The announcement at CERN tomorrow of a likely-looking signal for a 125 GeV mass Standard Model Higgs will probably unleash a flood of hype from theorists claiming this as evidence for their favorite Beyond the Standard Model scenario. One obvious problem with any such claim is that the CERN results correspond well so far to the Standard Model with no additions whatsoever, so spinning them as providing support for things like supersymmetry and string theory will require some work.
For the last decade we have known that the Higgs mass is above 114 GeV (from LEP) and unlikely to be very much higher than that (from precision electroweak results). This summer’s LHC results disfavored masses above about 130 GeV, so for the last few months we’ve known that if the Standard Model Higgs is there, it should be between 114 and about 130 GeV. For a couple weeks news has been circulating widely from ATLAS and CMS that they are both seeing something around 125 GeV.
First out of the gate in the hype derby is Gordy Kane, who is quoted by Davide Castelvecchi at Scientific American claiming that string theory predicts the Higgs mass to be between 122 and 129 GeV:
“If it’s in that range it’s an incredible success for connecting string theory to the real world,” Kane says. He says he is confident that the upcoming LHC announcements, if they pan out as predicted, will constitute evidence for string theory. “I don’t think my wife will let us bet our house, but I’ll come close,” he says.
It’s unclear exactly what he’s willing to bet the house on. If it’s just that the Higgs is in that range, this might have something to do with the plots from the experiments widely circulating privately the last few days. In a remarkable coincidence, after more than 25 years of unsuccessfully trying to extract a definite experimental prediction from string theory, Kane and collaborators were able to achieve the holy grail of the subject (a prediction of the one unknown parameter in the SM, the Higgs mass) just a week before the CERN announcement. They submitted their paper to the arXiv the evening of Monday December 5, a few days after rumors of a 125 GeV Higgs were posted on blogs Friday December 2.
The paper deals with a “prediction” you get based on a host of assumptions about which particular class of string theory compactifications to look at. The main result is that in this particular class of models, you can relate the Higgs mass to the parameter tan(β) that occurs in SUSY extensions of the SM. As you increase tan(β) from around 2, the Higgs mass lies in a band, increasing from 105 GeV and a maximum of about 129 GeV:
We will demonstrate that, with some broad and mild assumptions motivated by cosmological constraints, generic compactiﬁed string/M -theories with stabilized moduli and low-scale supersymmetry imply a Standard Model-like single Higgs boson with a mass 105 GeV < M_h < 129 GeV if the matter and gauge spectrum surviving below the compactiﬁcation scale is that of the MSSM, as seen from Figure 1. For an extended gauge and/or matter spectrum, there can be additional contributions to M_h.
This conclusion and Figure 1 correspond closely to what is in the slides of Kane’s talk at String Phenomenology 2011 this past August. The plot of Higgs masses as a function of tan(β) is there, giving a range of 108 GeV to 127 GeV. There is an intriguing comment on the conclusion slide:
Single light Higgs boson, mass about 127 GeV unless gauge group extended.
I can’t tell where the number 127 came from. Since 127 GeV is the top limit in the figure, and the wording “unless gauge group extended” is used, one guess would be that Kane meant that 127 GeV was the upper bound on the Higgs mass in this class of models.
There’s nothing in Kane’s August talk about a 122-129 GeV range for the Higgs mass, but in the December 5 paper it appears explicitly three times:
When the matter and gauge content below the compactiﬁcation scale is that of the MSSM, it is possible to make precise predictions. In this case, we predict that there will be a single Standard Model-like Higgs boson with a calculable mass 105 GeV < M_h < 129 GeV depending on tan β (the ratio of the Higgs vevs in the MSSM). For tan β > 7, the prediction is : 122 GeV < M_h < 129 GeV.
I don’t see where the tan β > 7 comes from, presumably it’s in one of their other papers.
Furthermore, in G2-MSSM models  we find that the range of possible Higgs masses is apparently much smaller, 122 GeV < M_h <129 GeV.
For instance, in G2-MSSM models arising from M theory, Witten’s solution to the doublet-triplet splitting problem  results in μ being suppressed by about an order of magnitude. Hence, in these vacua, the Higgs mass sits in the range 122 GeV < M_h < 129 GeV.
Kane has chosen Lubos Motl’s blog as the place to guest post and promote this string theory “prediction”, concluding there:
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.
I don’t quite see how finding a SM Higgs at 125 GeV is going to give all these different numbers and pieces of information. Kane claims that these string theory predictions also predict gluinos visible at the LHC within months from now:
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.
In addition, there’s a dark matter prediction that should be tested in “1-2 years”.
If I were Kane, I wouldn’t bet my house (or go to the press claiming the 125 GeV Higgs as a “huge success” for string theory) just yet. Assuming he’s right, within months the gluinos will be there, and his ticket to Stockholm will be assured.
Update: My prediction in the first paragraph is coming true faster than I thought. In tonight’s hep-ph listings one finds:
http://arxiv.org/abs/1112.2415 (m_H= 127 +/- 5 GeV)
http://arxiv.org/abs/1112.2462 (m_H < 128 GeV)
http://arxiv.org/abs/1112.2659 (m_H =126 +/- 3.5 GeV)
http://arxiv.org/abs/1112.2696 (m_H > 120 GeV)
There are going to be a lot of these…
Update: Over at a Nature live chat, Kane is giving the public some interesting explanations:
“for a higgs to be meaningful it must be part of a supersymmetric theory, so the superpartners should be found. The form it takes implies that gluinos should be found with masses around a TeV, maybe less, by summer, and decaying mainly into topquarks and bottom quarks.”
“Recently we have published string theory calculations that imply the higgs boson mass is 125 GeV so if it is there are strong implications for connecting string theory to the real world, and for what the higgs discovery implies. we did that before the data.”
“string theories are now well enough understood to predict higgs physics”
There will be another live chat involving Kane tomorrow, this one at Science magazine.
Update: Just took a look at the Science chat. Kane seems to have completely lost touch with reality, somehow deciding that the two experiments have reached the 5 sigma level needed to claim a discovery. As far as I know, he’s the only one in the world to think this.
YES. an experimenter from one experiment can’t say that, but theorists see that two different experiments both saw a signal at about the same mass, and also saw additional channels, so it’s a discovery!
The 5 sigma is a criteria people have chosen. i think as soon as the data are combined from two detectors, which is entirely legitimate, then the signal will indeed be over 5 sigma.
The following claims make about the same amount of sense as the discovery one:
Comment From Tom
Does the existence of a 125 Gev Higgs give any support to supersymmetry?
Yes. first, for a long time it has been known that the lightest higgs boson of supersymmetry should be lighter than about 135 GeV (actually closer to 140 GeV but people make assumptions), so this is consistent. Then the supersymmetric string theories as i mentioned do predict the 125 number and it is a supersymmetric lightest higgs boson.
Update: The hype goes on, with a column today at Nature.