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Nucleon-Nucleon Potential and its Non-locality in Lattice QCD

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arxiv 1103.0619 v2 pith:VDEIIQFL submitted 2011-03-03 hep-lat nucl-th

classification hep-latnucl-th
keywords latticelocalpotentialsapproximationcentraldifferentenergyerrors
verification ladder T0 review T1 audit T2 compute T3 formal

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By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the delivative expansion of the general nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) \delta^3(r-r') is studied. The relative kinetic energy between two nucleons is introduced through the anti-periodic boundary condition in the spatial directions. On a hypercubic lattice with the lattice spacing a ~ 0.137 fm and the spatial extent L_s ~ 4.4 fm with the pion mass m_{\pi} ~ 530 MeV, the local potentials for two different energies (E ~ 0 MeV and 45 MeV) are compared and found to be identical within statistical errors, which validates the local approximation of U(r,r') up to E=45 MeV for the central and tensor potentials. Central potentials in the spin-singlet channel for different orbital angular momentums (l=0 and l=2) at E ~ 45 MeV are also found to be the same within the errors, which also supports the local approximation.

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    hep-lat 2019-09 conditional novelty 6.0 of 10

    A formalism is given to convert the non-Hermitian HAL QCD potential into a Hermitian one order by order, with exact treatment at next-to-leading order, and the NLO correction for Xi-Xi(1S0) is small.

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