Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson chiral perturbation theory

TL;DR

This paper computes scattering lengths between light pseudoscalar and heavy mesons to fourth order in chiral perturbation theory, fitting lattice QCD data, and predicts possible bound states including a narrow $ar{K}\Xi_{cc}$ state.

Contribution

It provides a detailed calculation of scattering lengths at $ ext{O}(p^4)$ in heavy meson chiral perturbation theory, including novel predictions for bound states and guidance for experimental searches.

Findings

Scattering lengths tend to converge at fourth order in most channels.

The $DK (I=0)$ scattering length is accurately obtained in the iterated method.

Predicted bound states in $ar{K}\Xi_{cc}$ and $ar{K}\Xi_{bb}$ channels.

Abstract

We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK (I=0)$, which involves the bound state $D_{s0}^{*}(2317)$, is obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels $\bar{K}\Xi_{cc}(I=0)$ and $\bar{K}\Xi_{bb}(I=0)$. We strongly urge the LHCb Collaboration to look for the very narrow $\bar{K}\Xi_{cc}$ state with $IJ^P=0{1\over 2}^-$ through either the electromagnetic decay or the iso-spin violating strong decay $\Omega_{cc} \pi$.