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We present an approach for computing the real parts of the nonleptonic B toDP and B to D-bar P (P=K,pi) decay amplitudes by using lattice QCD methods.While it remains very challenging to calculate the imaginary parts of thesematrix elements on the lattice, we stress that their real parts play asignificant role in extracting the angle gamma in the b-d unitarity triangle ofthe CKM matrix. The real part on its own gives a lower bound to the absolutemagnitude of the amplitude which is in itself an important constraint fordetermining gamma. Also the relevant phase can be obtained by using B-decays inconjunction with relevant charm decay data. Direct four-point functioncalculations on the lattice, while computationally demanding, does yield thereal part as that is not impeded by the Maiani-Testa theorem. As anapproximation, we argue that the chiral expansion of these decays is valid in aframework similar to that of hard-pion chiral perturbation theory. In additionto constructing the leading-order operators, we also discuss the features ofthe next-to-leading order chiral expansion. These include the contributionsfrom the resonance states, as well as the generic forms of the chirallogarithms.

Possible lattice approach to B to D pi (K) matrix elements