Chiral and Heavy Quark Symmetry Violation in B Decays

Abstract

The most general Lagrangian consistent with chiral, heavy quark, and strong interaction symmetries to order $1/M$ and to linear order in the SU(3) vector and axial currents is presented. Two new dimensionful and five dimensionless couplings arise at this order. The heavy to light flavor changing current is derived to the same order, giving rise to two additional dimensionful constants and six dimensionless ones. The dimensionless parameters are shown to be irrelevant at \ord. The leading nonanalytic heavy quark and chiral symmetry violating corrections to heavy meson decay constants are computed, and implications to B decays are discussed; measurements of the experimentally accessible form factors for $D \to πl ν$ and $B \to πl ν$, along with knowledge of the $D^* D π$ coupling, determine the eight decay constants $f_D$, $f_{D_s}$, $f_{D^*}$, $f_{D_s^*}$, $f_B$, $ f_{B_s}$, $f_{B^*}$, and $f_{B_s^*}$, as well as one relation among the $B \to πl ν$ form factors, to \ord~. The ratio $R_1 = \frac{f_{B_s}}{f_B}/\frac{f_{D_s}}{f_D}$ is expressed in terms of two dimensionful couplings.