Radiative processes $[\overrightarrow{\tau }\mu \gamma ,$ $\overrightarrow{\mu }e\gamma$ and $\left(g-{2)}_{\mu }\right]$ as probes of the extended supersymmetric standard model in SO(10)

The extended supersymmetric standard model (ESSM), motivated on several grounds, introduces two vectorlike families $(16+\overline{16})$ of $\mathrm{SO}\mathrm{}\left(10\right)\mathrm{}$ with masses of the order of one TeV. It is noted that the successful predictions of prior work on fermion masses and mixings, based on the MSSM embedded in $\mathrm{SO}\mathrm{}\left(10\right),$ can be retained rather simply within the ESSM extension. These include an understanding of the smallness of $V_{\mathrm{cb}}\approx 0.04$ and the largeness of the ${\nu }_{\mu }-{\nu }_{\tau }$ oscillation angle, ${\sin }^{2}2{\theta }_{{\nu }_{\mu }{\nu }_{\tau }}^{\mathrm{osc}}\approx 1.$ We analyze the new contributions arising through the exchange of the vectorlike families of the ESSM to radiative processes including $\overrightarrow{\tau }\mu \gamma ,$ $\overrightarrow{\mu }e\gamma ,$ $\overrightarrow{b}s\gamma ,$ the EDM of the muon and the muon $\left(g-2\right).$ We show that the ESSM makes significant contributions especially to the decays $\overrightarrow{\tau }\mu \gamma$ and $\overrightarrow{\mu }e\gamma$ and simultaneously to muon $\left(g-2\right).$ For a large and plausible range of relevant parameters, we obtain $a_{\mu }^{\mathrm{ESSM}}\approx +\left(10\mathrm{}-40\right)\times {10}^{-10},$ with a correlated prediction that $\overrightarrow{\tau }\mu \gamma$ should be discovered with an improvement in its current limit by a factor of 3–20. The implications for $\overrightarrow{\mu }e\gamma$ are very similar. The muon EDM is within reach of the next generation experiments. Thus, the ESSM, with heavy leptons being lighter than about 1 TeV (say), can be probed effectively by radiative processes before a direct search for these vectorlike leptons and quarks is feasible at the CERN LHC.