Impact of a light strange-beauty squark onBsmixing and direct search

If one has Abelian flavor symmetry, $s_R-b_R$ mixing could be near maximal. This can drive a “strange-beauty” squark $\left({\widetilde{\mathrm{sb}}}_1\right)$ to be rather light, but still evade the $b\to s\gamma$ constraint. Low-energy constraints imply that all other superpartners are at TeV scale, except for a possibly light neutralino, ${\tilde{\chi }}_1^0.$ Whether light or heavy, the ${\widetilde{\mathrm{sb}}}_1$ can impact on the $B_s$ system: $\Delta m_{B_s}$ and the indirect $\mathrm{CP}$ phase, even for $B_s\to \phi \gamma .$ A direct search is similar to the usual $\tilde{b}\to b{\tilde{\chi }}_1^0,$ but existing bounds are weakened by the ${\widetilde{\mathrm{sb}}}_1\to s{\tilde{\chi }}_1^0$ possibility. All of these effects could be studied soon at the Fermilab of Tevatron.