Possible Aoki phase for staggered fermions

Abstract

The phase diagram for staggered fermions is discussed in the context of the staggered chiral Lagrangian, extending previous work on the subject. When the discretization errors are significant, there may be an Aoki-like phase for staggered fermions, where the remnant SO4 taste-symmetry is broken down to SO3. We solve explicitly for the mass spectrum in the 3-flavor degenerate mass case and discuss qualitatively the 2 1-flavor case. From numerical results we find that current simulations are outside the staggered-Aoki phase. As for near-future simulations with more-improved versions of the staggered action, it seems unlikely that these will be in the Aoki phase for any realistic value of the quark mass, although the evidence is not conclusive.

A two-loop relation between inclusive radiative and semileptonicB-decay spectra

“…We need as inputs the heavy-quark parameters λ 2 = 0.12 GeV 2 , λ 1 = (−0.25 ± 0.10) GeV 2 , and the quark masses m b = (4.61 ± 0.06) GeV [16], m s = (90 ± 25) MeV [33,34], and m c /m b = 0.222±0.027 [13]. Here m b is defined in the shape-function scheme at a scale µ * = 1.5 GeV, m s is the running mass in the MS scheme evaluated at 1.…”

Finite volume effects for meson masses and decay constants

“…Once this level of accuracy will be reached, our formulae will become particularly useful. First, in order to correct for these effects in all applications which require a high precision, like the evaluation of the F K /F π ratio which, as suggested by Marciano [34], leads to a determination of V us [38]. Second, if one wants to use these finite size effects as a means to determine low energy constants on the lattice.…”

“…Lattice QCD with staggered fermions and N f = 2 or N f = 2 + 1 violates flavour (or taste) symmetry and low energy unitarity, properties our analysis relies on. Under the assumption that these effects disappear in the continuum limit 6 , the finite volume shift of an observable like F π /F K can be calculated in staggered chiral perturbation theory (this is what the MILC Collaboration does [38]), but one cannot enjoy the benefits of the Lüscher formula. We stress that no such conceptual issues arise with dynamical Wilson-type fermions.…”

“…6. In his analysis Marciano uses the MILC Collaboration result F K /F π = 1.201(8)(15) [35,36]. Among the various data sets they have, those with the smallest M π L and thus most likely to be affected by sizeable finite volume corrections, have …”

Towards measuring the mass with staggered fermions

“…The 16 3 × 32 configs were used to test our algorithms and were generated at the University of Liverpool. The 20 3 × 64 configurations are "coarse" MILC lattices with a ≈ 0.12fm [14,15]. All are produced with the "Asqtad" improved action [16,17,18].…”