Finite mass corrections forB→(D¯(*),D¯**)ℓνdecays in the Bakamjian-Thomas relativistic quark model

Abstract

The Bakamjian-Thomas relativistic quark model for hadron current matrix elements, while noncovariant at finite mass, is successful in the heavy quark limit: form factors are covariant and satisfy Isgur-Wise scaling and Bjorken-Uraltsev sum rules. Motivated by the so-called ``$1/2$ vs $3/2$ puzzle'' in $\overline{B}$ decays to positive parity ${D}^{**}$, we examine the implications of the model at finite mass. In the elastic case ${\frac{1}{2}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\frac{1}{2}}^{\ensuremath{-}}$, the heavy quark effective theory (HQET) constraints for the $O(1/{m}_{Q})$ corrections are analytically fulfilled. A number of satisfying regularities is also found for inelastic transitions. We compute the form factors using the wave functions given by the Godfrey-Isgur potential. We find a strong enhancement in the case ${\frac{1}{2}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\frac{1}{2}}^{+}$ for ${0}^{\ensuremath{-}}\ensuremath{\rightarrow}{0}^{+}$. This enhancement is linked to a serious difficulty of the model at finite mass for the inelastic transitions, namely a violation of the HQET constraints at zero recoil formulated by Leibovich et al. These are nevertheless satisfied in the nonrelativistic limit for the light quark. We conclude that these HQET rigorous constraints are crucial in the construction of a sensible relativistic quark model of inelastic form factors.