Further one-loop results in O(a) improved lattice QCD

Using the Schr\"odinger functional we have computed a variety of renormalized on-shell correlation functions to one-loop order of perturbation theory. By studying their approach to the continuum limit we have determined the O($a$) counterterms needed to improve the quark mass and a number of isovector quark bilinear operators.Comment: 3 pages Latex using espcrc2.sty, to appear in the conference proceedings of Lattice '97, Edinburg

Some remarks on O(a) improved twisted mass QCD

Twisted mass QCD (tmQCD) has been introduced as a solution to the problem of unphysical fermion zero modes in lattice QCD with quarks of the Wilson type. We here argue that O(a) improvement of the tmQCD action and simple quark bilinear operators can be more economical than in the standard framework. In particular, an improved and renormalized estimator of the pion decay constant in two-flavour QCD is available, given only the Sheikholeslami-Wohlert coefficient c_sw and an estimate of the critical mass m_c.Comment: Lattice2001(improvement), 3 page

The running quark mass in the SF scheme and its two-loop anomalous dimension

The non-perturbatively defined running quark mass introduced by the ALPHA collaboration is based on the PCAC relation between correlation functions derived from the Schr\"odinger functional (SF). In order to complete its definition it remains to specify a number of parameters, including the ratio of time to spatial extent, $T/L$, and the angle $\theta$ which appears in the spatial boundary conditions for the quark fields. We investigate the running mass in perturbation theory and propose a choice of parameters which attains two desired properties: firstly the two-loop anomalous dimension \d1SF is reasonably small. This is needed in order to ease matching with the non-perturbative computations and to achieve a precise determination of the renormalization group invariant quark mass. Secondly, to one-loop order of perturbation theory, cut-off effects in the step-scaling function are small in O($a$) improved lattice QCD.Comment: 17 pages, gzipped tar-fil

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1,2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacing a. Based on the generalised transfer matrix, we define the tmQCD Schrodinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.Comment: 31 pages latex, no figure

The Schr\"odinger functional in QCD

The Schr\"odinger functional in Wilson's lattice QCD leads to a sensible classical continuum theory which can be taken as starting point for a perturbative analysis. In dimensional regularization, the saddle point expansion of the Schr\"odinger functional is performed to one-loop order of perturbation theory. The divergences are partly cancelled by the usual coupling constant and quark mass renormalization. An additional divergence can be absorbed in a multiplicative renormalization of the quark boundary fields. The corresponding boundary counterterm being a local polynomial in the fields we confirm the general expectation expressed by Symanzik~\cite{Symanzik}.Comment: 3 pages in postscript (no figures), talk presented at Lattice '94 in Bielefeld 9/27--10/1/9