Saturday, January 13, 2007

Phenomenology 2006: mirage mediation

Hyung Do Kim whom I know from Santa Cruz told me what he - and probably many others - consider to be the two most important directions of research in particle phenomenology of 2006:
• hiding Higgs,
• mirage mediation.
We have already discussed Dermíšek's and Gunion's idea about a possible 105 GeV Higgs. Their work has led to some activity of other physicists - including Schuster and Toro of Harvard University - who have tried to modify some assumptions and avoid the 114 GeV lower bound on the Higgs mass.

Mirage mediation

The second development is a new kind of supersymmetry breaking. It is usually dubbed "mirage mediation" and was started by Choi, Jeong, Kobayashi, Okumura at the end of 2005. They described it as a mixed modulus-anomaly mediation of supersymmetry breaking. This scenario may be interpreted as a consequence of the canonical string-theoretical KKLT models: this acronym is well-known to everyone who likes to talk about the "landscape".

For an appropriate type of uplifting potential, the little hierarchy problem is solved by canceling the integrated RG running of the Higgs mass between the GUT scale and the TeV scale. It just naturally happens that the total RG evolution of the Higgs mass is compensated by the anomaly-mediated contribution to its mass. The result is that the Higgs is light and one generates a little hierarchy between the Higgs mass and the supersymmetry scale that happens to be "sqrt(8).pi" times heavier than the Higgs.

The models that solve the hierarchy problem usually want to predict a nearly degenerate spectrum of the superpartners. It's because all superpartners must be heavier than the experimental lower bound. If the superpartner masses were too diverse, some of the superpartners would have to be far heavier which would lead to imperfect cancellations of the corrections to the Higgs mass and a stronger required tuning ("fine-tuning" could be too strong a word for the 1% accuracy).

The mirage mediation model is no exception. Indeed, the gaugino masses are nearly degenerate. The lightest superpartner (LSP) is not just a neutralino - it is, in fact, a pure Higgsino. Stop and gaugino masses are related and SUSY flavor and CP violation is suppressed. This mechanism leads to a fictitious (mirage) unification at an intermediate scale around 10^{10-11} GeV.

Let me say that the RG running to the Higgs mass is dominated by the dominant Yukawa coupling - the top Yukawa coupling - and the corresponding superpartner mass - the stop mass. Because it is a running effect, it depends on the logarithm:
• Delta (mHiggs:u2) = -3/(4 pi2) yt2 mstop2 ln (mGUT/mstop)
That's pretty big and it wants to make the stop squark as light as the Higgs which seems incompatible with the experiments. Everyone who became interested should read the paper by Choi et al. and its followups. But let me say the following: if this realization of supersymmetry breaking were observed at the LHC, it would be not only a proof of SUSY but also a very strong circumstantial evidence in favor of the flux compactifications of string theory and maybe even the landscape itself although we would have to think twice before making such a conclusion.