Finite mass corrections for B -> D(*), D** \ell \nu decays in the Bakamjian-Thomas relativistic quark model

TL;DR

This paper evaluates the Bakamjian-Thomas relativistic quark model's finite mass corrections for B to D(*) and D** semileptonic decays, highlighting its successes and limitations in satisfying HQET constraints.

Contribution

It demonstrates the model's compliance with HQET constraints at finite mass for elastic transitions and explores the challenges in inelastic transitions, emphasizing the importance of HQET constraints.

Findings

Model satisfies HQET constraints in elastic transitions.

Small deviations from heavy quark limit in inelastic form factors.

Finite mass effects cause violations of HQET constraints in some inelastic cases.

Abstract

The Bakamjian-Thomas relativistic quark model for hadron current matrix elements, while non-covariant 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 B decays to positive parity D**, we examine the implications of the model at finite mass. In the elastic case 1/2^- -> 1/2^-, the 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. For 1/2^- \to 3/2^+ the departures from the heavy quark limit are small, but we find a strong enhancement in 1/2^- -> 1/2^+ (for 0^- -> 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 non-relativistic 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.