What can we learn from the radiative decays of the $D_{s1}(2460)$ meson?

TL;DR

This work proposes radiative decays of $D_{s1}(2460)$ as a probe of the nature of $D_{s0}^*(2317)$ and $D_{s1}(2460)$, focusing on the two-body channel $D_{s1}\to \gamma D^{*}_{s0}$ and the three-body channels $D_{s1}\to \gamma D^0K^+$ and $\gamma D^+K^0$. The authors decompose the decay amplitude into a loop piece $\kappa_{\rm loop}(q^2)$ and a short-range contact term $\kappa_{\rm cont}$, compute $\kappa_{\rm loop}$ in unitarised chiral perturbation theory (finding $\kappa_{\rm loop}(m^2_{D^{*}_{s0}})=0.190\pm0.004$), and determine the short-range parameter $\alpha_{\rm cont}$ by fitting radiative-decay ratios to data. They then calculate the three-body radiative widths, which depend on $\kappa_{\rm cont}$ through the $D_{s1}\to \gamma D^{*}_{s0}$ vertex, and show that the ratio ${\mathcal R}$ of the two- to three-body widths is highly sensitive to $\kappa_{\rm cont}$, enabling experimental constraints to discriminate between molecular and compact pictures. The results indicate that a measured ${\mathcal R}$ could pin down the short-range dynamics and thus clarify the nature of the $D^{*}_{s0}(2317)$ and $D_{s1}(2460)$, with potential implications for related heavy-mhadron processes and heavy-quark symmetry predictions.

Abstract

We study the radiative decays $D_{s1}(2460)\toγD^{*}_{s0}(2317)$ and $D_{s1}(2460)\to γD^0K^+/γD^+K^0$ and argue that their simultaneous experimental measurement, or at least a constraint on the ratio of the corresponding branching fractions, can allow one to probe the nature of the $D^{*}_{s0}(2317)$ and $D_{s1}(2460)$ mesons.

Figures (7)

• Figure 1: The loop and contact contributions to the decay amplitude $D_{s1}(2460)\to \gamma D^*_{s0}(2317)$.
• Figure 2: Momentum dependence of the effective loop coupling $\kappa_{\rm{loop}}(q^2)$ in Eq. \ref{['kappaloop']}. For presentation purposes, here the loop integration in Eq. \ref{['J0int']} (see also Appendix \ref{['app:J']}) is performed for the masses of $D^{(*)+}$ and $K^0$. The vertical dash-dotted line shows the position of $q^2=m_{D^*_{s0}}^2$ relevant for the two-body decay $D_{s1}(2460)\to\gamma D^*_{s0}(2317)$ (see Eqs. \ref{['kappadef']} and \ref{['kappaon']}). The gray shaded region shows the range of the phase space integration in $p_{12}^2=q^2$ in the three-body decay $D_{s1}(2460)\to\gamma D^0K^+$, $(m_{D^{0}}+m_{K^{+}})^2\leqslant q^2\leqslant m_{D_{s1}}^2$ (see Eq. \ref{['WidthDs1DKgamma']}). The plot for the decay $D_{s1}(2460)\to\gamma D^+K^0$ looks similar and is not shown. Note also that in the actual calculations performed in this work the spin-average masses in Eq. \ref{['masses1']} are used.
• Figure 3: Contributions to the decay amplitude $D_{s1}\to \gamma DK$ as given in Eq. \ref{['chains']}. The structure of the vertex $D_{s1}\to \gamma D^*_{s0}$ in diagram (b) is shown in Fig. \ref{['fig:Ds1Ds0gamma']}. Details concerning the vertex $D_{s1}\to \gamma D_{s}^*$ in diagram (c) can be found in Refs. Cleven:2013rkfCleven:2014okaFu:2021wde.
• Figure 4: Width of the radiative decay $D_{s1}(2460)\to\gamma D^*_{s0}(2317)$ in Eq. \ref{['widthkappa']} for the strength of the contact interaction $\kappa_{\rm cont}$ in Eq. \ref{['Lagcont']} varied in a natural range $[-0.4,0.4]$.
• Figure 5: $DK$ invariant mass distributions for the three-body radiative decay $D_{s1}(2460)\to \gamma D^+K^0$ (left) and $D_{s1}(2460)\to \gamma D^0K^+$ (right) obtained from Eq. \ref{['WidthDs1DKgamma']} upon partial integration over the phase space of the final state. In both plots, the red curve corresponds to $\kappa_{\rm cont}=0.2$ as suggested by Eq. \ref{['kappacont']} and the red band around it comes from the uncertainty in the determination of the contact parameter $\alpha_{\rm cont}$ as given in Eq. \ref{['alphanum']}; in both cases we use three times the corresponding standard deviation for the uncertainty of $\alpha_{\rm cont}$ to increase its visibility. The gray bands correspond to $\alpha_{\rm cont}$ fixed to its central value in Eq. \ref{['alphanum']} and $\kappa_{\rm cont}$ varied in the range $[-0.4,0.4]$.