Measuring |V_{td} / V_{ub}| through B -> M \nu \bar\nu (M=\pi,K,\rho,K^*) decays

Abstract

We propose a new method for precise determination of |V_{td} / V_{ub}| from the ratios of branching ratios BR(B -> \rho \nu \bar \nu ) / BR(B ->\rho l \nu ) and BR(B -> \pi \nu \bar \nu ) / BR(B -> \pi l \nu ). 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 \gamma) / (\sin \beta) 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 d\Gamma(B -> K^* \nu \bar \nu ) / dq^2 and the ratio of the differential rates dBR(B -> \rho \nu \bar \nu )/dq^2 / dBR(B -> K^* \nu \bar \nu )/dq^2 as well as BR(B -> \rho \nu \bar \nu ) / BR(B -> K^* \nu \bar \nu) and BR(B -> \pi \nu \bar \nu ) / BR(B -> K \nu \bar \nu).