GUT relation in Neutrino-Induced Flavor Physics in SUSY SU(5) GUT

In the SUSY SU(5) GUT with the right-handed neutrinos, the neutrino Yukawa coupling induces the flavor-violating mass terms for the right-handed down squarks and left-handed sleptons, and they lead to imprint on the flavor physics in the hadronic and leptonic sectors. In this paper we study CP violation in $B_d^0$ and $B_s^0$, which is induced by the tau-neutrino Yukawa coupling. In particular, we notice the correlation of the CP asymmetries in $B_d^0\to \varphi K_s$ ($S_{\varphi K_s}$) and $B_s^0\to J\mathrm{/}\psi \varphi$ ($S_{J/\psi \phi}$)withotherobservables,suchas$Br(\tau\to\mu\gamma)$, the muon EDM ($d_{\mu }$), and the mixing-induced CP asymmetry in $B_d^0\to M_s^0\gamma$ ($A_{bsg}$), since they have a common origin of the CP and flavor violation. The measurements are expected to play a significant role for consistency check of the SUSY SU(5) GUT. The hierarchical right-handed neutrino masses make the correlation better. We find that the current bound on $Br(\tau \to \mu \gamma )$ constrains the allowed region for $S_{\varphi K_s}$ in this model.