Schrödinger functional at negative flavour number

Abstract

The scaling of the Schrödinger functional coupling is studied numerically and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved bosonic spinor field. This corresponds to QCD with minus two light flavours and is used as a numerically less costly test case for real QCD. A suitable algorithm is developed, and the influence of the matter fields on the continuum limit and the lattice artefacts are studied in detail.

First results on the running coupling in QCD with two massless flavours

“…1 for several couplings. Where available we include together with our present N f = 2 data also quenched and bermion [19] (N f = −2) results. We conclude that lattice artefacts behave non-pathologically and similar to perturbative expectations.…”

The running coupling of QCD with four flavors

“…In addition to the various improvement terms in the action and c A in (5.7) we exploit our knowledge of δ 1 and δ 2 from the perturbative calculation of with the coefficients taken from [26]. For N f = 4 we have L/a δ 1 δ 2 4 −0.0102 0.0073 6 −0.0045 0.0013 8 −0.0024 0.00013…”

Properties of the renormalized quark mass in the Schrödinger functional with a non-vanishing background field

“…For the case of N f = −2 ("bermions"), one gets good results by linear extrapolation of the results for N f = 2 and N f = 0 [31]. However, the improvement of the action is not sufficient to improve the expectation value of every composite operator.…”

“…In order to compute the step scaling function non-perturbatively, one has to simulate a sequence of lattice pairs with decreasing lattice spacing and fixed coupling u and extrapolate the Monte Carlo data to the continuum limit. In this procedure, the perturbative expansion of δ(u, a/L) may be used to remove the cutoff effects up to 2-loop order from the non-perturbative values of the step scaling function Σ(u, a/L) [31].…”

“…There have, however, been recent results in full QCD with two flavours [27]. A less expensive toy model are so called bermions, which is a theory with N f = −2 [28,29,30,31]. Although this is of course no realistic model of the physical world, bermions may be used to study structural properties of the theory.…”