Lattice QCD with light Wilson quarks

Abstract

Wilson's formulation of lattice QCD is attractive for many reasons, but perhaps mainly because of its simplicity and conceptual clarity. Numerical simulations of the Wilson theory (and of its improved versions) tend to be extremely demanding, however, to the extent that they rapidly become impractical at small quark masses. Recent advances in simulation algorithms now allow such simulations to be pushed to significantly smaller masses without having to compromise in other ways. Contact with chiral perturbation theory can thus be made and many physics questions can be addressed that previously appeared to be inaccessible.

Light dynamical fermions on the lattice: toward the chiral regime of QCD

“…These values are significantly smaller that those reported in Ref. [57], determined by : Parameters of the lattices generated in Refs. [17,18] with the Wilson gauge action and Wilson (W /W ) and SW non-perturbative improved (W /SW ) fermions are given in the tables.…”

Stability of lattice QCD simulations and the thermodynamic limit

“…Another form of the stability bound is obtained by multiplication with the ratio B = m 2 π /2m, which is known to be practically independent of the quark mass [5,6]. For lattices of size 2L × L 3 , this leads to the inequality…”

“…In particular, the fact that the massive Wilson-Dirac operator is not protected from arbitrarily small eigenvalues may lead to instabilities in numerical simulations. Such instabilities were not observed, however, in recent simulations of the twoflavour Wilson theory on large lattices, not even at the smallest quark masses consid-ered [4][5][6]. It is tempting to attribute the absence of instabilities in these simulations to the use of a new simulation algorithm, but this explanation cannot be right, because the distribution of the spectral gap of the lattice Dirac operator (and thus the probability to find exceptionally small eigenvalues) is determined by the lattice action and the functional integral, and not by the method used to evaluate the latter.…”

“…Evidently, the gap is a well-defined function of the gauge field and so is the spectral asymmetry 5) where N ± are the numbers of positive and negative eigenvalues of Q m .…”

QCD with light Wilson quarks on fine lattices (I): first experiences and physics results

“…The results for the reference scale obtained in this way are summarized in table 2. In order to avoid any confusions, we mark all quantities evaluated at the reference point with a subscript The lattice spacings calculated here are significantly smaller than those previously published by us in a conference report [21], where the Sommer radius [24] was used as reference scale. Larger lattice spacings are also obtained if the scale is set by the K and K * masses, similarly to what was done here, but at larger sea-quark masses (see fig.…”