Renormalization of the momentum density on the lattice using shifted boundary conditions

Abstract: In order to extract transport quantities from energy-momentum-tensor (EMT) correlators in Lattice QCD there is a strong need for a non-perturbative renormalization of these operators. This is due to the fact that the lattice regularization explicitly breaks translational invariance, invalidating the non-renormalization-theorem. Here we present a non-perturbative calculation of the renormalization constant of the off-diagonal components of the EMT in SU(3) pure gauge theory using lattices with shifted boundary conditions. This allows us to induce a non-zero momentum in the system controlled by the shift parameter and to determine the normalization of the momentum density operator.