CP asymmetry in the decays B→(X_s,X_d)μ⁺μ⁻ with four generations

Abstract

We estimate the CP asymmetry A_CP(q²) in the decays B→X_sμ⁺μ⁻ and B→X_dμ⁺μ⁻ in the standard model (SM) with an additional fourth generation. We use a parametrization that allows us to explore the complete parameter space of the 4×4 quark mixing matrix, and constrain these parameters from the current data on B decays. We find that the enhancement in A_CP (q²) depends strongly on the mass of the t′, the up-type quark in the fourth generation. For m_t′ around 400 GeV, the CP asymmetry in the high- q² region (q²>14.4  GeV²) can be enhanced by more than an order of magnitude for B→X_sμ⁺μ⁻ and up to a factor of 6 for B→X_dμ⁺μ⁻. There is no enhancement in the low- q² region (1<q²<6  GeV²). With increasing m_t′, A_CP(q²) in the high- q² (low- q²) region first decreases (increases) and then saturates at a value a few times the SM prediction. In the high- q² region of B→X_sμ⁺μ⁻, this saturation value may be up to 25 times the SM expectation.