Twisted valence quarks and hadron interactions on the lattice

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We consider QCD with valence and sea quarks obeying different boundary conditions. We point out that the energy of low lying two hadron states do not depend on the boundary condition of the sea quarks (up to exponentially small corrections). Thus, the advantages in using twisted boundary conditions on the lattice QCD extraction of nucleon-nucleon phase shifts can be gained without the need of new gauge configurations, even in fully unquenched calculations.