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

TL;DR

This work provides the first lattice-QCD study of $S$-wave interactions between ground-state doubly charmed baryons $B_{cc}$ and Goldstone bosons $\phi$, using four $N_f=2+1$ CLQCD ensembles at $a=0.07746$ fm and $M_\pi \simeq 210$ and 300 MeV. By constructing $B_{cc}\phi$ interpolating operators, applying a variational method to extract finite-volume energy levels, and employing Lüscher’s formula, the authors obtain near-threshold phase shifts and $S$-wave scattering lengths for four elastic channels; they also perform a pole analysis of the scattering amplitude. The results show that the $\Xi_{cc}K^{(1,0)}$ channel is attractive (energy levels below threshold) with a near-threshold virtual-state pole at $p^2 \approx -0.03\ \mathrm{GeV}^2$, while the other channels are repulsive. Extrapolating to the physical pion mass yields $a_0^{\mathrm{phy}}$ for each channel, which are broadly consistent with chiral perturbation theory expectations and provide crucial ab initio input for the spectroscopy and dynamics of doubly heavy baryons, including future coupled-channel analyses.

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, $M_π\sim 210$ and $\sim 300~\mathrm{MeV}$. Energy levels are extracted for four single channels, $Ω_{cc}\bar{K}^{(-2,1/2)}$, $Ξ_{cc}K^{(1,1)}$, $Ξ_{cc}K^{(1,0)}$, and $Ξ_{cc}π^{(0,3/2)}$, where the superscripts $(S,I)$ denote strangeness $S$ and isospin $I$. Our results indicate that the $Ξ_{cc}K^{(1,0)}$ channel is attractive, exhibiting negative energy shifts relative to the non-interacting two-hadron thresholds, while the other three channels are repulsive. Using Lüscher'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 $Ξ_{cc}K^{(1,0)}$ scattering amplitude. These results provide ab initio input to enable high-precision studies of the properties and spectroscopy of doubly heavy baryons.

Figures (15)

• Figure 1: Energy levels of two-hadron systems for the four single channels. (a) $M_\pi \sim 300$ MeV; (b) $M_\pi \sim 210$ MeV. The blue data points are the finite-volume energies, and the black bands indicate free energies of the non-interacting threshold with different momenta.
• Figure 2: ERE fit results truncated at $\mathcal{O}(p^2)$ (green bands) and $\mathcal{O}(p^4)$ (yellow bands) for four single channels using DRC energy levels. The left and right panels correspond to pion masses $M_{\pi}\sim300$ MeV and 210 MeV, respectively. The red and blue points show $p\cot\delta_0$ extracted via Lüscher's formula (eq. (\ref{['eq:Luscher.formula']})), while the grey solid curve is $ip=\pm |p|$ versus $p^2$.
• Figure 3: Extrapolation of the $S$-wave scattering lengths $a_0$ to the physical pion mass. The results of $a_0$ labeled by '' DRC" from table \ref{['tab:ERE.FitRslts.UpToP2']} are adopted in the extrapolation. The EOMS- and HB-ChPT predictions, taken from refs. Liang:2023scpMeng:2018zbl respectively, are also shown for easy comparison.
• Figure 4: The pion effective mass plots for four ensembles. Each panel displays the results for the five lowest momenta, $\mathbf{p}$ = (0, 0, 0), (0, 0, 1), (0, 1, 1), (1, 1, 1), and (0, 0, 2), in units of $2\pi/L$. The horizontal lines with bands indicate the fitted masses and the fitting ranges.
• Figure 5: The kaon effective mass plots for four ensembles. The description is the same as in figure \ref{['fig:pion.meff']}.