Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit: Covariant Quark Model Approach

TL;DR

This paper demonstrates that a covariant quark model approach accurately describes heavy-to-light form factors in the large energy limit, aligning with QCD predictions and revealing only three independent form factors.

Contribution

It proves the covariance and scaling laws of heavy-to-light form factors within a Bakamjian-Thomas quark model in the relevant limits, confirming its consistency with QCD.

Findings

Form factors satisfy the sqrt(M)z(E) scaling law.

Only three independent form factors describe B -> pi(rho) transitions.

The model maintains covariance and aligns with QCD relations.

Abstract

We prove the full covariance of the heavy-to-light weak current matrix elements based on the Bakamjian-Thomas construction of relativistic quark models, in the heavy mass limit for the parent hadron and the large energy limit for the daughter one. Moreover, this quark model representation of the heavy-to-light form factors fulfills the general relations that were recently argued to hold in the corresponding limit of QCD, namely that there are only three independent form factors describing the B -> pi (rho) matrix elements, as well as the factorized scaling law sqrt(M)z(E) of the form factors with respect to the heavy mass M and large energy E. These results constitute another good property of the quark models \`a la Bakamjian-Thomas, which were previously shown to exhibit covariance and Isgur-Wise scaling in the heavy-to-heavy case.