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The coupled channel approach to the $\Lambda_c N-\Sigma_c N$ system in lattice QCD

T. Miyamoto, for HAL QCD Collaboration

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf


We study the interaction of s-wave $\Sigma_c N$ state in the $I(J^P) = \frac{1}{2}(1^+)$ channel. Since this state couples to the s-wave $\Lambda_c N~(J^P=1^+)$ state, we have utilized the extension of the HAL QCD method to extract the coupled channel potential for the $\Lambda_c N-\Sigma_c N$ system. In our simulation, we employ gauge configurations generated by the PACS-CS Collaboration at $a = 0.0907(13)$ fm on a $L^3 \times T = 32^3 \times 64$ lattice ($La = 2.902(42)$ fm). We employ three ensembles corresponding to $m_\pi = 410, 570, 700$ MeV to study the quark mass dependence of the $\Lambda_c N-\Sigma_c N$ interactions. To reduce the discretization error coming from the heavy quark mass, we employ the relativistic heavy quark (RHQ) action for the charm quark. The phase shifts and scattering length obtained from the extracted potential matrix show that the $\Sigma_c N$ interaction is attractive at low energy stronger than the $\Lambda_c N$ interaction though no bound state at $m_\pi \ge 410$ MeV.