$Σ_cN$ interaction in chiral perturbation theory

Abstract

We adopt the heavy baryon chiral perturbation theory to calculate the $Σ_cN$ 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 $Σ_cN$ interaction from HAL QCD calculation with $m_π\approx 410$ MeV and $m_π\approx 570$ MeV, and then extrapolate it to the physical pion mass. The $^3S_1(I=1/2)$ $Σ_{c}N$ interaction is weakly attractive but no bound solution is found. We also propose a quark model to estimate the leading order $Σ_cN$ 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 $^1S_0(I=3/2)$ $Σ_{c}N$ channel and a two-body bound state.