Chiral $1/M^2$ corrections to $B^{(*)}\rightarrow D^{(*)}$ at Zero-Recoil in Quenched Chiral Perturbation Theory

D. Arndt (graduate Student)

Knowledge of the $B^{(*)}\rightarrow D^{(*)}$ form factors at the zero-recoil point is crucial to extract the element of the Cabbibo-Kobayashi-Maskawa matrix that parameterizes the amount of mixing between the b and c quarks, $V_{cb}$, from experiment. In the limit that the heavy quarks are infinitely heavy, heavy quark effective theory (HQET) predicts that the form factors $h_+$, $h_{A_1}$, and $h_1$ are equal. The formally dominant correction due to breaking of heavy quark symmetry comes from the inclusion of a $\sim 1/M$ dimension-three operator in the Lagrangian that leads to hyperfine-splitting between the heavy pseudoscalar and vector mesons. These leading order corrections are $\sim 1/m_c^2, 1/m_b^2$ as required by Luke's theorem. Recent lattice simulations using the quenched approximation of QCD have made a big step forward in determining these zero-recoil form factors. Presently, however, the simulations use light quark masses that are much heavier than the physical ones and therefore rely on a chiral extrapolation down to the physical quark masses.

In this work we calculate the dominant corrections to the form factors $h_+$, $h_{A_1}$, and $h_1$ in quenched chiral perturbation theory (Q$\chi$PT) and determine the non-analytic dependence on the light quark masses. Using these results to extrapolate the quenched QCD lattice measurements of these form factors down to the physical pion mass should give a more reliable estimate of the errors associated with the chiral extrapolation.