Abstract
The heavy-light mesons are studied within the framework of Dyson-Schwinger equations of QCD. Inspired by the axial-vector Ward-Takahashi identity resulting from the chiral symmetry, we propose a truncation scheme beyond the ladder approximation without introducing any additional parameters. For the pseudoscalar and vector heavy-light mesons, the obtained mass spectrum has the level of relative errors at 5% compared with experimental data and lattice-QCD results. For the leptonic decay constants, our results are comparable with those from experiments and/or lattice QCD. For some channels, the discrepancies are sizable but significantly smaller than those using the equal spacing rule. The truncation scheme proposed in this work is simple and could be improved and applied to study other open flavor hadrons including both mesons and baryons.
Highlights
In recent decades, many heavy-light mesons are observed in experiments [1], which has attracted a lot of interest
Inspired by the axial-vector Ward-Takahashi identity resulting from the chiral symmetry, we propose a truncation scheme beyond the ladder approximation without introducing any additional parameters
With the parameters fixed in previous subsections, we can directly compute the properties of heavy-light mesons since the kernel beyond the ladder approximation, i.e., Eq (28), does not introduce any new parameters
Summary
Many heavy-light mesons are observed in experiments [1], which has attracted a lot of interest. The study of heavy-light mesons provides a way to understand dynamical chiral symmetry breaking (DCSB) [2,3,4]–one of the most fascinating features of the quantum chromodynamics (QCD). Since the interaction model absorbs the dressed effects of the quark-gluon interaction vertex and the gluon propagator, for light quark systems, it has much larger strength compared with that of the realistic gauge-sector interaction at infrared momenta [49] and the one determined by solving the coupled equations of the quark propagator and the quark-gluon interaction vertex [56]. It is expected that the RL truncation provides a reasonable approximation for the systems involving only heavy quarks so long as one employs a smaller strength
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