$\Sigma_cN$ interaction in chiral perturbation theory

TL;DR

This paper uses chiral perturbation theory and lattice QCD data to analyze the $\Sigma_cN$ interaction, predicting a bound state in a specific channel and providing insights into heavy baryon interactions.

Contribution

It combines chiral effective field theory with quark model estimates to predict $\Sigma_cN$ interactions and potential bound states, extending previous lattice QCD results.

Findings

Weak attraction in $^3S_1(I=1/2)$ channel with no bound state.

Prediction of a very attractive $^1S_0(I=3/2)$ channel leading to a bound state.

Extrapolation from lattice QCD data to physical pion mass.

Abstract

We adopt the heavy baryon chiral perturbation theory to calculate the $\Sigma_cN$ interaction to the next-to-leading order. We consider the contact interactions, one-pion-exchange contributions, two-pion-exchange diagrams, and renormalization effects of the vertices, masses and wave functions. With the pion mass dependent expression, we fit the $\Sigma_cN$ interaction from HAL QCD calculation with $m_{\pi}\approx 410$ MeV and $m_{\pi}\approx 570$ MeV, and then extrapolate it to the physical pion mass. The $^3S_1(I=1/2)$ $\Sigma_{c}N$ interaction is weakly attractive but no bound solution is found. We also propose a quark model to estimate the leading order $\Sigma_cN$ contact interaction with the $NN$ interaction as input. This approach combining the quark model and the chiral effective field theory predicts a very attractive interaction in $^1S_0(I=3/2)$ $\Sigma_{c}N$ channel and a two-body bound state.