Atmospheric neutrinos can make beauty strange

Abstract

The large observed mixing angle in atmospheric neutrinos, coupled with grand unification, motivates the search for large mixing between right-handed strange and bottom squarks. Such mixing does not appear in the standard Cabibbo-Kobayashi-Maskawa phenomenology, but may induce significant $\stackrel{\ensuremath{\rightarrow}}{b}s$ transitions through gluino diagrams. Working in the mass eigenbasis, we show quantitatively that an $O(1)$ effect on CP violation in ${B}_{d}^{0}\ensuremath{\rightarrow}\ensuremath{\varphi}{K}_{S}$ is possible due to a large mixing between ${s}_{R}$ and ${b}_{R},$ while still satisfying constraints from $\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma}.$ We also include the effect of ${b}_{L}\ensuremath{-}{b}_{R}$ mixing proportional to ${m}_{b}\ensuremath{\mu}\mathrm{tan}\ensuremath{\beta}.$ In the case where ${m}_{b}\ensuremath{\mu}\mathrm{tan}\ensuremath{\beta}\ensuremath{\ll}{M}_{\mathrm{SUSY}}^{2}$ there may be a large effect in ${B}_{s}$ mixing correlated with a large effect in ${B}_{d}^{0}\ensuremath{\rightarrow}\ensuremath{\varphi}{K}_{S},$ typically yielding an unambiguous signal of new physics at Tevatron run II.