Spin-orbit splittings in heavy-light mesons and Dirac equation

TL;DR

This paper explains the suppression of spin-orbit splitting in heavy-light mesons using Dirac theory, showing that relativistic effects and symmetries account for the small observed splittings.

Contribution

It provides a qualitative understanding of spin-orbit suppression in mesons through Dirac theory and clarifies that a special dynamical symmetry is not necessary.

Findings

Spin-orbit splitting is suppressed in heavy-light mesons.

Dirac theory with Coulomb-like potential explains small spin-orbit splitting.

Relativistic effects naturally account for the observed suppression.

Abstract

The spin-orbit splitting in heavy-light mesons is seen to be suppressed experimentally. It is shown that it can be understood qualitatively in the frame work of Dirac theory. An alternative derivation of a relativistic dynamical symmetry for the Dirac Hamiltonian, which suppresses spin orbit splitting, is also given. However it is shown that such a symmetry is not needed since the spin-orbit splitting in Dirac theory with Coulomb like potential (as is the case for the one gluon exchange potential in pQCD) is small anyway.