Electroweak form factors of heavy-light mesons -- a relativistic point-form approach

TL;DR

This paper develops a relativistic point-form framework within constituent-quark models to calculate electroweak form factors of heavy-light mesons, confirming heavy-quark symmetry and providing analytical and numerical results.

Contribution

It introduces a Poincaré invariant approach using point-form relativistic quantum mechanics for heavy-light mesons, addressing cluster separability issues and deriving the Isgur-Wise function.

Findings

Heavy-quark symmetry is confirmed in the heavy-quark limit.

An analytical expression for the Isgur-Wise function is provided.

Electromagnetic and weak form factors are calculated with harmonic-oscillator wave functions.

Abstract

We present a general relativistic framework for the calculation of the electroweak structure of heavy-light mesons within constituent-quark models. To this aim the physical processes in which the structure is measured, i.e. electron-meson scattering and semileptonic weak decays, are treated in a Poincar\'e invariant way by making use of the point-form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the 1-$\gamma$ and 1-$W$-exchange amplitudes that result from a Bakamjian-Thomas type mass operator for the respective systems. The covariant decomposition of these currents provides the electromagnetic and weak (transition) form factors. Problems with cluster separability, which are inherent in the Bakamjian-Thomas construction, are discussed and it is shown how to keep them under control. It is proved that the heavy-quark limit of the electroweak form factors leads to one universal function, the Isgur-Wise function, confirming that the requirements of heavy-quark symmetry are satisfied. A simple analytical expression is given for the Isgur-Wise function and its agreement with a corresponding front-form calculation is verified numerically. Electromagnetic form factors for $B^-$ and $D^+$ and weak $B\rightarrow D^{(\ast)}$-decay form factors are calculated with a simple harmonic-oscilllator wave function and heavy-quark symmetry breaking due to finite masses of the heavy quarks is discussed.