Abstract
We perform an analysis of QCD lattice data on charmed meson masses. The quark-mass dependence of the data set is used to gain information on the size of counter terms of the chiral Lagrangian formulated with open-charm states with J^P= 0^- and J^P =1^- quantum numbers. Of particular interest are those counter terms that are active in the exotic flavour sextet channel. A chiral expansion scheme where physical masses enter the extrapolation formulae is developed and applied to the lattice data set. Good convergence properties are demonstrated and an accurate reproduction of the lattice data based on ensembles of PACS-CS, MILC, ETMC and HSC with pion and kaon masses smaller than 600 MeV is achieved. It is argued that a unique set of low-energy parameters is obtainable only if additional information from HSC on some scattering observables is included in our global fits. The elastic and inelastic s-wave pi D and eta D scattering as considered by HSC is reproduced faithfully. Based on such low-energy parameters we predict 15 phase shifts and in-elasticities at physical quark masses but also for an additional HSC ensemble at smaller pion mass. In addition we find a clear signal for a member of the exotic flavour sextet states in the eta D channel, below the bar K D_s threshold. For the isospin violating strong decay width of the D_{s0}(2317) we obtain the range (104-116) keV.
Highlights
Systems with one heavy and one light quark play a important role in the spectroscopy of QCD [1,2,3,4]
Either one may construct an effective chiral Lagrangian formulated in terms of heavy-quark multiplet fields [1,2,5] or one may start with an effective chiral Lagrangian with fully relativistic fields, wherein the low-energy constants are correlated by constraints from the heavy-quark spin symmetry [6,7]
We would argue that a precise determination of aΔc and therewith the physical charm-quark mass for a given ensemble requires the quantitative control of the chiral extrapolation formulas for the D-meson masses
Summary
Systems with one heavy and one light quark play a important role in the spectroscopy of QCD [1,2,3,4]. We follow a different path and try to use the recent data set on the quark-mass dependence of the D-meson ground-state masses [17,18,19,20,21,22,23] This dynamics is driven in part by the counterterms that have a significant impact on the open-charm coupled-channel systems as discussed above. The authors presented a novel chiral extrapolation scheme for the quark-mass dependence of the baryon octet and decuplet states that is formulated in terms of physical masses [32,33,34,35] It is the purpose of our study to adapt this scheme to the open-charm sector of QCD and apply it to the available lattice data set.
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