Bs0-B¯s0 mixing and B→πK decays in stringy leptophobic Z′

We consider a leptophobic Z′ scenario in a flipped SU(5) grand unified theory obtained from heterotic string theory. We show that the allowed Z′ mass, flavor conserving and flavor changing couplings of the Z′ to the down-type quarks are strongly constrained by the mass difference in Bs-B¯s system and the four branching ratios of B→πK decays. It is shown that even under these constraints large deviations in direct and/or indirect CP asymmetries of B→πK decays from the SM expectations are allowed. Especially it is possible to accommodate the apparent puzzling data in B→πK CP asymmetries.