The $D_{s1}(2460)$ and other open-charm $1^+$ states in relativistic chiral effective field theory

Abstract

We derive the pertinent chiral potentials for charmed vector meson interactions with light pseudoscalar bosons in a relativistic U(3) chiral effective field theory up to next-to-leading order. Predictions for the $S$- and $P$-wave scattering lengths are obtained for all the relevant elastic channels. A comparison with the most recent -- and currently the sole -- lattice QCD data on the $S$-wave $I=1/2$ $D^\ast\pi$ scattering length at a pion mass of $391$~MeV reveals good agreement, thereby validating the estimation of low energy constants via heavy quark spin symmetry. Within the relativistic formalism, we confirm that the $D_{s1}(2460)$ can be identified with a bound state pole, while the $D_1(2430)$ corresponds to the interplay of two poles: a lower one on the second Riemann sheet and a higher one on the third Riemann sheet. We show that the $D_{s1}(2460)$ and the lower $D_1(2430)$ pole originate from the same flavor SU(3) triplet, whereas the higher $D_1(2430)$ pole belongs to the SU(3) sextet. All these states are not of $\bar{q}q$ nature, as they flow to complex infinity in the large $N_C$ limit. Our results provide quantitative benchmarks for future lattice QCD and femtoscopic studies.