Low-energy constants of heavy meson effective theory in lattice QCD

We consider effective theory treatment for the lowest-lying $S$- and $P$-wave states of charmed mesons. In our analysis, quantum corrections and contributions from leading chiral and heavy quark symmetry breakings are taken into account. The heavy meson mass expressions have abundance parameters, low-energy constants, in comparison to the measured charmed mesons masses. The experimental and lattice QCD data on charmed meson spectroscopy are used to extract, for the first time, the numerical values of the full set of low-energy constants of the effective chiral Lagrangian. Our results on these parameters can be used for applications on other properties of heavy-light meson systems.

Figure 1

The representation of the masses of the charmed meson states of ${\frac{1}{2}}^{-}$ and ${\frac{1}{2}}^{+}$ doublets. All masses are taken from the PDG [12] excluding the mass of $D_1^{\prime }$, which is reported by the BELLE Collaboration [13]. We only take the isospin average of $D^0$ and $D^{\pm }$ ($D^{*0}$ and $D^{*\pm }$) to obtain the mass of nonstrange ground state $D$ ($D^{*}$); for details, please refer to the text.

Figure 2

Extracted numerical values for the combinations (a) ${\eta }_H$, (b) ${\xi }_H$, (c) ${\eta }_S$, and (d) ${\xi }_S$ are plotted against the corresponding pion masses. Different symbols are given to the experiment and two lattice ensembles according to the key in the ${\xi }_S$ plot.