By Gordon Kane, Distinguished University Professor of Physics, University of Michigan
Originally posted on Dec 7th
Let me begin by thanking Luboš Motl for the opportunity to explain our string theory prediction for the Higgs boson mass more fully. Our paper arXiv:1112.1059 is, we hope, complete and clear, but it is written for workers in the field and has the usual reliance on jargon. A lot of jargon is needed to communicate at all, but here I will try to say things a little differently.
Update: An answer by Prof Kane to the KKLT-like guest was added to the fast comments, and copied at the end of this article, too.A number of collaborators have been crucial in doing the basic work I describe here. Most important is Bobby Acharya, a remarkable physicist who is an impressive string theorist and phenomenological theorist and Atlas experimenter, at ICTP, Trieste and at King’s College, London. Without Acharya this work would not have been done. Impressive and essential younger theorists include Piyush Kumar, currently Columbia postdoc; Konstantin Bobkov, moving to UCSF; Jing Shao, postdoc at Syracuse University, Scott Watson, assistant professor at Syracuse University; Eric Kuflik, postdoc at University of Tel Aviv; and Ran Lu and Bob Zheng, very good graduate students. Discussions with people at the annual International String Phenomenology Meetings and workshops of the NSF supported String Vacuum Project have been very important in leading to progress.
Our basic argument is fairly simple to state. To make predictions for our 4D world one has to “compactify” the 10 or 11D string/M-theory to 4D. The extra dimensions show up after compactifying via the presence of “moduli” fields, basically the modes of the extra dimensional graviton. The moduli take on non-zero values in the vacuum, and those values determine the sizes and shapes of the curled up small dimensions. The jargon is “stabilizing” the moduli. As modes of the extra dimensional graviton the moduli quanta couple to all matter and are therefore unstable quanta. The moduli lifetime is long if they are light because the decay is only via the very weak gravitational interaction, and if they decay during nucleosynthesis when the light elements we observe today are made they would prevent the nuclei from forming as the universe cooled and we would not get a universe like ours. Therefore they have to be heavier (it turns out) than about 30 TeV.
Next, one can show that in a theory with a broken supersymmetry (as is typical in string/M-theories) that the graviton (the quantum of gravity) is accompanied by a superpartner, the gravitino. The mass of the gravitino measures the amount of supersymmetry breaking and sets the scale for all particle and superpartner masses. One can also show the lightest moduli have masses of order the gravitino mass or less. Since the moduli must be heavier than about 30 TeV, the gravitino must also be. Connecting the moduli and gravitino masses is a new, crucial ingredient in predicting the Higgs boson mass. In a theory where the supersymmetry is a local symmetry, as we expect, the field theory description is called supergravity, and gives prescriptions for calculating the Lagrangian of the theory and all predictions. In particular, it tells us that all the scalar particles of the theory (squarks, sleptons, Higgs sector scalars) have masses about the same as the gravitino mass, which we have seen is about 30 TeV or more. That is much heavier than scalars were naively expected to be until it was recognized that the arguments summarized above led to the heavier particles. With the scalars being heavy, all the particles in the higgs sector get heavy too, except for one light higgs boson which is the one we all hope can be detected at LHC. That one behaves very much like the single higgs boson of the Standard Model theory. The full theory has additional Higgs bosons, but they are too heavy to detect with any collider the world can afford (as are the squarks). The full calculation also requires knowing the matter content and gauge group of the theory below the string scale, which we assume is the MSSM. If not the calculations could be repeated for extensions, which shift the Higgs mass somewhat. The result also necessarily depends on the vacuum values of the two Higgs fields themselves, particularly through their ratio “tan β”. In principle these vacuum values and their ratio can be calculated, but not yet with good accuracy.
Over the years some clever theorists have noticed that having heavy scalars was allowed by other constraints, and constructed models to implement that. I won’t describe such work and the authors here, partly for time reasons, and partly because here we are in a full theory where the breaking of the electroweak symmetry and the size of the scalar masses are derived in the theory, rather than guessed or ignored.
Since compactified string/M-theories generically have moduli, the above arguments hold in the ground states (vacuum states) of any string theory or M-theory. Basically the moduli properties determine what our string vacuum is like. Other properties of the vacua can be different for different limits of string theory. Whether the gluinos and the lightest superpartner that is a candidate for the dark matter are much lighter than the squarks is not yet known for all string theories – they are for the M-theory compactification. Then the gluino should be detected at LHC, and because of the heavy scalars the gluino decays are different from the ones usually discussed, being dominantly to third family quarks, top and bottom quarks. I won’t explain that here because of space and time; we can return to it as the gluinos are being detected in coming months. They have not yet been systematically searched for. The gluinos and the dark matter provide important consistency checks on the theory here, as does the requirement that the squarks not be found, and that rare decays from squarks and sleptons in loops not show deviations from SM predictions.
Which superpartner(s) make up the dark matter is not cleanly derivable yet, but the theory probably implies the dark matter is mostly wino (superpartner of the neutral W boson), with some higgsino and bino mixture. There are tests of this from “indirect detection”, observing the products of dark matter annihilations throughout the galaxy, particularly positrons, antiprotons, and photons. The PAMELA satellite reported an excess over backgrounds of positrons that can be well described by wino annihilation if its mass is in the 150-200 GeV range, which fits well with the expected gluino masses of about a TeV or less. The next data relevant to the indirect detection may come from the AMS2 detector on the space station, which has been taking data since last July. Such an LSP also predicts a spin independent scattering rate on protons that is being searched for by the “direct detection” experiments. The expected cross section is less than about 10-45 square cm, a rate that the experiments should reach in 1-2 years.
In these theories, then, at LHC, in addition to the light Higgs boson gluinos should be detected, and also one light chargino and two light neutralinos. If the LSP is indeed wino-like then the chargino and the LSP are nearly degenerate so it is difficult to detect, although it’s production rate is large. Probably the best way is to get a sample of gluinos and look at those events for charginos in the decay chain – the charginos should cross one or two layers of the tracking before decaying.
Gauge coupling unification works well in these theories. It is also possible to solve the “µ problem”. Interestingly, it turned out that the way µ is embedded in M-theory gives a somewhat larger Higgs mass than the way it seems to be embedded in Type II theories and Heterotic theories, so the value of the Higgs mass may point toward how that issue is solved. The connection between the Higgs mass and µ is via the way the electroweak symmetry is broken. Having a stable LSP via a conserved R-parity or equivalent quantum number also should be derivable in a full theory. Actually it seems that the R-parity may not be absolutely conserved, but broken by higher order interactions. In M-theory the LSP lives much longer than the lifetime of the universe so the dark matter is effectively stable, but there is some uncertainty whether it lives long enough for its decay products to avoid detection by satellite experiments. For pure winos that make all the dark matter there may also be a problem with the monoenergetic gammas from dwarf stars. The M-theory compactification accommodates string axions and considerably reduces or eliminates difficult constraints on them, and provides an axion solution to the strong CP problem. It also has no weak CP problem. It provides a mechanism for baryogenesis that can explain the ratio of baryons to dark matter.
In any approach to deriving realistic predictions from any theory one must address the issue of the large cosmological constant. We do not have a solution of the fundamental CC problem. The standard way of dealing with it when making predictions for particular string vacua is to ensure the CC is very small, which can be imposed in most theories. We and others assume the CC problem will be solved by some mechanism that is decoupled from the low energy particle physics. In particular there are no known examples of the CC affecting the physics of systems not neutral under charges (any charges, such as color charge, SU(2) charge, hypercharge, etc), and the Higgs particles all carry SU(2) charge and hypercharge. Of course we cannot be sure the CC issues do not affect physics such as the Higgs boson mass until the CC problem is solved, but it does not seem to be a worrisome issue. There is an analogy that supports this approach – the strong CP problem of QCD is a similar issue, where the Lagrangian can have a term ten orders of magnitude or more larger than its naïve value. In practice if it had the naïve value many observables would be affected, but everyone proceeds as if one can set that term to zero and ignore any consequences even though we do not know how that problem is solved. Such a procedure does not lead to any known problems.
If generic compactified string theories with stabilized moduli correctly predict there is effectively a single Higgs boson and correctly predict its mass, it will be a huge success for the main directions of particle physics beyond the Standard Model, for supersymmetry and for string theory, both of which are crucial for the prediction. It will be a huge success for LHC and the accelerator physicists and experimenters who made the collider and the detectors and the analysis work. It will put us firmly on the path to understanding our own string vacuum, and toward the ultimate underlying theory. The value of the Higgs boson mass not only confirms the approach that predicts it, remarkably depending on its numerical value it may allow an approximate measurement of tan β, the µ parameter, the squark and gravitino masses, that the gauge group and matter content of the theory below the string scale is that of the MSSM, and that light (TeV scale) gluinos and dark matter are likely.
7 December, 2011
Appendix: Answer to Guest (see fast comments)
I agree with everything you say (including the errors you mention). It illustrates what issues there are for non-generic compactifications such as KKLT. First they have to add a constant to the superpotential tuned to 14 orders of magnitude to get a TeV scale. While they argue one can do that via warping there is no derivation. Our M-theory compactification successfully derives the TeV scale from the Planck scale, while they have to set it, and there is no guarantee that can be done. Second, it is increasingly thought that the sequestering they need does not work. Beyond what you mention, there is the paper of Berg, McAllister et al 1012.1858 and also David Marsh, 1108.4687. In addition they have not worried about the moduli cosmology constraints. They have lighter moduli in addition to the heavy one that is usually mentioned. Generic constructions are always possible, attempts at non-generic ones may or may not be – they often go wrong in subtle ways.
Dear same guest,
Thanks for the nice words. You are right that the gluino properties can point to the squark masses, but not through the decay width – the lifetime is about 10^-19 seconds and the gluinos decay in the beam pipe. But the gluino branching ratios for 3rd family final states are enhanced because the third family squarks run down to a Tev faster. Then the signatures are mainly decays to top’s and b’s. Atlas and CMS have actually not looked explicitly for those channels since they started with the unmotivated msugra ones and mostly have not changed their analysis programs for tagging 3 or more b’s (with two b’s the top-topbar background is too large). I guess there is a good chance of seeing the gluino signals with 5 fb-1 with the analyses optimized for b’s and missing energy. We wrote about that for 14 TeV earlier arxiv:0901.3367 and updated for 7 TeV 1101.1963.