Flavor symmetry breaking and zero mode shift for staggered fermions

Abstract

On the lattice a “fermionic topological charge”, Q , can be used to measure the physically relevant fluctuations of the number of “zero modes” of the lattice Dirac operator. It is shown that the mass dependence of Q for small quark mass is related to the flavor symmetry breaking for staggered fermions and an estimate is given for the mass scale below which this breaking of flavor symmetry cannot be neglected. Also the renormalization of Q is discussed.