Measuring |V_td/V_ub| (=sin γ/sin β within the SM) through B→Mνν̄ (M=π,K,ρ,K*) decays

We propose a new method for the precise determination of |V_td/V_ub| from the ratios of branching ratios B(B→ρνν̄)/B(B→ρlν) and B(B→πνν̄)/B(B→πlν). 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 (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*νν̄)/dq² and the ratio of the differential rates dB(B→ρνν̄)/dq²/ dB(B→K*νν̄)/dq² as well as B(B→ρνν̄)/B(B→K*νν̄) and B(B→πνν̄)/B(B→Kνν̄).