The effects of a family non-universal Z′Z′ boson in the B¯s→πK, πK⁎πK⁎, ρK decays and BdBd–B¯d mixing

We revisit B¯s→πK, πK⁎πK⁎ and ρK   decays within QCDF formalism and examine the possible effects of a family non-universal Z′Z′ boson in these decays. In our evaluations, the strong constraints from BdBd–B¯d mixing on the strength of the left-handed flavor-changing d–b  –Z′Z′ coupling BdbL (∼0.2×10−3∼0.2×10−3) is also included. Numerically, we find that a new weak phase ϕdL∼−50° involved in BdbL, the negative combination of the u–u  –Z′Z′ and d–d  –Z′Z′ couplings PudR and/or DudL with larger absolute value are crucial to improve the agreement of B(B¯s→π−K+) between the SM prediction and the experimental measurement. Generally, B(B¯s→π−K+) could be reduced by about 18% at most by Z′Z′ contributions. Moreover, combining with the recent updated measurement on βsβs by CDF and D0 Collaborations, we also find that Z′Z′ effects in B¯s→π−K+ decays are very important for examining whether the CKM-like hierarchy persists in a family non-universal Z′Z′ coupling matrix.