and collective effort, even in the theoretical areas. Where the contribution of each one begins and ends is becoming increasingly less obvious…. One conclusion we can draw from all this: the Nobel Prize, with its anachronistic rules, is unable to represent fairly the nuances and historical details of any scientific discovery.”

The theoretical mechanism to which the year’s awardees made significant contributions explains how elementary particles are endowed with mass and has now generally come to be called the Higgs mechanism, and the associated massive particle that the theory predicts is the Higgs boson. Even though an understanding of the origin of mass was the result of the work of many physicists, only Higgs’ name has been associated with it, perhaps, because he was the first to write down a model for the mechanism that explicitly included the equations of motion of the particle.

Interestingly, the Swedish Academy’s background document has chosen to call the mechanism the Brout-Englert-Higgs (BEH) mechanism rather than just the Higgs mechanism as physicists do. By doing so, it would seem that there was an attempt to place the work of these three above that of the others who made equally significant contributions to the theory and to justify their decision to award just two. Englert, the co-winner, had worked independently of Higgs with his colleague Robert Brout in formulating the theory. But for the fact that the latter passed away in 2011, he too would have been included as the third recipient of the award.

The mechanism should rightly have been called the Anderson-Brout-Englert-Higgs-Guralnik-Hagen-Kibble mechanism after Philip W. Anderson of Princeton University, Gerald S. Guralnik of Brown University, Carl R. Hagen of the University of Rochester and Tom W.B. Kibble of Imperial College London. Anderson, in fact, can be said to have provided the fundamental insight into the mechanism though he addressed the problem in a non-relativistic and non-particle physics setting. Indeed, it was his work that triggered investigations by the others to realise the idea in particle physics. It is not surprising, therefore, that there has been considerable criticism from the physics community of the Nobel Committee’s decision to award only two of the many whose work laid the foundation for the Higgs (or, more appropriately, Anderson-Higgs) mechanism and the subsequent experimental discovery of the associated particle.

**Spontaneous symmetry breaking**

The concept of “spontaneous symmetry breaking” (SSB) is central to the theory of mass generation through the Higgs mechanism. SSB occurs when the lowest energy state of a quantum system does not respect a certain symmetry but the system’s equations of motion do. Yôichirô Nambu (Nobel Prize 2008) was the first to introduce the concept in particle physics, in 1960, after he succeeded in explaining the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity in terms of the spontaneous breaking of the so-called gauge symmetry of electromagnetism in superconductors (
*Frontline*, December 5, 2008). The ground state in a system of subatomic particles and fields is the vacuum state, and SSB in such a system means that the vacuum violates the inherent symmetry of the system.

A quantum system is said to have gauge symmetry when its equations of motion remain unchanged under a certain abstract mathematical operation on its variables called “gauge transformation”. Gauge invariance forms an important symmetry in quantum field theory. The invariance of the equations describing the electromagnetic field under gauge transformations, for example, implies zero mass for the photon, the carrier of the electromagnetic field.

**Abelian gauge symmetry**

The electromagnetic case is an example of what is called “abelian gauge symmetry”, where the order in which successive symmetry operations (that is, gauge transformations) are performed does not matter, and the photon is, therefore, called an “abelian gauge field”. But there are also the more complex “non-abelian gauge transformations” where the order does matter. The strong nuclear force between quarks—the constituents of particles such as the proton and the neutron—is described by equations with non-abelian gauge symmetry (called Yang-Mills equations). Correspondingly, the theory called quantum chromodynamics (QCD) has eight associated massless fields called “gluons” (as against one photon in the abelian case of electromagnetism). These are “non-abelian gauge fields”. The non-abelian nature of these fields implies that gluons, unlike the electrically neutral photon, carry a strong charge (called colour) and, therefore, interact among themselves (
*Frontline*, July 27, 2012) besides mediating the force between quarks.

The bid, by Sheldon Glashow, Abdus Salam and J.C. Ward in 1961, to unify the long-range electromagnetic force with the short-range weak nuclear force (which causes radioactive decay and nuclear fusion in the sun) into a single electroweak theory led to a mathematical framework that had non-abelian gauge symmetry with four corresponding force carrier fields—the photon, two charged vector bosons (W
^{+} and W
^{-}) and one neutral vector boson (Z
^{0}). Gauge symmetry of the theory means that if one replaces the photon field in the system of equations by some linear combination of W
^{±} and Z
^{0} fields the equations remain invariant.

However, there was a price to pay for this mathematical elegance; in analogy with the photon of electromagnetism, this implied that the weak force carriers too should be massless. Gauge symmetry also required that matter fields—quarks and leptons (an electron is one of the leptons)—too remained massless. This, however, is not the real world. The short range of the weak force implies that its carrier particles should be massive. Also, all matter has mass, and so the theory should have a mechanism that gives mass to matter fields as well.

Although not explicitly stated, implicit in Nambu’s model particle physics system was a fundamental feature of SSB: that is, for every spontaneously broken symmetry, there is a zero-mass scalar particle in the theory. Indeed, in 1961, Jeffrey Goldstone was able to show this as an unavoidable and general feature of all theories with SSB. Soon after, Steven Weinberg, Salam and Goldstone proved this as a rigorous mathematical theorem. Such zero-mass particles that arise in the theory because of SSB are, therefore, called Nambu-Goldstone bosons.

This was, in some sense, a setback to the hope of unifying the disparate electromagnetic and weak forces in a single theory because it meant that if one was able to construct any realistic quantum field theory with SSB one would have to contend with unwanted zero-mass particles, and there seemed to be no way of getting rid of them. The SSB route to building a unified electroweak theory seemed closed because of the Goldstone theorem. Indeed, this apparent dead end led the Nobel laureate Julian Schwinger to ask whether a massive vector boson always came with a massless particle.

**A major step**

In 1962, prompted by Schwinger’s remark, Anderson, who won the 1977 Nobel Prize for his work in condensed matter systems, investigated the question in a specific non-relativistic model of charged plasma. He found that the system could be described by a theory with spontaneously broken gauge symmetry. The photons in the plasma propagated as if they had “mass”, and there was no associated massless particle or mode either. He also showed that Nambu’s treatment of superconductivity could be interpreted as a system with a massive vector boson. Although Anderson did not demonstrate this in a relativistic theory, his work was a major step in showing that one could have massive vector bosons without accompanying massless particles. That is, one could have situations in which the Goldstone theorem could be avoided.

Thus, Anderson formulated the general underlying principle of mass generation in theories with spontaneously broken gauge symmetry two years before Higgs and others discovered the mechanism in relativistic field theoretic models. In fact, with remarkable foresight, he had predicted its applicability to its relativistic extensions in the context of particle physics. He wrote in his landmark paper of 1963: “We conclude, then, that the Goldstone zero-mass difficulty is not a serious one because we can probably cancel it off against an equal Yang-Mills [non-abelian] zero-mass problem.”

It is at this point of time that, taking the cue from Anderson’s work, a number of physicists began to construct relativistic field theoretic models, with the manifest gauge symmetry of the equations broken by the vacuum, to demonstrate that the theory resulted in massive vector bosons with no unwanted massless scalar particles à la Goldstone popping up in the end. In the latter half of 1964, the Englert-Brout duo, Higgs and the Guralnik-Hagen-Kibble (GHK) trio—independently and in that chronological order—published results of their investigations on the problem from different perspectives. By providing different pieces of the solution to the whole question, it is their work together—with Anderson’s and Nambu’s work being critical to the concept—that gives us a complete picture of how the mechanism works.

To achieve SSB in all the above models, the key ingredient is the introduction of a complex scalar field (with two real components) that has a specific form for its potential energy, which breaks the gauge symmetry of the vacuum. In a representation of the quantum states of the system with respect to the vacuum with broken symmetry, the equations of the complex scalar field (the Higgs field) get transformed such that one of its components behaves like a massive scalar particle (the Higgs boson) and the other component couples to the vector field in a such a way so as to transform it into a massive vector field. In effect, the second scalar component provides the additional degree of freedom needed for the massless gauge boson to become massive. In a loose manner of speaking, one says that the vector boson eats up the Goldstone boson and acquires mass.

Finally, in 1967, following these important theoretical developments, Weinberg, and independently Salam, combined the idea of the Higgs mechanism—the vacuum of the Higgs field spontaneously breaking the manifest gauge symmetry present—with the unified electroweak theory of Glashow (and Salam-Ward) to provide masses for the W
^{+}, W
^{-} and Z
^{0} bosons, the weak force-mediating vector particles. The different masses of the matter fields arose in the theory from their relative strengths of interaction with the scalar field (Nobel Prize 1979).

But this alone was not sufficient for the Glashow-Salam-Weinberg (GSW) model to be a workable unified field theory of electroweak interactions. The theory should be able to give finite and precise numerical predictions, which can be tested experimentally. An important criterion for this is what is known as “renormalisability” of the theory, which ensures that the results of calculations of electroweak processes do not give infinities. While the abelian theory of electromagnetism, called quantum electrodynamics (QED), is renormalisable, it was believed that the electroweak theory (a non-abelian gauge theory) may not be. It was only in 1971 that Gerard ‘t Hooft and Martinus Veltman showed that a spontaneously broken non-abelian gauge theory is indeed renormalisable (Nobel Prize 1999; *Frontline*, November 19, 1999).

It was not until the mid-1980s, after years of dedicated experiments, in particular the discovery of the weak force carriers W
^{+}, W
^{-} and Z
^{0} with the masses as predicted, that it was conclusively shown that the GSW model was the correct one among the many that were proposed. Combining the GSW model with the unbroken non-abelian gauge theory of QCD for the strong force constitutes the Standard Model of elementary particles and three forces of nature (electromagnetic, weak and strong).

The Standard Model is constructed in such a way that among the leptons only the charged ones—the electron and its cousins, the muon and the tau—acquire masses and the corresponding neutral leptons, the neutrinos, do not. This was in agreement with the observations of massless neutrinos until the 1970s. Since then, refined experiments have revealed that neutrinos do have tiny masses. The Standard Model cannot accommodate massive neutrinos, and the belief is that some higher theory, such as supersymmetry, of which the Standard Model is a low-energy approximation, may provide the answer. Similarly, the Standard Model leaves out gravity, which again, it is hoped, will be accommodated in a higher theory.

**Origin of mass in the universe**

The way one now understands the origin of mass in the universe is as follows. The space is filled with the Higgs field, and other fields—the gravitational field, the electromagnetic field, the quark fields and all other fields. But unlike other fields, which vanish at the lowest energy level, the vacuum state, the Higgs field does not; it has a non-zero value even in the vacuum state. Particles acquire mass through their interactions with the Higgs field, with the masses depending on the respective strengths of interaction with the Higgs field.

At the time of the Big Bang—when the universe began—there was complete symmetry; all particles were massless and all forces were united as a single primordial force. This original order does not exist anymore. Something happened about 10
^{-11} seconds after the Big Bang. The Higgs field lost its equilibrium and underwent a phase transition (like water freezing into ice) and found a stable vacuum configuration that violated the original symmetry.

The Standard Model has been experimentally verified over the last three decades with utmost precision. The only remaining piece was to show whether the symmetry was indeed broken by a complex scalar field à la Higgs and others. This meant that the massive scalar particle (the Higgs boson), which arises in the Standard Model as a result of spontaneous breaking of the electroweak gauge symmetry, had to be found. The Standard Model itself cannot predict the mass of the Higgs boson, and data from particle decays only give a broad range for it. Earlier accelerator experiments both at CERN and Fermilab, United States, had set lower limits to the Higgs mass, which were essentially the energy limits that these machines could reach in their search for the particle.

The search had to wait until the LHC was built, and in July 2012, within two years of its commissioning in 2010, experimentalists succeeded in settling the question by discovering a new particle with a mass of 125 gigaelectronvolts (GeV) and properties that the Higgs boson should have according to the Standard Model.

Subsequent to the discovery, continued experiments at CERN have confirmed that the particle is indeed the missing piece in the model, the Higgs boson (
*Frontline*, December 4, 2009; January 29, 2010; September 23, 2011; January 13 and July 27, 2012).

**Delayed announcement**

It is unfortunate that the restrictive rule of “three awardees”, in effect, downplays the contributions of others. It is not clear how the conundrum could have been remedied without amending the statutes of the Nobel Foundation. It is interesting that the announcement of the prize by the Nobel Committee was delayed by more than an hour. The recommendations of winners by the Nobel Committee have to be formally approved by the full 615-member Swedish Academy through a majority vote. The formal announcement is made only after that.

When asked about the delay, Staffan Normark, the academy’s permanent secretary, told the Associated Press: “It takes time. This is one of the biggest prizes. *There were many people who had a lot to say*.” But what was the nature of the discussions or why the announcement was delayed will not be known for another 50 years because the Nobel award deliberations are, by the instituted rules, secret for that length of time.

Woit has argued that at least Anderson could have been awarded (for the second time) along with Englert and Higgs for his fundamental contribution. From the detailed background provided, it would seem that the Swedish Academy regarded demonstrating the concept in a relativistic model as crucial, which Anderson had failed to do. But as the physicist John Preskill has commented on Twitter, “The emphasis [in the background document] on finding a relativistic model may be misplaced, though. Anderson understood the mechanism well.”

**Anderson’s account**

Anderson’s account of his work, as narrated by him in his long interview in November 1999, is interesting:

“…during this period I was in fairly close contact with Bob Brout…. Bob spent several summers with us down at Bell [Labs] and… I talked many of these things over with him. So he was definitely one of my sources for knowledge about particle physics, along with John Ward to a much, much lesser extent. Therefore, when I was recently helping edit one of the accounts of the recent Nobel Prize… I realised that actually Brout and Englert had a fairly considerable influence on the whole development (
*must have gotten their ideas from me*). So I had thought that it [my work] just fell into a black hole and Higgs reinvented it and everybody called it the Higgs mechanism because of that….

“I realised that this mechanism eliminated the Goldstone boson and replaced it with a massive excitation which eventually I realised was itself a boson. Then, from that point I basically understood the Higgs mechanism even in the context of superconductivity.... I finally wrote this paper up which I submitted in ‘62, which does seem, looking back at it, to embody the Higgs mechanism in rather final explicit form.”

In another recounting of history, Anderson has said: “It was not published as a paper in *Condensed Matter Physics*. It was published as a paper in *Particle Physics*. Brout paid attention to it. And he and Englert two years later produced a model of symmetry breaking
*... and there’s no way Brout was not perfectly aware of my work* and I would be surprised if the Brout-Englert paper doesn’t reference it rather than Higgs or along with Higgs. So in fact it didn't fall completely on deaf ears.” But the interesting fact is that the Brout-Englert paper does not refer to Anderson’s 1963 paper.

Hagen of the GHK group also commented recently on the background document provided by the Swedish Academy: “In their desire to marginalise the GHK paper, they have failed to understand its real contribution and have certainly failed to comprehend that the… work makes totally credible and understandable the route whereby the expected Goldstone boson is eliminated from the physical sector.” In fact, Ian Simple writes in his book *Massive*: “…some regard GHK as the most comprehensive version of the theory”. There is thus an obvious feeling of hurt and injustice in the GHK camp about the Nobel award.

Shivaji Sondhi, who interviewed Anderson in 1999, wrote on November 15 in *The Indian Express*: “[B]y staring into a piece of metal, Anderson had divined the solution to a puzzle about fundamental particles…. So, the discovery of the Higgs particle is a triumph for this syncretic view built into modern physics…. I believe the [Nobel] committee missed an opportunity in not including Anderson along with Higgs and Englert. It would have been a more accurate accounting of the credit on this particular discovery and a deserved honour for a man whose contributions are legion. Above all, it would have paid tribute to the remarkable intellectual unity of modern physics.”

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