Wednesday, August 29, 2012

Conformal Standard Model and the second \(325\GeV\) Higgs boson

Does Peter Higgs (or God) have a secretive brother?

Křištof Meissner and Hermann Nicolai released a short preprint
\(325\GeV\) scalar resonance seen at CDF?
in which they use a strange accumulation of four events of the type\[

p\bar p \to \ell^+ \ell^- \ell^+ \ell^-

\] observed by CDF, a detector at the defunct Tevatron, that happen to have the invariant energy \(E=325\GeV\) within the detector resolution, to defend some interesting models in particle physics. The probability that four events of this kind are clumped this accurately is (according to the Standard Model and some simple statistical considerations) smaller than 1 in 10,000. I would still bet it's a fluctuation. But it is unlikely enough for us not to consider the authors of papers about this bump to be leaves blown around by a gentle wind.

Three previous TRF articles have discussed possible signals near \(325\GeV\): this very four-lepton signal, a different signal at D0 indicating a different particle, a new top-like quark, and some deficits near that mass at the LHC: yes, a convincing confirmation of the \(325\GeV\) by the European collider doesn't seem to exist.

At the end of their new article, Meissner and Nicolai mention that this bump, if real, could be the heavier new Higgs boson in the Minimal Supersymmetric Standard Model in which, I remind you, the God particle has five faces.

This is the possibility that every particle phenomenologist is aware of but most of the new Polish-German article is actually dedicated to a different, non-supersymmetric explanation. They exploited the excess to promote their old, 2006 idea about the Conformal Standard Model:
Conformal Symmetry and the Standard Model
In this interesting model, one doubles the number of the Higgs boson but the justification is a different one than the supersymmetric justification. And they conclude that this Conformal Standard Model stabilizes the hierarchy because it is conformally invariant classically; and it may remain consistent all the way up to the Planck scale, too.

That paper is designed to explain the unbearable lightness of the Higgs' being in an unusual, yet seemingly very natural way: things are light because in an approximation, they're massless. Their being massless is a consequence of the conformal symmetry and this symmetry should be imposed at the tree level. What does it mean? Which terms violated the conformal invariance at the classical level?

Well, it's easy to answer this question. The only conformally non-invariant terms are those that have dimensionful (i.e. not dimensionless) coefficients and in the Standard Model, the only such classical terms are the \(-\mu^2 h^2\) quadratic terms for the Higgs field. In the Standard Model, this term is the source of the low-energy, electroweak scale and all other masses such as the Higgs mass, Z-boson mass, W-boson mass, and top quark mass (and, with some suppression, other fermion masses) are controlled by this quadratic term.

This quadratic term is also what makes the Standard Model unnatural.

Obviously, particle physics wouldn't work if you just erased this term: the electroweak symmetry couldn't be broken at all. So they have to emulate its functions – well, more precisely, they have to prove that Nature emulates its functions – differently. "Differently" means that the electroweak symmetry is broken by quantum (i.e. virtual loop) effects: they need a "radiative" (="by quantum loops") electroweak symmetry breaking.

This idea has been around for a long time because of the work of two rather well-known men, Coleman and Weinberg. However, in the context of the Standard Model, it's been a failing idea. The most obvious bug is that the radiatively generated quadratic term still had to be rather small compared to the quartic one – because it's just a "quantum correction" – which means that the Coleman-Weinberg model predicted a Higgs boson much lighter than the Z-boson, about \(10\GeV\). That's too bad because we have known that the Higgs mass is \(126\GeV\) since the Independence Day and we have realized that the mass exceeds \(100\GeV\) for more than a decade. If you tried to achieve this heavy Higgs boson in the Coleman-Weinberg framework, you would need such a strong quartic self-interaction for the Higgs that it would die of the Landau pole disease right behind the corner, within the energies that the LHC is already probing.

Meissner and Nicolai chose to incorporate right-handed neutrinos with both Dirac (shared with left-handed neutrinos) and Majorana mass terms and the seesaw mechanism; and the extra scalar field that is helpful for a particular realization of the seesaw mechanism. They have also changed the detailed logic of how the conformal symmetry is allowed to be violated (to arguments centered around the dimensional regularization). I don't quite understand the change yet and I don't see whether this change is quite independent from their other "update", the addition of the new neutrino and scalar fields. However, what I understand is that their model treats the two Higgs doublets "democratically" when it comes to the Higgs potential terms (and there is a quartic term mixing them). However, the Yukawa couplings are different for the two Higgs doublets; the normal one is responsible for the quarks and charged leptons while the new one is responsible for the neutrinos.

At any rate, they compute the one-loop effective potential for the old light Higgs field \(h\) and their new, now arguably \(325\GeV\)-weighing scalar field \(\phi\). These one-loop terms in the potential contain some logarithms and for dimensional reasons, the arguments of the logarithms have to be dimensionless. This forces them to introduce a new scale \(v\). What's different about this \(v\) relatively to "generic" scales that appear in similar quantum field theories is that its powers never enter the effective Lagrangian; it only appears through its logarithm.

The renormalization group flows are modified in the presence of the two scalar doublets. I don't understand the reason "conceptually" but they claim that because of the extra scalar doublet, the Landau pole is delayed to super-high energies above the Planck scale so the theory may be OK up to the scale of quantum gravity.

In the new 2012 paper, the authors also offer some reasons not to worry that the hypothetical new particle at \(325\GeV\) is not showing up in events with missing energy or events with two jets instead of two of the four leptons. If you offered me 1-to-1 odds, I would bet that their model isn't realized in Nature but it is neither impossible nor "insanely implausible", I think.


  1. Thanks Lumo for the interesting (and even to me not completely inaccessible) discussion of this "competitor" of the MSSM :-)

    If this were realized in nature and the updates work as expected, would this model make SUSY dispensible up to the Planck scale (at most) only? How (if at all) is it related to higher energy physics at scales where quantum gravity kicks in? Can it be derived as an effective QFT from higher energy physics in a similar way as it can be done for the MSSM ? Does it contradict String theory.

    No I've bombarded you with enough potentially stupid questions ... :-P
    I mean no harm by it but I am confused about what implications (if any) this model would have for the "broader picture" of fundamental physics.

  2. If this 325 GeV signal survives, would you bet on the supersymmetric explanation?

    On another note, what do you think of Tom Banks's new paper?

  3. Hi! I think the bump will go away, especially because it should already be there at the LHC as well if real, but if it doesn't go away, yes, I would bet on MSSM.

    Tom's paper expresses ideas he has believed for many years. I think that the existence of a larger number of solutions to string theory has been pretty much established; I think that the character and classification of all transitions between them isn't completely understood and some widely believed transitions could be forbidden while other unknown transitions could exist; while Tom's claims are therefore right in spirit, I don't believe in his superstrict segregation of the landscape to individual vacua.

    He would probably need to convince one of the Calabi-Yau etc. professionals to co-write a paper with some convincing maths - before he would convince me. Incidentally, if the swampland-like ideas could exclude new slow-roll inflation and Tom were right about his ban on the landscape interpretation, string theory could easily ban inflation of all known types. I don't really believe it can be the case so at most one of the bans is likely and the ban on the slow-roll condition seems much more justified to me than Tom's ban on CDL-like tunneling on the landscape etc.

    However, there are many "more abstract" aspects of this stuff where Tom could be importantly wrong, like the illegitimacy of talking about the degrees of freedom inside and outside an eternal-inflation decaying universe at the same moment. I am not using his precise words but I think this is one of the things he also believes. The space and therefore time on both sides is "qualitatively different" and complementarity etc. could prohibit double counting etc. etc.

    All the best,

  4. In the same vein as Dilaton, does this allow supersymmetry breaking at a higher energy scale, above or below the GUT scale, for a larger QFT?

  5. Dear Dilaton, good questions. Well, the hierarchy problem is just 1 reason among 5-10 major reasons why people like me believe in SUSY preserved well below the Planck scale. There's no strict proof that SUSY plays all the roles tthat it could play according to the "most SUSY-dominated" description of physics. I am almost totally ready to believe that there's a different logic that is important to explain why the Higgs is so light. But even if it is so, I still see lots of other reasons why SUSY is preserved up to scales that are much closer to the LHC scale than the Planck scale.

    The model by Meissner and Nicolai is fun as an "isolated idea" trying to solve an "isolated problem" but there are lots of reasons why I don't really believe it's possible or it's the right logic at all if you consider all of physics. The adjustment of the field content to avoid the Landau pole seems kind of ad hoc but I have a more conceptual reason why I think that the very philosophy is unsustainable in the big picture. They demand the classical Lagrangian of the effective field theory to be scale-invariant. But we know that the total one is not: there is the Einstein-Hilbert action, S = integral R/16.pi.G, suppressed by the dimensionful Newton's constant i.e. associated with the Planck scale. So when one considers the effective action at the Planck scale, the dimensionful constants are inevitably there and the same Planckian physical phenomena are now free and eager to produce lots of other terms with dimensionful coefficients, too.

    The idea that the conformal invariance holds "classically" requires one to deny the existence of gravity and that's too strong a denial for me. ;-)

  6. Yes, it's an idea independent of SUSY but of course, the parts of the overall theory that are relevant up to lower energy scales are the "more important ones" in phenomenology, so if the Conformal Standard Model were right and applied to a 325 GeV scalar boson, and SUSY were higher, SUSY would be irrelevant.

    When I say "they're independent", it's about the list of possibilities only. Of course that SUSY would change the detailed RG running and everything would have to be redone if there were also extra fields.

    Note that the "splitting of the roles" between the two Higgses is different in MSSM and different in the Conformal Standard Model so one could need 4 Higgs doublets in a combined "conformal MSSM". I am not going to work on these combined theories because already Conformal Standard Model looks like a stretch to me, see my reply to Dilaton.

  7. Thanks Lumo for this enlightening answer :-)

  8. Dear Lubos,

    I found this discussion on your blog on the subject which I have also studied for quite some time. The point about the MN original paper is that it is technically incorrect, as their CW potential is plugged by the problem of large logs. This problem is the same problem one accounts in pure $\phi^4$ theory, and it has been discussed in the classic paper by Coleman & Weinberg. So, it is not entirely clear whether their calculations are reliable. In the simplest models like the MN model you typically end up with the Landau pole at energies much below the Planck mass, if you do proper computations (see, e.g. our paper arXiv:0704.1165)

  9. Dear Lubos,

    I found this discussion on your blog on the subject which I have been also working for quite of some time. Concerning the original MN paper I would like to point out that it is technically incorrect. The CW potential there is plugged by the large log problem. This is the same problem you account for in pure \phi^4 theory, and it has been known since the pioneering paper by Coleman & Weinberg. So, MN computations seems to be unreliable. In the simplest models like that you typically account Landau poles much below the Planck mass, if you do computations correctly (see, e.g. our paper 0704.1165).

  10. Unless you believe a conformal gravity is possible. I don't understand them very well, but try these papers:
    Tell me what you think.
    The ideas seem interesting enough, I'd like to know your oppinion.
    My mail is

  11. Except it is possible a conformal gravity.
    What do you think about it? It pretends to explain dark energy, dark matter, and is renormalizable. It is compatible with a Higgs conformal theory.
    The idea is to take an action based on the weyl tensor.

  12. Hi, it's just a less sophisticated cousin of "asymptotic safety" (because the author of your papers isn't quite a Steven Weinberg)

    which is itself incompatible with basic properties of quantum gravity such as the dominance of ever larger black holes as microstates of high mass, and their entropy scaling. One may try to find a role for conformal gravity in various contexts but in ordinary nearly flat space we know, conformal gravity can be a good approximation neither at very high energies nor at very low energies which makes it unlikely that our world could in any sense be a "broken phase" of such a theory.