## Monday, November 12, 2012 ... /////

### Superstringy compactifications compatible with the $B\to\mu^+\mu^-$ decays seen by LHCb

By Gordon Kane, Distinguished University Professor of Physics, University of Michigan and a Lilienfeld Prize winner

Intro by LM: The HCP 2012 conference in Kyoto, Japan began today. Pallab Ghosh of BBC immediately told us that "SUSY has been certainly put in the hospital". This statement boils down to the recently exposed measurements at the LHCb detector of the rarest decay of the B-mesons so far (paper in PDF, public info), namely $B_s^0\to\mu^+\mu^-$, whose observed branching ratio $3.2^{+1.5}_{-1.2}\times 10^{-9}$ (about 99% certainty it is nonzero) agrees with the Standard Model's prediction of $(3.54\pm0.30)\times 10^{-9}$. See also a few days old LHCb paper on another decay and texts by Harry Cliff at the Science Museum Discovery blog, Michael Schmitt, Tommaso Dorigo, and Prof Matt Strassler on the muon decay. But what do actual supersymmetric stringy compactifications predict about this decay? Are they dead?
I want to thank Luboš Motl for his interest and for inviting me to summarize our rare decay predictions for the data that is appearing this week. Basically the prediction for supersymmetry based on compactified string/M theories is that any rare decay rate should equal the Standard Model one within an accuracy of a few per cent.

Although many string/M theory predictions can not yet be made accurately, some can, in particular the prediction for $B_s\to \mu^+\mu^-$. The short summary of the argument is that compactified string/M theories have moduli that describe the shapes and sizes of the small dimensions. The moduli fields have quanta, scalar particles, that decay gravitationally so they have long lifetimes. In order to not destroy the successes of nucleosynthesis the moduli have to be heavier than about $30\TeV$. One can show that the lightest eigenvalue of the moduli mass matrix is connected to the gravitino mass in theories with softly broken supersymmetry, and in turn that in such theories the squark and slepton (and Higgs scalar) masses are essentially equal to the gravitino masses. Thus the squarks and sleptons are heavier than about $30 \TeV$, and they are predicted to be too heavy to observe at LHC or via the rare decays. The LHCb result agrees with this prediction. While the scalars are too heavy to be seen easily, gluinos and neutralinos and one chargino should be seen at LHC.

LHCb detector coils

A review article summarizing compactified M-theory predictions including those for the $B_s\to\mu^+\mu^-$, many of which also hold for other corners of string theory, was recently published by Bobby Acharya, Piyush Kumar, and myself,
Compactified String Theories — Generic Predictions for Particle Physics (PDF).
The same theory led to the prediction (before the data) of the Higgs boson mass to be $126\pm 2\GeV$ including all supergravity constraints (details in the review article). Some people used phenomenological arguments to suggest scalars were heavy and thus expected similar results for rare decays. It should be emphasized that our predictions start from the Planck scale M/string theory and derive the results for supersymmetric $\TeV$ scale theories. Getting the Standard Model result for $B_s\to \mu^+\mu^-$ is the only prediction derived in a supersymmetric theory, and adds to the evidence for supersymmetry and for M/string theories beginning to become a meaningful predictive and explanatory framework for particle physics and cosmology.

P.S. by LM: On page 26 of the April 2012 review above, you may read that the branching ratio has SUSY contributions going like $(\tan\beta)^6$, but because the result is virtually indistinguishable from the Standard Model, one may only conclude that $\tan\beta\lessapprox 20$. The upper limit "twenty" may get reduced a bit in the wake of the new LHCb measurement.

#### snail feedback (14) :

So susy remains consistent with Kane. As I understand he predicts also a gluino well within lhc bounds and if i fooow correctly has said with some degree of confidene that it is less than a tev in models otherwise sm compatible. So what is evidence on that? Are the triggers even useful to that search? Have I misunderstood?

Wow, thanks Prof Kane for giving these nice explanations here !

After noting that some media and certain bloggers are reporting about these new measurements in a very misleading up to dishonest manner again (!) it is, as I already said at Physics SE, a joy and relieve to come here and getting reassured that still all is well and in order by such a great expert :-)

Cheers

Dear Prof. Kane, how your scenario may be compared to current measurements for the Higgs boson, which slightly deviate from predictions of the SM? Could this be due to any (yet undiscovered) superpartners? Thanks

Dear Professor Kane,

Could you clarify briefly how the standard results of big bang nucleosynthesis would be spoiled if the moduli masses were lighter than 30 TeV? What is puzzling me is that according to the Wikipedia article, the results of about 25% helium-4 by mass, and about 0.01% deuterium by mass, are rather robust, and the helium result is not even sensitive to the initial conditions, although the deuterium result is.

Via Chris Austin:

Dear Professor Kane, Could you clarify briefly how the standard results of big bang nucleosynthesis would be spoiled if the moduli masses were lighter than 30 TeV? What is puzzling me is that according to the Wikipedia article, the results of about 25% helium-4 by mass, and about 0.01% deuterium by mass, are rather robust, and the helium result is not even sensitive to the initial conditions, although the deuterium result is.

From Gordy Kane: If the moduli decay during nucleosynthesis, the decay products include photons and other particles that will dissociate deuterons and even helium, both of whom have binding energies in the MeV range, while the decay products can have GeV energies. The usual insensitivity only holds if no new particles decay during nucleosynthesis.

From Gordy Kane: Logically the calculation of the Higgs boson mass is independent of its decay branching ratios. The mass depends strongly on the scalars of the soft breaking Lagrangian being or order the gravitino mass, plus the mu prediction. The branching ratios could be affected by extra matter that has little effect on the mass. But in practice there are major constraints from other data and theory, so it is unlikely that a decoupling higgs sector can have significant BR deviations.

From Gordy Kane: Thanks. I also find it baffling that people are willing to write mistaken and misleading things.

From Gordy Kane: The now successful compactified M theory prediction that the Bs decay to mu+mu- should equal the SM value is several years old and very robust, only needs that the scalars are equal to the gravitino in mass. The HIggs mass successful prediction has

the same derivation, plus that the derivation that the mu parameter is suppressed an order of magnitude or more compared to the gravitino mass. The argument that the gluino should be light is much more complicated, and depends on cancellation of the F terms from the gauge matter and from the chiral fermions and is much more dependent on details of the theory. Most statements about gluino searches do not take into account that most of the gluinos predicted by the M theory compactification decay into third family final states, and that the cross section is low because squarks are heavy. Very recent data may probe M-theory gluinos at about a TeV or a little more, in which case our initial estimates would be wrong. The theory still implies that gluinos should be close to a TeV, and should certainly be observable after the energy upgrade if not before.

Wow :-)

Dear Prof. Kane, thanks for the clear and interesting answers you gave to our questions, I like all of them.

Seing people writing mistaken and misleading things by intent is very annoying, it always drives me up the wall. Prof. Strassler has written a new update on his posts explaing why SUSY is far from dead etc. Seing how he gets almost lynched by the subtrolls the TROLL has lead to the site by repeatedly linking to it makes me vomit :-(

Dear Lumo, I see that Prof. Kane did not directly write here. How did you get his answers, by Mail ?

Cheers

this prediction of m theory happens to agree with standard model . i would choose the standard model for simplicity . can you predict something that the standard model cannot? what about the negative views on susy ? is your blog objective?

Dear acdc, as your last question indicates, your comment is partly dedicated to me. Yes, I chose Gordy Kane because he is an objective source.

Views may differ but the scientific research isn't about "views". It's about evidence.

When you're choosing the Standard Model, you're not solving the task to explain the same body of observations as if one chooses M-theory. In particular, you don't say anything about gravity at all and it can't be easily incorporated to the Standard Model; you don't say anything about the identity of dark matter, details of inflation, baryogenesis, and tons of other things.

It's a basic misconception to think that M-theory and the Standard Model are "competitors". Instead, the Standard Model is a limit of M-theory - we say that it's a low-energy effective theory. Your statement is similar to saying that you prefer Newton's theory over GR. That's nice but we know that beyond some point, it's just not appropriate, e.g. because it disagrees with special relativity. This much was known before any direct evidence in favor of GR.