Approximate degeneracy of heavy-light mesons with the same L

Abstract

Careful observation of the experimental spectra of heavy-light mesons tells us that heavy-light mesons with the same angular momentum L are almost degenerate. The estimate is given how much this degeneracy is broken in our relativistic potential model, and it is analytically shown that expectation values of a commutator between the lowest order Hamiltonian and L→2 are of the order of 1/mQ with a heavy quark mass mQ. It turns out that nonrelativistic approximation of heavy quark system has a rotational symmetry and hence degeneracy among states with the same L. This feature can be tested by measuring higher orbitally and radially excited heavy-light meson spectra for D/Ds/B/Bs in LHCb and forthcoming BelleII.