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Beyond Higgs: on Supersymmetry (or lack thereof)


Image from CERN, from Wikimedia Commons

Image from CERN, from Wikimedia Commons

With the search for the Higgs boson, the last missing piece of the Standard Model of particle physics, apparently reaching its long-anticipated-and-finally-successful conclusion, anticipation of the next set of discoveries is growing.

Recently the Stanford campus hosted a smallish gathering celebrating the 60th birthday of Savas Dimopoulos, justly acclaimed by each of the attendees as the (or at least one of the few) most insightful particle physics model builders of the last 30 years. (And my PhD adviser.) Now you’d think that the leading topic of discussion at such an event would be the details of the ongoing Higgs search – has it or hasn’t it been discovered? Does the fact that the two relevant experiments at CERN’s Large Hadron Collider (LHC) – ATLAS and CMS – both have a signal indicative of a new particle with the same mass? And what about the supportive analysis coming from Fermilab’s Tevatron?

Surprisingly (to the outsider) this was all considered old news. Repeatedly, the theorists joked that, with the exception of the actual CERN experimentalists present, all of us know that the Higgs has now been discovered with a mass of 125 GeV/c2. (It hasn’t, quite, but the hints are strong.) The message was clear: “We’ve known for decades that the Higgs is going to be found. So break open the champagne and get the celebrating over with, because what we really want to know is -- which is the correct version of Beyond the Standard Model physics?” With a brief nod to large extra dimensions (a Dimopoulos, and associates A, D and also I, idea) and a fond farewell to Technicolor (another idea that Dimopoulos helped advance), the focus turned again and again to the likely suite of Supersymmetric (SUSY) particles (yet another stock in which Dimopoulos is heavily invested).

Supersymmetry – a theory that posits that for every known particle there is another (or more than one) yet-to-be-discovered partner particle – is the leading candidate for physics Beyond the Standard Model. It is central to string theory (a.k.a. super-string theory), required for gauge coupling unification (see below), useful for solving the Higgs Fine Tuning Problem (definitely see below) and also gives us the leading candidate for dark matter – the Lightest Supersymmetric Particle (LSP).

But I’m getting way ahead of myself, and probably you. Especially since I and my colleagues have come to believe that the principal indictment of the Standard Model, which has been used to argue so forcefully for Beyond the Standard Model (BSM) physics is, hmmm, dubious. Or as one of those colleagues would say – completely wrong. A main rationale for supersymmetry evaporates on closer inspection.

So what is Beyond The Standard Model (BSM) physics, why are people so convinced it is around the corner, and should they be?

At least since the discovery of the W and Z particles at CERN in 1983, physicists have been pretty much convinced that the Standard Model (SM) that emerged from the late 1960s and early 1970s is the correct model of fundamental physics. At least at energies below the so-called weak-scale – a few hundred GeV – or maybe a few times that. But particle theorists variously hoped/expected/knew that at higher energies the Standard Model was not the whole story, and a more fundamental theory would need to be found.

There are two types of reasons to doubt the completeness of the Standard Model – aesthetic (philosophical) and mathematical.

Aesthetic problem number one, physicists adore simplicity. Zero and one are our favorite numbers. Two can be suffered. After two comes “too many”, although identical copies (twins, triplets, ...) may receive special dispensation. The Standard Model has too many too-many’s: three fundamental forces (a.k.a. gauge groups); way too many fundamental fermions (particles that make up matter)-- three generations each with at least 5 representations (groups) of them -- plus three sets of gauge bosons and the set of particles of which the Higgs boson is a member. It also has far too many (more than 20) independent parameters.

Aesthetic problem number two –– for no apparent reason the weak scale is much (as in about 1016 times) smaller than what we believe to be the fundamental energy scale of physics – the Planck scale (about 1019 GeV), a scale set by the strength of gravity (the one fundamental force not included in the Standard Model). This is known as the (Weak) Hierarchy Problem – and can also be understood in terms of the absolutely enormous strength of the three Standard Model forces compared to that of gravity between pairs of fundamental particles separated by appropriately microscopic scales.

It is however the technical problem that has carried the most weight in convincing people that there must be physics beyond the Standard Model. It is the story we tell our children -- quantum mechanics makes the Standard Model unstable. Quantum mechanics teaches us that, as a particle such as a Higgs boson travels along, it can emit and reabsorb another particle. This process represents a “loop contribution” to the mass of the Higgs boson, so-called because a pictorial representation of the process – Feynman diagrams – depicts these processes as loops attached to the traveling Higgs boson.

Unfortunately, when you add up the loop contributions to the mass of the Higgs boson from all possible particles with all possible energies and momenta, they appear to be infinite or at least proportional to the maximum possible momentum that can be carried. For technical reasons these are called quadratic divergences and are widely derided. For the actual Higgs boson mass to be finite, there must apparently be subtle and precise cancellation of the loop contributions against the underlying “tree” (loop-free) mass. This Higgs Fine-Tuning Problem, so the lore tells us, must be remedied.

BSM physics is the proposed remedy. Supersymmetry cancels the loop of every known particle against the loop of an as-yet-to-be-discovered partner particle. Technicolor eliminates the Higgs boson – replacing it by a composite of new particles called techni-quarks. If there are large extra dimensions then the largest momentum that can circulate in a loop is actually only a little larger than the weak scale. Clearly BSM physics is not just desirable but essential.

Recently, however, my colleague Bryan Lynn suggested, and together with Katie Freese and Dmitry Podolsky, he and I explained, how the Standard Model actually comes up with a remedy all on its own.

The Higgs boson is one member of a set of quadruplets in the Standard Model. At energies below the weak scale, its three siblings get eaten – they get incorporated into the W and Z bosons. According to a famous theorem due to MIT’s Jeffrey Goldstone (hence “Goldstone’s Theorem”), the masses of the three siblings must be exactly zero. In particular, the quadratically divergent contribution to their masses are zero.

Although this doesn’t force the mass of the Higgs boson to be zero (a good thing, since it seems likely to be about 125 GeV/c2), it does mean that the quadratic divergences in the Higgs mass that have worried us for decades are not a problem of the Standard Model after all.

Now, not everybody buys our argument. Some of them prefer to focus on the aesthetic challenge of the Weak Hierarchy Problem, while others argue that we have no choice but to add quantum gravity to the Standard Model, inevitably resurrecting the Higgs Fine Tuning Problem.

We would counter that the absence of a Higgs Fine Tuning Problem in the Standard Model is such a virtue that, absent any hard evidence for BSM physics, preserving the Standard Model’s Goldstone miracle should be taken as a requirement of any proposed BSM theories.

The implication is clear. If there is no problem, there may be no need for a solution. Beyond the Standard Model Physics isn’t ruled out by the absence of a Higgs Fine Tuning Problem in the Standard Model, but it does mean that the Standard Model may well be the whole story, or at least the whole story at the energies that the LHC can command. In short, don’t be surprised if the Higgs is the last new particle discovered by the LHC. Theorists may hunger for physics beyond the Standard Model, but nature may be quite content without it, thank you very much.


Related at Scientific American: Is Supersymmetry Dead?

The views expressed are those of the author and are not necessarily those of Scientific American.

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