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

TL;DR

This paper proposes a lattice QCD approach to compute the real parts of B to D pi(K) decay amplitudes, which are crucial for constraining the CKM angle gamma, by focusing on direct four-point functions and chiral expansion techniques.

Contribution

It introduces a novel lattice QCD method to calculate the real parts of nonleptonic B decay matrix elements, emphasizing their importance in CKM parameter extraction.

Findings

Real parts can be computed via lattice four-point functions.

Chiral expansion provides a valid approximation framework.

Discussion of next-to-leading order chiral effects.

Abstract

We present an approach for computing the real parts of the nonleptonic B to DP 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 these matrix elements on the lattice, we stress that their real parts play a significant role in extracting the angle gamma in the b-d unitarity triangle of the CKM matrix. The real part on its own gives a lower bound to the absolute magnitude of the amplitude which is in itself an important constraint for determining gamma. Also the relevant phase can be obtained by using B-decays in conjunction with relevant charm decay data. Direct four-point function calculations on the lattice, while computationally demanding, does yield the real part as that is not impeded by the Maiani-Testa theorem. As an approximation, we argue that the chiral expansion of these decays is valid in a framework similar to that of hard-pion chiral perturbation theory. In addition to constructing the leading-order operators, we also discuss the features of the next-to-leading order chiral expansion. These include the contributions from the resonance states, as well as the generic forms of the chiral logarithms.