Strong decays and effective spin-symmetry-breaking corrections in excited charm-strange mesons

Abstract

We study two-body pseudoscalar-emission decays of excited charm-strange mesons in heavy meson effective field theory, where phenomenological \(1/m_c\) corrections are encoded as effective relative shifts between \(DP\) and \(D^*P\) amplitudes, referred to here as effective spin-symmetry-breaking corrections. Using \(D_{s2}^*(2573)\) data to calibrate the \(T(3/2^+)\) doublet, we obtain \(h'=0.407\pm0.034\) and \(\epsilon_T=-0.207\pm0.109\), indicating a natural effective correction of order \(20\%\). Applying this input to the \(D_{s1}(2460)\) and \(D_{s1}(2536)\) system, the Belle and LHCb partial-wave data constrain the mixing angle to \(0^\circ<\theta_P\lesssim22.0^\circ\) and \(0^\circ<\theta_P\lesssim14.6^\circ\), respectively, confirming that \(D_{s1}(2536)\) is dominantly a \(T(3/2^+)\) state with only a small \(S(1/2^+)\) admixture. In the radial sector, the pure-\(2S\) assignment gives \(R_{2700}^{\rm LO}=0.919\), consistent with the observed \(D^{*0}K^+/D^0K^+\) ratio of \(D_{s1}^*(2700)\), but predicts only \(\Gamma_{\rm ps}[D_{s0}(2590)]\simeq20\) MeV. Allowing mixing between \(D_{s1}^*(2700)\) and \(D_{s1}^*(2860)\), together with a relative strong phase and effective spin-symmetry-breaking corrections, substantially increases this width while preserving agreement with the vector-state widths and \(R_{2700}\). This scenario further gives \(R_{1,2860}=0.911\), far from the pure-\(X\) leading-order value \(R_{1,2860}^{\rm pure\,X}=0.242\), so the spin-one \(D^*K/DK\) ratio near \(2.86\) GeV offers a clear discriminator between the mixed and unmixed assignments. Overall, this scenario reduces but does not remove the \(D_{s0}(2590)\) width tension, leaving room for non-pseudoscalar channels, threshold effects, or coupled-channel dynamics. Reference decay patterns for \(D_{s3}^*(2860)\), \(D_{s1}(2933)\), and \(D_{sJ}(3040)\) are also given.