$B_s$ Mixing and New Physics in hadronic $b \to s \bar{q} q$ transitions

Abstract

We study the implication of the recent $\Delta m_s$ measurement on $ b \to s \bar{q} q$ transitions. We show that it is possible, in the presence of a flavour symmetry, that the phase in $B_s$ mixing may be unobservable even with new CP odd phases in $b \to s$ transitions. These phases may then produce new CP odd effects in certain $b \to s \bar{q} q $ transitions like $ B \to K \pi$ but not in others like $ B_d \to \phi K_s$. Working in a two higgs doublet model of new physics we discuss the allowed NP contribution to $B \to K \pi$ and $ B_d \to \phi K_s$ decays with the new $ Delta m_s$ measurement.