New CP phase of $B_s-{\bar{B}}_s$ mixing on $\mathrm{T}$ violation in $B_{d(s)}\to K^{\ast }(\varphi ){\ell }^{+}{\ell }^{-}$

Abstract

A large CP-violating phase uncovered recently by CDF and D$Ø$ collaborations in the time-dependent CP asymmetry (CPA) of the $B_s\to J/\Psi \varphi$ decay clearly indicates that a non-Cabibbo-Kobayashi-Maskawa (CKM) phase has to be brought into the $b\to s$ transition. We find that the model with $SU(2{)}_L$ singlet exotic quarks can not only provide the new phase induced from the Z-mediated flavor changing neutral current (FCNC) at tree level, but also strongly relate the $B_s-{\bar{B}}_s$ mixing, $B_q\to V_q{\ell }^{+}{\ell }^{-}$ ($V_{d[s]}=K^{\ast }[\varphi ])$ and $B_s\to {\mu }^{+}{\mu }^{-}$ together. In particular, we show that the new CP phase can be unambiguously exposed by the large statistical significances of $T$ violating observables in $B_q\to V_q{\ell }^{+}{\ell }^{-}$, while the branching ratio of $B_s\to {\mu }^{+}{\mu }^{-}$ can be enhanced to be $O(10^{-8})$.

10 pages, 2 figures, version revised, references added, version to appear in Physics Letters B

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