Constraint on the low energy constants of Wilson chiral perturbation theory

Abstract

Wilson chiral perturbation theory (WChPT) is the effective field theory describing the longdistance properties of lattice QCD with Wilson or twisted-mass fermions. We consider here WChPT for the theory with two light flavors of Wilson fermions or a single light twisted-mass fermion. Discretization errors introduce three low energy constants (LECs) into partially quenched WChPT at O(a 2 ), conventionally called W ′ 6 , W ′ 7 and W ′ 8 . The phase structure of the theory at non-zero a depends on the sign of the combination 2W ′ 6 + W ′ 8 , while the spectrum of the lattice Hermitian Wilson-Dirac operator depends on all three constants. It has been argued, based on the positivity of partition functions of fixed topological charge, and on the convergence of graded group integrals that arise in the ǫ-regime of ChPT, that there is a constraint on the LECs arising from the underlying lattice theory. In particular, for W ′ 6 = W ′ 7 = 0, the constraint found is W ′ 8 ≤ 0. Here we provide an alternative line of argument, based on mass inequalities for the underlying partially quenched theory. We find that W ′ 8 ≤ 0, irrespective of the values of W ′ 6 and W ′ 7 . Our constraint implies that 2W ′ 6 > |W ′ 8 | if the phase diagram is to be described by the first-order scenario, as recent simulations suggest is the case for some choices of action.

Determination of low-energy constants of Wilson chiral perturbation theory

“…[47]. It relies on the measurement of pseudoscalar meson masses involving Wilson twisted mass fermions.…”

“…A similar pattern holds for the mass of the "connected neutral pion" mass, M π (0,c) . The PQWχPT expressions for these three meson masses at LO read [47,[49][50][51],…”

“…We observe that the conditions W 8 < 0 and W 6 > 0 are fulfilled by the lattice data, in agreement with the bounds derived in refs. [29,30,35,47]. In order to quote the values of the Wilson LECs W 6,8 , the systematic effects from quark-mass dependence, residual lattice artifacts and finite volume effects have to be addressed.…”

Realization of the Sharpe-Singleton scenario

“…(13). Since this works for the graded generating functional it also works for the spectral density itself [12].…”

“…Considerable progress, both analytically [11][12][13][14][15][16] and numerically [17][18][19][20][21][22][23], has been made recently in the determination of these constants. However, a complete picture has not yet emerged.…”