## Tuesday, February 27, 2007

### Sweet spot supersymmetry

Ryuichiro Kitano of Stanford gave an enthusiastic talk about what he calls the first supersymmetric model worth considering although it is not necessarily guaranteed that all people attending the talk have displayed the same degree of enthusiasm. ;-) Some of the talk may be found in hep-ph/0611111.

If you want to break SUSY in some way or any way, it's not hard. You start with something like the O'Raifeartaigh model: I usually prefer longer words instead of short screams but let me admit that O'Raifeartaigh is an exception. In this model, you have a gauge-singlet chiral superfield S. The Kähler potential contains
• K = ... + Sdagger.S + (Sdagger.S)^2 / Lambda^2
while the superpotential contains a linear term for S,
• W = m^2 S + ...
This linear term is enough to guarantee that the stationary points of the normal potential "V" won't be stationary points of "W" - a linear function "S" doesn't have too many stationary points: this minimum of "V" will therefore break supersymmetry. This fact about the simplified picture won't be modified even after you add some extra terms involving quarks and other visible matter.

Now, add bilinear terms in quarks into "K" and a Yukawa interaction of "S" with quarks into "W". You're in the process to communicate the breaking in the hidden "S" sector to the visible sector of the Standard Model - a process that will give additional masses to the superpartners of known particles needed to explain why SUSY hasn't been seen before 2007.

It is almost universally assumed that the supersymmetry breaking can be divided to these parts - the hidden SUSY breaking sector plus some form of its interaction with the visible sector: this interaction is the "mediation". Although the assumption could be wrong, the sweet model is no exception.

Ryuichiro classified the types of mediations according to the gravitino mass. As the mass increases, you go from direct mediation through gauge mediation and gravity mediation to anomaly mediation and finally to split supersymmetry.

His model is intended to be a viable hybrid of gauge mediation and gravity mediation. Alternatively, you may want to think about it as gauge mediation where some previously neglected effects of gravity are included. The gravitino mass is around 1 GeV here. The Higgs mass term in the superpotential - the mu-term - is governed by the same parameter as the SUSY breaking, he says. He presents the Higgs and/or "S" and/or the GUT Higgs breaking SU(5) as composites of two objects from a set {a quark and an antiquark or a "T"}. This compositeness should only work at low energies and the abrupt transition to higher energies where the Higgs is assumed to be weakly coupled wasn't quite clear to many physicists in the audience.

In some more precise realization of the hidden sector, he argued that SO(9) is the most natural gauge group for the SUSY-breaking sector. If you want to know, SO(9) x SU(5) from the GUT can't be embedded into a single E8 which, I believe, means that the grade from string theory to his model is B or worse. ;-)

At any rate, if you believe all the positive comments, you simultaneously solve all astrophysical bounds, mu-problem, doublet-triplet splitting problem, proton decay problem, FCNC problems, CP-violation problems, all remaining SUSY phenomenology problems except for some little hierarchy problem, and with some modest heuristic input ;-) apparently also the cosmological constant problem.

If you care about my impression, you are somewhere in the middle of some parameter space where all these problems are half-solved, half-unsolved. ;-) But maybe this is the right compromise that Nature likes, who knows.