### Creeping Up on the MSSM

There’s an interesting paper by Diaconescu, Florea, Kachru and Svrček
on gauge-mediated supersymmetry-breaking in String Theory. In perturbative heterotic string theory and, I think, in heterotic M-theory as well, supersymmetry-breaking is generally expected to occur in a hidden sector, associated to the second $E_8$, and is communicated only indirectly to the visible sector via gravity-mediation. Gauge mediation requires a messenger field charged under both the visible and the hidden gauge group. There *are* such fields in the heterotic string but their masses are string-scale in the weakly-coupled heterotic string and super-Planckian in heterotic M-theory. So gravity-mediation typically dominates^{1}.

Gauge-mediated SUSY-breaking is attractive, because it solves the “flavour problem” by making the SUSY-breaking squark masses flavour-independent. That’s because the messenger(s) couple directly only to the gauge sector of the Standard Model. Gaugino masses are a 1-loop effect. Squark and slepton masses are a 2-loop effect, and are flavour-independent. Gravity-mediation (despite the name) has no such flavour-universality (*a-priori*).

Diaconescu *et al* find some new classes of heterotic models in which gauge-mediated SUSY-breaking dominates. In the dual F-theory picture (these models all have F-theory duals), SUSY is broken on a stack of D3-branes probing a singularity corresponding to a shrunken del Pezzo. The corresponding quiver gauge theories are known to be supersymmetric to all orders in perturbation theory, but to dynamically break supersymmetry at the nonperturbative level (see also Berenstein *et al* and Bertolini *et al*).

If this stack of D-branes is located sufficiently close to the stack on which the Standard Model arises, then the ground states of the open strings between the two stacks are the desired messengers for gauge-mediated SUSY-breaking.

Most of the discussion takes place in the context of the elliptically-fibered Calabi-Yaus explored by the Penn Group (for some recent papers getting ever-closer to the precise MSSM field content and couplings, see Bouchard and Donagi and Braun, He, Ovrut, and Pantev). So there’s a good chance that one can actually build a fully-realistic compactification along these lines. (Foes of F-theory flux vacua are permitted, at this point, to go berserk.)

So much for “top-down,” what about “bottom-up”? What will we be able to learn about SUSY at the LHC? I’ve mentioned before the paper by Arkani-Hamed, Kane, Thaler and Wang, which has finally appeared. In it, they discuss the “inverse problem” of deducing a model in the MSSM parameter space from the LHC data. To study the question, they simulate a huge number of MSSM models, look at the experimental signatures they produce. When the sleptons are somewhat heavy (so that they don’t appear in the decay-chain of neutralinos which result in opposite-sign dilepton events), there’s a relatively large^{2} degeneracy (~10-100 models), corresponding to different orderings of the slepton masses. If the sleptons are lighter, then the degeneracies are smaller, and they present a rough taxonomy of some of the degenerate models.

- Flippers
- The spectrum of masses of the Electroweak 'inos is fixed, but the identities of which ino has which mass are exchanged.
- Sliders
- The Electroweak 'ino masses are moved up or down, keeping the mass splittings fixed.
- Squeezers
- The information of some of the Electroweak 'inos is hidden because the mass splittings are small enough that the leptons in the decay products are too soft to be seen.

With the limited available signatures, the LHC will be unable to distinguish between these radically models.

But, before losing hope, one of the key messages to take away from their paper is that, if you have some reason to choose between the degenerate models (either a theoretical prejudice, or some experimental signature that they did not consider), then the LHC data can determine the parameters of that single model to very high accuracy.

^{1} There *are* exceptions to this general rule, in certain orbifold models, as my colleague, Vadim Kaplunovsky, is fond of pointing out. Perhaps that’s true more generally.

^{2} On the other hand, the degeneracy isn’t $\sim 10^6$, as you might have feared.

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