Soft-Collinear Chiral Perturbation Theory for $B \to π$ form factors at large recoil
We develop an effective hadronic theory for heavy-meson decays into energetic pions, organized by the approximate heavy-quark and chiral symmetries. The dynamical degrees of freedom of the theory consist of quasi-static heavy-meson fields coupled to soft and collinear pions, relevant for exclusive $B \to π$ transitions at large recoil energy ${E_π\simeq M_B/2}$. Our approach exploits the factorization of soft and collinear quarks in Soft-Collinear Effective Theory (SCET), leading to an emergent duplication of chiral symmetry in the two kinematic sectors. Promoting the soft and collinear chiral transformations to local symmetries enables us to systematically match non-local four-quark operators in SCET -- governing the soft-overlap contribution to heavy-to-light form factors -- onto effective operators constructed from hadronic fields below the scale of chiral symmetry breaking. As a first application, we compute the logarithmically enhanced pion-mass dependence of the $B \to π$ form factors at large recoil by calculating the one-loop matrix elements of the leading hadronic operators. We find that the non-local transition currents in our effective theory lead to a pattern of chiral-logarithmic corrections that is not compatible with the existing formulation provided by Hard-Pion Chiral Perturbation Theory.