${\Sigma }_{c}N$ interaction in chiral perturbation theory

Abstract

We adopt the heavy baryon chiral perturbation theory to calculate the ${\Sigma }_{c}N$ 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 ${\Sigma }_{c}N$ 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 ${}^3{S}_1(I=1/2)$ ${\Sigma }_{c}N$ interaction is weakly attractive but no bound solution is found. We also propose a quark model to estimate the leading order ${\Sigma }_{c}N$ 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 ${}^1{S}_0(I=3/2)$ ${\Sigma }_{c}N$ channel and a two-body bound state.

arXiv comment11 pages, 9 figures

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