Chiral shifts in heavy-light mesons

Abstract

After the experimental discovery of the Ds(2317) and Ds(2460) mesons [1], a necessity to study the chiral dynamics in heavy-light mesons became quite clear. The masses of these states proved to be much lower than expected values in ordinary quark models while their widths were surprisingly small. The problem was studied in different approaches: in relativistic quark model calculations [2]–[4], on the lattice [5], in QCD Sum Rules [6,7], in chiral models [8,9] (for reviews see also [10,11]). The masses of Ds(0 ) and Ds(1 +′) in closed-channel approximation typically exceed by ∼ 140 and 90 MeV their experimental numbers. The main theoretical goal seems for us to understand dynamical mechanism responsible for such large mass shifts of the 0 and 1 ′ levels and explain why the position of other two levels remains practically unchanged. The importance of second fact has been underlined by S.Godfrey in [3]. The mass shifts of the Ds(0 , 1 ′ ) mesons have already been considered in a number of papers with the use of unitarized coupled-channel model [12], in nonrelativistic Cornell model [13], in semirelativistic model with inverse heavy quark mass expansion [14], and in different chiral models [15]– [17]. Here we address again this problem with the aim to calculate also the mass shifts of the Ds(1 +′) and Bs(0 , 1 ′ ) states and the widths of the 2 and 1 states, following the approach developed in [16], for which strong coupling to the S-wave decay channel, containing a pseudoscalar (P ) Nambu-Goldstone (NG) meson, is crucially important. Therefore in this approach principal difference exists between vector-vector (V V ) and V P (or PP ) channels. This analysis of twochannel system is performed with the use of the chiral quark-pion Lagrangian which has been derived directly from the QCD Lagrangian [18] in the frame of the Field Correlator Method (FCM) and does not contain fitting parameters, so that the shift of the D s(0 ) state ∼ 140 MeV is only determined by the conventional decay constant fK . From the common point of view, due to spinorbit and tensor interactions the P -wave multiplet of a HL meson is split into four levels with J = 0, 1+L , 1 + H , 2 + [19]. Here we use the notation H(L) for the higher (lower) 1 state because a priori one cannot say which of them mostly consists of the light quark j = 1/2 contribution. In fact, starting with the Dirac’s P -wave levels, one has the states with j = 1/2 and j = 3/2. And 1+L,H eigenstates can be parameterized by introducing the mixing angle φ:

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Cite this paper

@inproceedings{Badalian2008ChiralSI, title={Chiral shifts in heavy-light mesons}, author={A . M . Badalian and Yu . A . Simonov and Michael Trusov}, year={2008} }