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The one-pion-exchange potential with contact terms from lattice QCD simulations

The pion-mass-dependent nucleon-nucleon ($NN$) potentials in term of one-pion exchange and contact terms are obtained from the latest lattice QCD simulations of two-nucleon system, which employ the forms of leading order (LO) $NN$ potential from the chiral effective field theory and thus are named as the LO chiral potential in this work. We extract the coefficients of contact terms and cut-off momenta in these potentials, for the first time, by fitting the phase shifts of $^1S_0$ and $^3S_1$ channels generated by the results of HALQCD collaboration with various pion masses from $468.6$ MeV to $1170.9$ MeV. The low-energy constants in the $^1S_0$ and $^3S_1$ channels become weaker and approach each other for larger pion masses. These LO chiral potentials are applied to symmetric nuclear and pure neutron matter within the Brueckner-Hartree-Fock method. At this moment, however, we do not have yet the information of the $P$-wave $NN$ interaction to be provided by the lattice QCD simulations for full description of nuclear matter. Our results will enhance the development of nuclear structure and nuclear matter by controlling the contribution of the pionic effect and illuminate the role of chiral symmetry of the strong interaction in complex system.