2,594 research outputs found

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

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    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(aa) 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

    The Schr\"odinger functional running coupling with staggered fermions and its application to many flavor QCD

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    We discuss the Schr\"odinger functional in lattice QCD with staggered fermions and relate it, in the classical continuum limit, to the Schr\"odinger functional regularized with Wilson fermions. We compute the strong coupling constant defined via the Schr\"odinger functional with staggered fermions at one loop and show that it agrees with the continuum running coupling constant in the Schr\"odinger functional formalism. We compute this running coupling in the ``weak coupling phase'' of many flavor QCD numerically at several values of the bare coupling and for several system sizes from L/a=4L/a=4 to 12. The results indicate that the ╬▓\beta-function for 16 flavors has the opposite sign than for few flavor QCD, in agreement with a recent claim, and with the perturbative prediction.Comment: 3 pages with 2 ps figures; to appear in the proceedings of Lattice '97, Edinburgh, Scotland, July 22--26, 199

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

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    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/LT/L, and the angle ╬Ş\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(aa) improved lattice QCD.Comment: 17 pages, gzipped tar-fil

    The Schr\"odinger functional in QCD

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    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

    The chirally rotated Schr\"odinger functional with Wilson fermions and automatic O(a) improvement

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    A modified formulation of the Schr\"odinger functional (SF) is proposed. In the continuum it is related to the standard SF by a non-singlet chiral field rotation and therefore referred to as the chirally rotated SF (¤ç\chiSF). On the lattice with Wilson fermions the relation is not exact, suggesting some interesting tests of universality. The main advantage of the ¤ç\chiSF consists in its compatibility with the mechanism of automatic O(aa) improvement. In this paper the basic set-up is introduced and discussed. Chirally rotated SF boundary conditions are implemented on the lattice using an orbifold construction. The lattice symmetries imply a list of counterterms, which determine how the action and the basic fermionic two-point functions are renormalised and O(aa) improved. As with the standard SF, a logarithmically divergent boundary counterterm leads to a multiplicative renormalisation of the fermionic boundary fields. In addition, a finite dimension 3 boundary counterterm must be tuned in order to preserve the chirally rotated boundary conditions in the interacting theory. Once this is achieved, O(aa) effects originating from the bulk action or from insertions of composite operators in the bulk can be avoided by the mechanism of automatic O(aa) improvement. The remaining O(aa) effects arise from the boundaries and can be cancelled by tuning a couple of O(aa) boundary counterterms. The general results are illustrated in the free theory where the Sheikholeslami-Wohlert term is shown to affect correlation functions only at O(a2a^2), irrespective of its coefficient.Comment: 51 pages, 2 figures, revised version: improved and extended discussion of Ward identities in section 3 and of the inclusion of counterterms in section 5; eliminated some typos, introduced new ones, results unchange

    Some remarks on O(a) improved twisted mass QCD

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    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

    Non-perturbative results for the coefficients b_m and b_a-b_p in O(a) improved lattice QCD

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    We determine the improvement coefficients b_m and b_a-bp in quenched lattice QCD for a range of beta-values, which is relevant for current large scale simulations. At fixed beta, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g_0^2. Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.Comment: 25 pages, 8 figures, minor change at figure
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