Four-momentum boosted Fermion fields

Abstract

A formulation of the fermion action is discussed which includes an explicit four momentum boost on the field prior to discretisation. This is used to shift the zero of lattice momentum to lie near one of the on-shell quark poles. The positive pole is selected if we wish to describe a valence quark, and negative pole for a valence anti-quark. Like NRQCD, the typical lattice momenta involved in hadronic correlation functions can be kept small: of order $O(a Λ_{\rm QCD})$, rather than $O(a m_Q)$ even when describing heavy quarks. If we expand around the particle pole, the anti-particle correlator will be poorly described for large $a m_Q$. However, in that case the anti-particle will be far off shell and will only affect unphysical, renormalization factors. The formulation produces the correct continuum limit, and preliminary results have been obtained (for an unimproved action) of both the one-loop self energy and a non-perturbative correlation function.