Fermions on the light front transverse lattice

TL;DR

This paper investigates fermion formulations on the light front transverse lattice in QCD, proposing methods to eliminate fermion doubling and analyzing their effectiveness through numerical studies.

Contribution

It introduces and compares approaches using forward/backward derivatives and symmetric derivatives, including staggered and Wilson formulations, to address fermion doubling.

Findings

No fermion doubling with forward/backward derivatives.

Doublers occur with symmetric derivatives due to decoupled lattice sites.

Even-odd helicity flip symmetry influences fermion doubling.

Abstract

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and backward derivatives. There is no fermion doubling and the helicity flip term proportional to the fermion mass in the full light front QCD becomes an irrelevant term in the free field limit. In the second approach with symmetric derivative (which has been employed previously in the literature), doublers appear and their occurrence is due to the decoupling of even and odd lattice sites. We study their removal from the spectrum in two ways namely, light front staggered formulation and the Wilson fermion formulation. The numerical calculations in free field limit are carried out with both fixed and periodic boundary conditions on the transverse lattice and finite volume effects are studied. We find that an even-odd helicity flip symmetry on the light front transverse lattice is relevant for fermion doubling.