Muon anomalous magnetic moment from effective supersymmetry

Abstract.

We present a detailed analysis on the possible maximal value of the muon $(g-2)_\mu \equiv 2 a_\mu$ within the context of effective SUSY models with R parity conservation. First of all, mixing among the second and the third family sleptons can contribute at one loop level to $a_\mu^{\mathrm{SUSY}}$ and $\tau \rightarrow \mu \gamma$ simultaneously. One finds that $a_\mu^{\mathrm{SUSY}}$ can be as large as $(10$–$20)\times 10^{-10}$ for any $\tan\beta$, imposing an upper limit on the $\tau\rightarrow \mu \gamma$ branching ratio. Furthermore, the two loop Barr–Zee type contributions to $a_\mu^{\mathrm{SUSY}}$ may be significant for large $\tan\beta$, if a stop is light and $\mu$ and $A_t$ are large enough ($\sim O(1)$ TeV). In this case, it is possible to have $a_\mu^{\mathrm{SUSY}}$ up to $O(10) \times 10^{-10}$ without conflicting with $\tau \rightarrow l \gamma$. We conclude that the possible maximal value for $a_\mu^{\mathrm{SUSY}}$ is about $\sim 20 \times 10^{-10}$ for any $\tan\beta$. Therefore the BNL experiment on the muon $a_\mu$ can exclude the effective SUSY models only if the measured deviation is larger than $\sim 30 \times 10^{-10}$.