Featured image: From left to right: Tom Kibble, Gerald Guralnik, Richard Hagen, François Englert and Robert Brout. Credit: Wikimedia Commons.
Sir Tom Kibble passed away on June 2, I learnt this morning with a bit of sadness that I’d missed the news. It’s hard to write about someone in a way that prompts others either to find out more about that person or, if they knew him or his work, to recall their memories of him when I myself would like only to do the former now. So let me quickly spell out why I think you should pay attention: Kibble was one of the six theorists who, in 1964, came up with the ABEGHHK’tH mechanism to explain how gauge bosons acquired mass. The ‘K’ in those letters stands for ‘Kibble’. However, we only remember that mechanism with the second ‘H’, which stands for Higgs; the other letters fell off for reasons not entirely clear – although convenience might’ve played a role. And while everyone refers to the mechanism as the Higgs mechanism, Peter Higgs, the man himself, continues to call it the ABEGHHK’tH mechanism.
Anyway, Kibble was known for three achievements. The first was to co-formulate – alongside Gerald Guralnik and Richard Hagen – the ABEGHHK’tH mechanism. It was validated in early 2013, earning only Higgs and ‘E’, François Englert, the Nobel Prize for physics that year. The second came in 1967, to explain how the mechanism accords the W and Z bosons, the carriers of the weak nuclear force, with mass but not the photons. The solution was crucial to validate the electroweak theory, and whose three conceivers (Sheldon Glashow, Abdus Salam and Steven Weinberg) won the Nobel Prize for physics in 1979. The third was the postulation of the Kibble-Żurek mechanism, which explains the formation of topological defects in the early universe by applying the principles of quantum mechanics to cosmological objects. This work was done alongside the Polish-American physicist Wojciech Żurek.
I spoke to Kibble once, only for a few minutes, at a conference at the Institute of Mathematical Sciences, Chennai, in December 2013 (at the same conference where I met George Sterman as well). This was five months after Fabiola Gianotti had made the famous announcement at CERN that the LHC had found a particle that looked like the Higgs boson. I’d asked Kibble what he made of the announcement, and where we’d go from here. He said, as I’m sure he would’ve a thousand times before, that it was very exciting to be proven right after 50 years; that it’d definitively closed one of the biggest knowledge gaps in modern theoretical particle physics; and that there was still work to be done by studying the Higgs boson for more clues about the nature of the universe. He had to rush; a TV crew was standing next to me, nudging me for some time with him. I was glad to see it was Puthiya Thalaimurai, a Tamil-language news channel, because it meant the ‘K’ had endured.
That’s an intriguing and, as he remarks, plausible speculation by the noted condensed-matter physicist Philip Warren Anderson. It appears in a short article penned by him in Nature Physics on January 26, in which he discusses how the Higgs mechanism as in particle physics was inspired by a similar phenomenon observed in superconductors.
According to the Bardeen-Cooper-Schrieffer theory, certain materials lose their resistance to the flow of electric current completely and become superconductors below a critical temperature. Specifically, below this temperature, electrons don’t have the energy to sustain their mutual Coulomb repulsion. Instead, they experience a very weak yet persistent attractive force between them, which encourages them to team up in pairs called Cooper pairs (named for Leon Cooper).
If even one Cooper pair is disrupted, all Cooper pairs in the superconductor will break, and it will cease to be a superconductor as well. As a result, the energy to break one pair is equivalent to the energy necessary to break all pairs – a coercive state of affairs that keeps the pairs paired up despite energetic vibrations from the atoms in the material’s lattice. In this energetic environment, the Cooper pairs all behave as if they were part of a collective (described as a Bose-Einstein condensate).
This transformation can be understood as the spontaneous breaking of a symmetry: the gauge symmetry of electromagnetism, which dictates that no experiment can distinguish between the laws governing electricity and magnetism. With a superconductor, however, the laws governing electricity in the material become different below the critical temperature. And when a gauge symmetry breaks, a massive1 boson is formed. In the case of BCS superconductivity, however, it is not an actual particle as much as the collective mode of the condensate.
In particle physics, a similar example exists in the form of electroweak symmetry breaking. While we are aware of four fundamental forces in play around us (strong, weak, electromagnetic and gravitational), at higher energies the forces are thought to become unified into one ‘common’ force. And on the road to unification, the first to happen is of the electromagnetic and weak forces – into the electroweak force. Axiomatically, the electroweak symmetry was broken to yield the electromagnetic and weak forces, and the massive Higgs boson.
Anderson, who first discussed the ‘Higgs mode’ in superconductors in a paper in 1958, writes in his January 26 article (titled Higgs, Anderson and all that),
… Yoichiro Nambu, who was a particle theorist and had only been drawn into our field by the gauge problem, noticed in 1960 that a BCS-like theory could be used to create mass terms for massless elementary particles out of their interactions. After all, one way to describe the energy gap in BCS is that it represents a mass term for every point on the Fermi surface, mixing the particle with its opposite spin and momentum antiparticle. In 1960 Nambu and Jona-Lasinio developed a theory in which most of the mass of the nucleon comes from interactions — this theory is still considered partially correct.
But the real application of the idea of a superconductivity-like broken symmetry as a source of the particle spectrum came with the electroweak theory — which unified the electromagnetic and weak interactions — of Sheldon Glashow, Abdus Salam and Steven Weinberg.
What is fascinating is that these two phenomena transpire at outstandingly different energy scales. The unification of the electromagnetic and weak forces into the electroweak force happens beyond 100 GeV. The energy scale at which the electrons in magnesium diboride become superconducting is around 0.002 eV. As Terry Pratchett would have it, the “aching gulf” of energy in between spans 12 orders of magnitude.
At the same time, the parallels between superconductivity and electroweak symmetry breaking are more easily drawn than between other, more disparate fields of study because their occurrence is understood in terms of the behavior of fundamental particles, especially bosons and fermions. It is this equivalence that makes Anderson’s speculative remark more attractive:
If superconductivity does not require an explicit Higgs in the Hamiltonian to observe a Higgs mode, might the same be true for the 126 GeV mode? As far as I can interpret what is being said about the numbers, I think that is entirely plausible. Maybe the Higgs boson is fictitious!
To help us along, all we have at the moment is the latest in an increasingly asymptotic series of confirmations: as reported by CERN, “the results draw a picture of a particle that – for the moment – cannot be distinguished from the Standard Model predictions for the Higgs boson.”
1Massive as in having mass, not as in a giant boson.
The International Conference on High Energy Physics (ICHEP) is due to begin on July 7 in Melbourne. This is the 26th episode of the most prestigious scientific conference on particle physics. In keeping with its stature, scientists from the ATLAS and CMS collaborations at the LHC plan to announce the results of preliminary tests conducted to look for the Higgs boson on July 4. Although speculations still will run rife within the high-energy and particle physics communities, they will be subdued; after all, nobody wants to be involved in another OPERAtic fiasco.
Earlier this year, CERN announced that the beam energy at the LHC would be increased from 3.5 TeV/beam to 4 TeV/beam. This means the collision energy will see a jump from 7 TeV to 8 TeV, increasing the chances of recreating the elusive Higgs boson, the “God particle”, and confirming if the Standard Model is able to explain the mechanism of mass formation in this universe. While this was the stated goal when the LHC was being constructed, another particle physics hypothesis was taking shape that lent itself to the LHC’s purpose.
In 1981, Howard Georgi and Savas Dimopoulos proposed a correction to the Standard Model to solve for what is called the hierarchy problem. Specifically, the question is why the weak force (mediated by the W± and Z bosons) is 1032 times stronger than gravity. Both forces are mediated by natural constants: Fermi’s constant for the weak force and for gravity, Newton’s constant. However, when operations of the Standard Model are used to quantum-correct for Fermi’s constant (a process that involves correcting for errors), its value starts to deviate from closer to Newton’s constant to something much, much higher.
Savas Dimopoulos (L) and Howard Georgi
Even by the late 1960s, the propositions of the Standard Model were cemented strongly enough into the psyche of mathematicians and scientists the world over: it had predicted with remarkable accuracy most naturally occurring processes and had predicted the existence of other particles, too, discovered later at detectors such as the Tevatron, ATLAS, CMS, and ZEUS. In other words, it was inviolable. At the same time, there were no provisions to correct for the deviation, indicating that there could be certain entities – particles and forces – that were yet to be discovered and that could solve the hierarchy problem, and perhaps explain the nature of dark matter, too.
So, the 1981 Georgi-Dimopoulos solution was called the Minimal Supersymmetric Standard Model (MSSM), a special formulation of supersymmetry, first proposed in 1966 by Hironari Miyazawa, that paired particles of half-integer spin with those of integer spin and vice versa. (The spin of a particle is the quantum mechanical equivalent of its orbital angular momentum, although one has never been representative of the other. Expressed in multiples of the reduced Planck’s constant, particle spin is denoted in natural units as simply an integer or half-integer.)
Particles of half-integer spin are called fermions and include leptons and quarks. Particles with integer spin are called bosons and comprise photons, the W± and Z bosons, eight gluons, and the hypothetical, scalar boson named after co-postulator Peter Higgs. The principle of supersymmetry (SUSY) states that for each fermion, there is a corresponding boson, and for each boson, there is a corresponding fermion. Also, if SUSY is assumed to possess an unbroken symmetry, then a particle and its superpartner will have the same mass. The superpartners are yet to be discovered, and if anyone has a chance of finding them, it has to be at the LHC.
MSSM solved for the hierarchy problem, which could be restated as the mass of the Higgs boson being much lower than the mass at which new physics appears (Planck mass), by exploiting the effects of what is called the spin-statistics theorem (SST). SST implies that the quantum corrections to the Higgs-mass-squared will be positive if from a boson, and negative if from a fermion. Along with MSSM, however, because of the existence of a superpartner to every particle, the contribution to the correction, Δm2H, is zero. This result leaves the Higgs mass lower than the Planck mass.
The existence of extra dimensions has been proposed to explain the hierarchy problem. However, the law of parsimony, insofar as SUSY seems validatable, prevents physicists from turning so radical.
MSSM didn’t just stabilize the weak scale: in turn, it necessitated the existence of more than one Higgs field for mass-coupling since the Higgs boson would have a superpartner, the fermionic Higgsino. For all other particles, though, particulate doubling didn’t involve an invocation of special fields or extrinsic parameters and was fairly simple. The presence of a single Higgsino in the existing Higgs field would supply an extra degree of freedom (DoF), leaving the Higgs mechanism theoretically inconsistent. However, the presence of two Higgsinos instead of one doesn’t lead to this anomaly (called the gauge anomaly).
The necessity of a second Higgs field was reinforced by another aspect of the Higgs mechanism: mass-coupling. The Higgs boson binds stronger to the heavier particle, which means that there must be a coupling constant to describe the proportionality. This was named after Hideki Yukawa, a Japanese theoretical physicist, and termed λf. When a Higgs boson couples with an up-quark, λf = +1/2; when it couples with a down-quark, λf = -1/2. SUSY, however, prohibits this switch to the value’s complex conjugate (a mass-reducing move), and necessitates a second Higgs field to describe the interactions.
A “quasi-political” explanation of the Higgs mechanism surfaced in 1993 and likened the process to a political leader entering a room full of party members. As she moved through the room, the members moved out of their evenly spaced “slots” and towards her, forming a cluster around her. The speed of the leader was then restricted because there were always a knot of people around her, and she became slowed (like a heavy particle). Finally, as she moved away, the members returned to their original positions in the room.
The MSSM-predicted superpartners are thought to have masses 100- to 1,000-times that of the proton, and require extremely large energies to be recreated in a hadronic collision. The sole, unambiguous way to validate the MSSM theory is to spot the particles in a laboratory experiment (such as those conducted at CERN, not in a high-school chemistry lab). Even as the LHC prepares for that, however, there are certain aspects of MSSM that aren’t understood even theoretically.
The first is the mu problem (that arises in describing the superpotential, or mass, of the Higgsino). Mu appears in the term μHuHd, and in order to perfectly describe the quantum vacuum expectation value of the Higgsino after electroweak symmetry breaking (again, the Higgsino’s mass), mu’s value must be of that order of magnitude close to the electroweak scale (As an analog of electroweak symmetry breaking, MSSM also introduces a soft SUSY-breaking, the terms of which must also be of the order of magnitude of the electroweak scale). The question is whence these large differences in magnitudes, whether they are natural, and if they are, then how.
The second is the problem of flavour mixing. Neutrinos and quarks exhibit a property called flavours, which they seem to change through a mechanism called flavour-mixing. Since no instances of this phenomenon have been observed outside the ambit of the Standard Model, the new terms introduced by MSSM must not interfere with it. In other words, MSSM must be flavour-invariant, and, by an extension of the same logic, CP-invariant.
Because of its involvement in determining which particle has how much mass, MSSM plays a central role in clarifying our understanding of gravity as well as, it has been theorized, in unifying gravity with special relativity. Even though it exists only in the theoretical realm, even though physicists are attracted to it because its consequences seem like favourable solutions, the mathematics of MSSM does explain many of the anomalies that threaten the Standard Model. To wit, dark matter is hypothesized to be the superpartner of the graviton, the particle that mediates the gravitational force, and is given the name gravitino (Here’s a paper from 2007 that attempts to explain the thermal production of gravitinos in the early universe).
While the beam energies were increased in pursuit of the Higgs boson after CERN’s landmark December 13, 2011 announcement, let’s hope that the folks at ATLAS, CMS, ALICE, and other detectors have something to say about opening the next big chapter in particle physics, the next big chapter that will bring humankind one giant leap closer to understanding the universe and the stuff that we’re made of.
