Open charm and beauty chiral multiplets in QCD

Abstract

We study the dynamics of the open charm and beauty mesons using QCD spectral sum rules (QSSR), where we observe the important rôle of the chiral condensate 〈ψ¯ψ〉 in the mass-splittings between the scalar–pseudoscalar mesons. Fixing the sum rule parameters for reproducing the well known D(0−) and Ds(0−) masses, we re-obtain the running charm quark mass: m¯c(mc)=1.13−0.04+0.08 GeV, which confirms our recent estimate from this channel [Phys. Lett. B 520 (2001) 115]. Therefore, using sum rules with no-free parameters, we deduce MDs(0+)≃(2297±113) MeV, which is consistent with the observed Ds(2317) meson, while a small SU(3) breaking of about 25 MeV for the Ds(0+)−D(0+) mass-difference has been obtained. We extend our analysis to the B-system and find MB(0+)−MB(0−)≃(422±196) MeV confirming our old result from moment sum rules [Phys. Lett. B 210 (1988) 238]. Assuming an approximate (heavy and light) flavour and spin symmetries of the mass-splittings as indicated by our results, we also deduce MDs*(1+)≃(2440±113) MeV in agreement with the observed DsJ(2457). We also get: fD(0+)≃(217±25) MeV much bigger than fπ=130.6 MeV, while the size of the SU(3) breaking ratio fDs(0+)/fD(0+)≃0.93±0.02 is opposite to the one of the 0− channel of about 1.14.