Comprehensive study of spectroscopic properties of $D_{(s)}$ mesons

Abstract

We decode the excited open charm mesons $D$ ($c\bar{q}$, $q=u,d$) and charm strange $D_s$ ($c\bar{s}$) families within a nonrelativistic quark-antiquark potential model based on the Cornell (Coulomb plus linear) potential supplemented by a Gaussian smeared spin-spin interaction. With only seven parameters determined by fitting the ground state masses, the numerically solved Schrödinger equation reproduces the masses of essentially every confirmed $D$ and $D_s$ state to better than $1\%$. The same wave functions are then employed to get a complete decay analysis including pseudoscalar and vector decay constants ($f_D=231.8$~MeV, $f_{D_s}=252.2$~MeV, the latter within $0.4\%$ of the world average), leptonic branching fractions reproducing the measured $\mu \nu$ and $\tau \nu$ modes, electromagnetic $E1$/$M1$ widths, and all kinematically open strong channels in heavy quark effective theory (HQET). Going beyond width ratios, we extract the full set of HQET couplings $g_H$, $g_S$, $g_T$, $g_X$, $g_Y$, $g_Z$, and $g_R$ directly from the measured total widths and convert our predictions into absolute widths. The $D$ and $D_s$ sector extractions of each coupling agree ($g_T=0.42$ vs. $0.39$, $g_X=0.22$ vs. $0.21$, $g_Y=0.39$ vs. $0.40$), a nontrivial test of heavy quark flavor symmetry, while the pure $c\bar{s}$ picture demands a $1^3{P}_0$ width nearly two orders of magnitude above the observed $D_{s0}^{\ast }(2317)$ bound demanding it to be of exotic nature. Linear and parallel Regge trajectories in the $(J,M^2)$ and $(n_r,M^2)$ planes, with slopes $\alpha \simeq 0.55-0.65$~GeV${}^{-2}$ and $\beta \simeq 0.36-0.39$~GeV${}^{-2}$, identify the assignments of $D_J(3000{)}^0$, $D_J^{\ast }(3000{)}^0$, and $D_2^{\ast }(3000{)}^0$ as the $3^1{S}_0$, $3^3{S}_1$, and $3^3{P}_2$ states. Our predictions provide concrete, testable targets for LHCb, BESIII, and Belle~II.