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Beyond Higgs: On Supersymmetry (or Lack Thereof)

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

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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?

Glenn Starkman About the Author: Glenn Starkman grew up and got his Bachelor's degree in Toronto, where he returned after a PhD at Stanford and a postdoc at the Institute for Advanced Study, Princeton. He lives with his wife and two children in Cleveland, where he is Professor of Physics and Director of the Institute for the Science of Origins at Case Western Reserve University. He has written several of Scientific American's most popular articles ever: on whether the universe is finite in size, on anomalies in the cosmic microwave background radiation, on whether cosmology is ultimately doomed as a science, and on the far future of life in the universe.

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

Comments 6 Comments

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  1. 1. lumidek 6:42 am 06/21/2012

    Exactly one year ago, Dmitry Podolsky, a co-author of yours, had a correspondence – about 10 e-mails – with me. He argued in favor of a simpler “argument” than your paper’s argument why there were no quadratic divergences to the Higgs mass.

    The claim was that they only affected the mass parameters so the quartic coupling wasn’t affected by them and the influence of the quadratic divergences on the Higgs mass is actually linked to the correction to the tadpole trying to change the vev (location of the minimum of the potential) which has to be zero for stability. So even the former thing is zero.

    For hours if not days, I was a bit confused but then I came back to my senses and wrote him an explanation – one that he never replied to again. The explanation is that the correction of the tadpole is indeed linked to the correction of the Higgs mass and the vev. That’s OK but *none* of these mutually related things is guaranteed to be zero by any principle. In fact, we know in particular theories it’s not zero. The quadratic divergences reflect the big sensitivity of the Higgs mass/vev on all the detailed parameters of any high-energy theory with start with. We may choose to say whether it’s the Higgs mass or the Higgs vev that is threatened by these divergent terms but both of them are!

    Now, the final paper of yours talks about the pions etc. It is a bizarre treatment. From the viewpoint of the fundamental theory, pions are composite objects and their properties are derived quantities. We don’t really have special counterterms for pions or even technipions in the Standard Model. They’re not fundamental parameters. So at most, you link the divergences to yet another quantity that isn’t guaranteed to be zero by any principle. At most, you are supplying a new principle but this principle is equivalent to saying “there shouldn’t be a hierarchy problem”. You don’t have any independent justification why it’s not there.

    It’s only the Goldstone bosons that have a reason to be massless, the Goldstone theorem, but there are only 3 of them, one for each broken generator, and the physical Higgs boson simply isn’t one of them. That’s why I believe that your paper boldly claiming that the quadratic divergences aren’t really there is wrong.

    Link to this
  2. 2. jctyler 7:32 am 06/21/2012

    “(It hasn’t, quite, but the hints are strong.)”

    where have I heard this before? I raise to 400

    Link to this
  3. 3. christinaak 8:10 am 06/21/2012

    I am with jctyler on this one. I am still betting they have not found the Higgs.

    Link to this
  4. 4. rloldershaw 11:01 am 06/21/2012

    The standard model cannot possibly be the final story, as all physicists know.

    I do not mean to be disrespectful or excessively negative, but it is important to keep in mind the true status of the Standard Model of particle physics when evaluating our present understanding of nature at the subatomic level.

    1. The Standard Model is primarily a heuristic model with 26-30 fundamental parameters that have to be “put in by hand”.

    2. The Standard Model did not and cannot predict the masses of the fundamental particles that make up all of the luminous matter that we can observe.

    3. The Standard Model did not and cannot predict the existence of the dark matter that constitutes the overwhelming majority of matter in the cosmos. The Standard Model describes heuristically the “foam on top of the ocean”.

    4. The vacuum energy density crisis clearly suggests a fundamental flaw at the very heart of particle physics. The VED crisis involves the fact that the vacuum energy densities predicted or measured by particle physicists (microcosm) and cosmologists (macrocosm) differ by up to 120 orders of magnitude (roughly 10^70 to 10^120, depending on how one ‘guess-timates’ the particle physics VED).

    5. The conventional Planck mass is highly unnatural, i.e., it bears no relation to any particle observed in nature, and calls into question the foundations of the quantum chromodynamics sector of the Standard Model.

    6. Many of the key particles of the Standard Model have never been directly observed. Rather, their existence is inferred from secondary, or more likely, tertiary decay products. Quantum chromodynamics is entirely built on inference, conjecture and speculation. It is too complex for simple definitive predictions and testing.

    Robert L. Oldershaw
    Discrete Scale Relativity
    Fractal Cosmology

    Link to this
  5. 5. anselm 1:45 am 06/28/2012

    “Quantum mechanical fluctuations can produce the the Mirror image of the, physical dark matter and the intervening string bundles caused by Dark energy, cascading towards the SINGULARITY , “If you would just, watch the CELESTIAL BODIES Rotation/ORBITALS revolving around the stars,their Geometrical TRIADS in Formation–at and precision FIXED TIME that evolves at extreme low energy limits — a focused interpretation and the TIME freeze Synchonization in SIMULTANEOUS CUSPS–just twist time and FLIP space the right way, you might physically commence production of the POSTULATED BEAUTY PHYSICALLY-” THE MAGNIFICIENT HIGGS !!!!!!!!!!

    Link to this
  6. 6. dpodolsky 4:59 pm 06/29/2012

    Dear Lumo,

    My memory tells me that it was me who made the last reply in that discussion but if I am wrong, I ask you to forgive me. My answer to your observation was more or less as follows.

    1. Stability

    Whether renormalized tadpole is zero on not shows one whether Higgs particles can be spontaneously produced from the vacuum or not. If they can be produced, then the vacuum is not stable. The particles will be produced from vacuum and the physical Higgs’ VEV will change until the renormalized tadpole becomes zero.

    A simple observation which goes back to work done by Bryan Lynn long time ago (and which is actually present in the textbook by Peskin and Schroder citing Bryan’s work) is that the quadratically divergent contribution to the Higgs’ mass coincides identically with the expression for the renormalized tadpole. Hence the first statement of the paper – if renormalized vacuum is stable w.r.t. spontaneous particle production, quadratic divergences are absent in the Higgs’ mass. This observation is actually well known to CMT physicists. There are plenties of phenomena in condensed matter physics involving spontaneously broken global symmetries, and none of them feature quadratic (or linear – because they are (2+1)d) divergences in the effective mass of quasiparticles.

    2. Massless modes

    I am afraid you cannot simply say that there are several independent generators of global symmetries, so divergences in Goldstone’s masses are unrelated to divergences in Higgs’ mass. Even if the global symmetry is broken spontaneously, effective potential should respect it in some way or another – that’s why the word “spontaneously” (instead of “explicitly”) is used. Whether pions are composite or fundamental objects again does not matter – once you have an effective renormalizable lagrangian for low energy degrees of freedom, you can and should study the fate of divergences appearing in the effective theory.

    It so happens that global symmetry relates some contributions to the masses of Goldstones and the Higgs, namely, quadratically divergent contributions. This statement is again known for years and can be found for example in Peskin and Schroder. So, if you want to see that the Goldstone theorem holds explicitly at a given energy scale (i.e, renormalized mass of Goldstones is zero), you should conclude that the quadratically divergent contribution to the Higgs’ mass also vanishes.

    I share very much your sentiment about the sensitivity of the Higgs’ mass to parameters of HE theories (that’s why we always thought we need SUSY, Technicolor, etc., etc., etc), but that’s unfortunately not how it works in these theories.

    Thanks for the link by the way!

    Link to this

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