Radiative decay of heavy-light mesons from lattice QCD

TL;DR

This work delivers the first systematic lattice-QCD determination of the radiative decay couplings for charmed mesons, using 2+1-flavor clover ensembles including a physical-pion-mass point and a fine lattice spacing. The authors extract the effective form factor $V_{\mathrm{eff}}(Q^2)$ from three-point and two-point correlators, perform joint fits to control excited-state contamination, and implement a $z$-expansion to extrapolate to $Q^2=0$. They then carry out combined chiral and continuum extrapolations, including $O(a)$-improvement for the neutral case, to obtain final couplings $g_{D^{\ast+}D^+\gamma}$, $g_{D^{\ast0}D^0\gamma}$, and $g_{D_s^{\ast+}D_s^+\gamma}$ with quantified uncertainties, and translate these into radiative widths. The results provide first-principles predictions for heavy-light meson radiative transitions, inform SU(3) flavor-breaking patterns, and highlight tensions with some experimental measurements, guiding future experimental and theoretical studies.

Abstract

We present the first systematic study of the radiative decays of charmed mesons using $2+1$-flavor clover fermion gauge ensembles generated by the CLQCD collaboration. One of the ensembles is at the physical pion mass, and one has a fine lattice spacing $a\sim 0.05 ~\text{fm}$. We determine the coupling constants to be $g_{D^{\ast+} D^+ γ} = -0.205(35)$ GeV$^{-1}$, $g_{D^{\ast0} D^0 γ} = 2.20(27)$ GeV$^{-1}$, and $g_{D_s^{\ast+} D_s^+ γ} = -0.125(21)$ GeV$^{-1}$, respectively. Compared with previous studies, our results demonstrate significant improvements in precision. In particular, we carefully estimate the systematic uncertainty arising from matrix element fits, momentum transfer extrapolations, and chiral and continuum limit extrapolations, which are included in the reported total uncertainties. These couplings yield the following predictions of decay widths: $Γ_{D^{\ast+} \rightarrow D^+ γ} = 0.255(87)$ keV, $Γ_{D^{\ast0} \rightarrow D^0 γ} = 29.4(7.2)$ keV, and $Γ_{D_s^{\ast+}\rightarrow D_s^+ γ} = 0.102(34)$ keV. This work establishes first-principles results of the charmed meson radiative transitions and provides inputs for understanding the structure and properties of heavy-light mesons.

Figures (10)

• Figure 1: The data points represent the effective energy extracted from two-point function on the F32P21 ensemble using Eq. (\ref{['corr']}), and the bands correspond to the fitted result using Eq. (\ref{['single']}). The $n^2$ in the legend labels the discrete momenta $p^2 = n^2\left({2\pi}/{L}\right)^2$. The dashed vertical line indicates the starting point of the fits.
• Figure 2: Dispersion relation results for the $D$ meson on the F32P21 ensemble. The data points are obtained under the fitting scheme as shown in Fig. \ref{['fig1']}. After converting the lattice momentum $ap$ to $2\sin(ap/2)$ and the lattice energy $aE$ to $2\sinh(aE/2)$, the slope in the plot, which corresponds to $c^2$, is consistent with one within 2 sigmas.
• Figure 3: Results for $V_{\text{eff}}^{D^{\ast+}D^+\gamma}$, $V_{\text{eff}}^{D^{\ast0}D^0\gamma}$ at $\left(Qa\right)^2=0.0682$ and $V_{\text{eff}}^{D_s^{\ast +}D^+_s\gamma}$ at $\left(Qa\right)^2=0.0685$ on the F32P21 ensemble. The blue bands represent the matrix elements obtained from the fits, while the data points depict the values after subtracting the excited-state contributions from original three-point function data points.
• Figure 4: The upper panel illustrates the distribution of $D^r_{\rm range}$ for the $D^{\ast 0}$ meson case, which accounts for the systematic uncertainty for the choice of fit ranges, while the lower panel shows the distribution of $D^r_{\rm method}$, which accounts for the systematic uncertainty for the choice of fitting methods. Both results are from the ensemble F32P21. See the main text for detailed discussion.
• Figure 5: Comparison of the two different fitting methods on the F32P21 ensemble for $V_{\text{eff}}^{D^{\ast0}D^0\gamma}$ with different momentum transfers. The blue band and data points represent the results from the two-state fit method, while the green ones are from the joint fit method.