Effective field theories for QCD with rooted staggered fermions

Abstract

Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the "rooting trick" is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalization of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to "rooted" staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-group based arguments for the correctness of the continuum limit and the success of rooted staggered chiral perturbation theory in fitting numerical results obtained with the rooting trick. In order to develop our argument, we need to assume the existence of a standard partially-quenched chiral effective theory for any local partially-quenched theory. Other technical, but standard, assumptions are also required.Comment: Minor changes, few references added; RevTeX, 35 page

On the foundations of partially quenched chiral perturbation theory

“…[24,28] for staggered fermions: 12 9) such that −π/2 < p j , q j ≤ π/2. Operators get relabeled as in 10) etc. Performing the sum over x in Eq.…”

“…PQChPT plays an important role in the development of the effective chiral theory for rooted staggered fermions [9,10], which in turn provides some evidence for the validity of the rooting procedure. For more discussion of these issues see Refs.…”

NeutralB-meson mixing from three-flavor lattice quantum chromodynamics: Determination of theSU(3)-breaking ratioξ<

“…The configurations we use in this analysis were generated using the fourth-root procedure for eliminating extra degrees of freedom originating from fermion doubling. Despite the nonlocal violations of unitarity of the rooted theory at non-zero lattice spacing [45,46], there are strong theoretical arguments [47][48][49][50], as well as other analytical and numerical evidence [51][52][53][54], that the local, unitary theory of QCD is recovered in the continuum limit. This gives us confidence that the rooting procedure yields valid results.…”

QCD equation of state at non-zero chemical potential

“…Several expansion coefficients as a function of N t for the free theory [3]. On the left, for nonvanishing coefficients, we show the the ratio to the Stefan-Boltzmann limit.…”