Low-energy interactions between doubly charmed baryons and Goldstone bosons from lattice QCD

Abstract

We perform a lattice QCD calculation of the $S$-wave interactions between the ground-state spin-$1/2$ doubly charmed baryons and Goldstone bosons. The lattice QCD simulations are carried out on four $2+1$ flavor Wilson-Clover ensembles generated by the CLQCD collaboration, with a lattice spacing $a=0.07746$ fm and two different pion masses, $M_\pi \sim 210$ and $\sim 300~\mathrm{MeV}$. Energy levels are extracted for four single channels, $\Omega_{cc}\bar{K}^{(-2,1/2)}$, $\Xi_{cc}K^{(1,1)}$, $\Xi_{cc}K^{(1,0)}$, and $\Xi_{cc}\pi^{(0,3/2)}$, where the superscripts $(S,I)$ denote strangeness $S$ and isospin $I$. Our results indicate that the $\Xi_{cc}K^{(1,0)}$ channel is attractive, exhibiting negative energy shifts relative to the non-interacting two-hadron thresholds, while the other three channels are repulsive. Using L\"uscher's finite-volume formula, we extract the near-threshold phase shifts and determine the $S$-wave scattering lengths. Furthermore, a virtual state pole is found in the $\Xi_{cc}K^{(1,0)}$ scattering amplitude. These results provide {\it ab initio} input to enable high-precision studies of the properties and spectroscopy of doubly heavy baryons.