Finite-size effects in lattice QCD with dynamical Wilson fermions (original) (raw)

On Scale Determination in Lattice QCD with Dynamical Quarks

2008

Dependence of a/r c (inverse Sommer parameter in units of lattice spacing a) on am q (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with β = 5.6 and 2 degenerate flavors of sea quarks on 16 3 × 32 lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the PCAC quark mass values am q from about 0.07 to below 0.015. Though scaling violations may indeed be present for relatively large am q , a consistent scenario at sufficiently small am q seems to emerge in the mass-independent scheme where for a fixed β , 1/r 0 and √ σ have linear dependence on m q as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale (a = 0.0805(7) fm, a −1 = 2.45(2) GeV) by chiral extrapolation to the physical point.

Non-perturbatively renormalised light quark masses from a lattice simulation with N f = 2

Nuclear Physics B, 2006

We present results for the light quark masses obtained from a lattice QCD simulation with N f = 2 degenerate Wilson dynamical quark flavours. The sea quark masses of our lattice, of spacing a ≃ 0.06 fm, are relatively heavy, i.e., they cover the range corresponding to 0.60 M P /M V 0.75. After implementing the non-perturbative RI-MOM method to renormalise quark masses, we obtain m MS ud (2 GeV) = 4.3 ± 0.4 +1.1

Tuning the strange quark mass in lattice simulations

Physics Letters B, 2010

QCD lattice simulations with 2+12+1 flavours typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass to its physical value and then the up-down quark mass. An alternative method of tuning the quark masses is discussed here in which the singlet quark mass is kept fixed, which ensures that the kaon always has mass less than the physical kaon mass. It can also take into account the different renormalisations (for singlet and non-singlet quark masses) occurring for non-chirally invariant lattice fermions and so allows a smooth extrapolation to the physical quark masses. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Results show the correct order for the baryon octet and decuplet spectrum and an extrapolation to the physical pion mass gives mass values to within a few percent of their experimental values.

Testing pseudofermion lattice QCD with small quark masses and large volumes

Canadian Journal of Physics, 1989

We report on extensive tests done on the pseudofermion algorithm in a simulation of lattice QCD with dynamical quarks. These tests are carried out in a more realistic context than many of the studies previously attempted as a lattice volume of lo3 x 32 sites and quark mass of about 50 to 200 MeV are used throughout the calculation. Wilson loop factors of various sizes, as well as chiral condensates and pion propagators, are shown to change by less than 5% when the pseudofermion algorithm is tuned to simulate QCD more accurately.

Lattice QCD at the physical point meets SU(2) chiral perturbation theory

Physical Review D, 2014

We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU (2) chiral perturbation theory (χPT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU (2) χPT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (ξ-expansion). We find that these expansions begin showing signs of failure around M π = 300 MeV for the typical percent-level precision of our N f = 2 + 1 lattice results. We further determine the LO low energy constants (LECs), F = 88.0 ± 1.3 ± 0.3 and B MS (2 GeV) = 2.58 ± 0.07 ± 0.02 GeV, and the related quark condensate, Σ MS (2 GeV) = (271 ± 4 ± 1 MeV) 3 , as well as the NLO ones,¯ 3 = 2.5 ± 0.5 ± 0.4 and¯ 4 = 3.8 ± 0.4 ± 0.2, with fully controlled uncertainties. Our results are summarized in . We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.

Monte Carlo calculation of hadron masses with light dynamical quarks

Physics Letters B, 1984

Ground state meson and baryon masses are numerically calculated in lattice QCD with unquenched Wilson fermions on an 8 4 lattice. The numerical calculation of the hadronic mass spectrum is one of the great challenges in lattice quantum chromodynamics. During the last years there was continuous progress in improving the calculational methods and in understanding and controlling the errors. Up to now the Monte Carlo calculations were done in the "quenched" (or "valence") approximation in which virtual quark loops are omitted (for an incomplete list of references see refs. [1-3]). The error introduced by the quenched approximation can be of the same order as the other errors investigated recently, like finite lattice size effects, effects of the lattice fermion doubling etc. Therefore it is important to study the effect of virtual loops, too. In this letter we present the results of a calculation of the simplest hadron masses (n, p, p and A) on an 84 lattice, including light virtual quark loops. The Monte Carlo updating with light dynamical quarks was performed by the hopping expansion method described and tested in ref. [4]. The hadron masses were also extracted by hopping expansion using the numerical iterative procedure [2]. In order to have a direct comparison with the quenched approximation, we performed a high statistics quenched calculation on the same sized lattice at/3 = 6/g 2 = 5.70. First we shall dei Supported by Bundesministerium ftir Forschung und Technologic, Bonn, Fed. Rep. Germany.

Free energies of heavy quarks in full-QCD lattice simulations with Wilson-type quark action

Nuclear Physics A, 2009

The free energy between a static quark and an antiquark is studied by using the color-singlet Polyakov-line correlation at finite temperature in lattice QCD with 2+1 flavors of improved Wilson quarks. From the simulations on 32 3 × 12, 10, 8, 6, 4 lattices in the high temperature phase, based on the fixed scale approach, we find that, the heavy-quark free energies at short distance converge to the heavy-quark potential evaluated from the Wilson loop at zero temperature, in accordance with the expected insensitivity of short distance physics to the temperature. At long distance, the heavy-quark free energies approach to twice the single-quark free energies, implying that the interaction between heavy quarks is screened. The Debye screening mass obtained from the long range behavior of the free energy is compared with the results of thermal perturbation theory.

The nucleon mass in N f =2 lattice QCD: finite size effects from chiral perturbation theory

Nuclear Physics B, 2004

In the framework of relativistic SU(2) f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O(p 4 ). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N f = 2 simulations of the UKQCD and QCDSF Collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD Collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.

Chiral dynamics with strange quarks in the light of recent lattice simulations

Journal of High Energy Physics, 2011

Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/or the decay constant in the N f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N f = 2 and N f = 3 chiral limits. We discuss the consequences for the ratio of decay constants F K /F π and the K ℓ3 form factor at vanishing momentum transfer.