Measuring |V_{td} / V_{ub}| through B -> M ν\barν(M=π,K,ρ,K^*) decays

Abstract

We propose a new method for precise determination of |V_{td} / V_{ub}| from the ratios of branching ratios BR(B -> ρν\bar ν) / BR(B ->ρl ν) and BR(B -> πν\bar ν) / BR(B -> πl ν). These ratios depend only on the ratio of the Cabibbo-Kobayashi-Maskawa (CKM) elements |V_{td} / V_{ub}|$ with little theoretical uncertainty, when very small isospin breaking effects are neglected. As is well known, |V_{td} / V_{ub}| equals to (\sin γ) / (\sin β) for the CKM version of CP-violation within the Standard Model. We also give in detail analytical and numerical results on the differential decay width dΓ(B -> K^* ν\bar ν) / dq^2 and the ratio of the differential rates dBR(B -> ρν\bar ν)/dq^2 / dBR(B -> K^* ν\bar ν)/dq^2 as well as BR(B -> ρν\bar ν) / BR(B -> K^* ν\bar ν) and BR(B -> πν\bar ν) / BR(B -> K ν\bar ν).