$Z_{cs}(3985)$ in next-to-leading-order chiral effective field theory -- the first truncation uncertainty analysis

Abstract

We revisit the $D_s^-D^{*0}$/$D_s^{*-}D^0$ interaction and the $Z_{cs}(3985)$ state in chiral effective field theory(EFT) up to the next-to-leading order. We examine the relative importance of the leading-order contact, one-eta exchange, next-to-leading-order contact, and two-kaon-exchange contributions. We show that the leading-order and next-to-leading-order contact contributions play the most important role such that the $Z_{cs}(3985)$ state qualifies as a $D_s^-D^{*0}$/$D_s^{*-}D^0$ resonance. On the other hand, the weak one-eta-exchange and weakly energy-dependent two-kaon-exchange contributions are less important in dynamically generating the $Z_{cs}(3985)$ state, indicating that chiral EFT is less predictive in the present situation. Furthermore, we apply the Bayesian method to estimate chiral truncation uncertainties and find that they are of similar magnitude as their statistical counterparts. Our study shows that if $Z_c(3900)$ exists, then SU(3)-flavor symmetry also predicts $Z_{cs}(3985)$ with a certain robustness, i.e., both can be accommodated in the chiral EFT with dominant contact contributions.