## October 15, 2007

### Gluino Masses

The MSSM is much-maligned for having many more parameters than the Standard Model. Of course, in the supersymmetric limit, it has no more parameters than the Standard Model. To the contrary, the Higgs quartic coupling is related to the gauge coupling, a simplification that is the source of a certain amount of trouble.

Supersymmetry breaking introduces a plethora of soft parameters. But, as we mentioned last time, we already have some quite stringent constraints on these parameters. And these have nontrivial implications for higher-energy physics.

But we’d like to do better. We’d like to extract some robust (that is to say, relatively model-independent) predictions for these soft parameters. The most promising place to look is at the gaugino masses, where Nilles and Choi have done a very nice analysis.

Both the gauge coupling and the gaugino masses arise from the holomorphic gauge coupling functions, $f_a$, in the supergravity action. The ratio $\tfrac{M_a(\mu)}{g^2_a(\mu)}$ is invariant under 1-loop renormalization group running. But it can receive important threshold corrections, in gauge-mediated supersymmetry breaking, from integrating out the heavy messenger fields, $\Phi$, which are charged under the Standard Model gauge group.

Writing the Wilsonian effective action at the cutoff scale, $\Lambda$ $\int d^4\theta C C^* \left(-3 e^{-K/3}\right) +\left[\int d^2\theta \left(\tfrac{1}{4} f_a W^{a\alpha}W^a_\alpha + C^3 W\right)+ h.c.\right]$