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Peter Weisz

Publications and source records attributed to Peter Weisz.

52 records · Page 3Linked to original sources
arXiv1998

Computation of the improvement coefficient $c_{\rm sw}$ to 1-loop with improved gluon actions

The coefficient $c_{\rm sw}$ appearing in the Sheikholeslami-Wohlert improved action is computed to one loop perturbation theory for improved gluon actions including six-link loops. The O($a$) improvement coefficients for the dimension three isovector composite operators bilinear in the quark fields are also computed to one loop order of perturbation theory with degenerate non-vanishing quark masses.

hep-lat↗
arXiv1998

Questionable and unquestionable in the perturbation theory of non-Abelian models

We show, by explicit computation, that bare lattice perturbation theory in the two-dimensional O(n) nonlinear $σ$ models with superinstanton boundary conditions is divergent in the limit of an infinite number of points $|Λ|$. This is the analogue of David's statement that renormalized perturbation theory of these models is infrared divergent in the limit where the physical size of the box tends to infinity. We also give arguments which support the validity of the bare perturbative expansion of short-distance quantities obtained by taking the limit $|Λ|\to\infty$ term by term in the theory with more conventional boundary conditions such as Dirichlet, periodic, and free.

hep-lat↗
arXiv1997

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

Using the Schrödinger 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.

hep-lat↗
arXiv1997

Further results on O(a) improved lattice QCD to one-loop order of perturbation theory

We present results at one-loop order of perturbation theory for various improvement coefficients in on-shell O($a$) improved lattice QCD. In particular we determine the additive counterterm required for on-shell improvement of the isovector vector current. Employing a general mass-independent renormalization scheme we also obtain the coefficients of the O($a$) counterterms which are proportional to the quark mass in the improved isovector pseudo-scalar, axial vector and vector operators. In the latter case a comparison with a recent non-perturbative study is made.

hep-lat↗
arXiv1996

Non-perturbative O(a) improvement of lattice QCD

The coefficients multiplying the counterterms required for O($a$) improvement of the action and the isovector axial current in lattice QCD are computed non-perturbatively, in the quenched approximation and for bare gauge couplings $g_0$ in the range $0 \leq g_0 \leq 1$. A finite-size method based on the Schrödinger functional is employed, which enables us to perform all calculations at zero or nearly zero quark mass. As a by-product the critical hopping parameter $κ_c$ is obtained at all couplings considered.

hep-lat↗
arXiv1996

Chiral symmetry and O(a) improvement in lattice QCD

The dominant cutoff effects in lattice QCD with Wilson quarks are proportional to the lattice spacing a. In particular, the isovector axial current satisfies the PCAC relation only up to such effects. Following a suggestion of Symanzik, they can be cancelled by adding local O(a) correction terms to the action and the axial current. We here address a number of theoretical issues in connection with the O(a) improvement of lattice QCD and then show that chiral symmetry can be used to fix the coefficients multiplying the correction terms.

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arXiv1995

Non-perturbative renormalization of lattice QCD at all scales

A general strategy to solve the non-perturbative renormalization problem in lattice QCD, using finite-size techniques and numerical simulations, is described. As an illustration we discuss the computation of the axial current normalization constant, the running coupling at zero quark masses and the scale evolution of the renormalized axial density. The non-perturbative calculation of O(a) correction terms (as they appear in Symanzik's improvement programme) is another important field of application.

hep-lat↗
arXiv1995

Lattice Investigations of the Running Coupling

A review of investigations of running couplings using lattice techniques is given. This includes i) studies of the running of particular non-perturbatively defined renormalized couplings in pure gauge theories over a range of energies, and ii) how estimates of $α_{\overline{MS}}(m_Z)$ in lattice QCD are presently obtained.

hep-lat↗
arXiv1995

Computation of the relation between the bare lattice coupling and the MSbar coupling in SU(N) gauge theories to two loops

The perturbation expansion of the MSbar coupling in the SU(N) gauge theory in powers of the bare lattice coupling is extended to two-loop order. A discussion of our results has already been published elsewhere. We here describe the calculation in some detail. It relies on the background field technique and a recently introduced coordinate space method to evaluate lattice Feynman integrals.

hep-lat↗
arXiv1995

Background field technique and renormalization in lattice gauge theory

Lattice gauge theory with a background gauge field is shown to be renormalizable to all orders of perturbation theory. No additional counterterms are required besides those already needed in the absence of the background field. The argument closely follows the treatment given earlier for the case of dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS, background gauge and shift symmetries of the lattice functional integral.

hep-lat↗
arXiv1995

Coordinate space methods for the evaluation of Feynman diagrams in lattice field theory

We describe an efficient position space technique to calculate lattice Feynman integrals in infinite volume. The method applies to diagrams with massless propagators. For illustration a set of two-loop integrals is worked out explicitly. An important ingredient is an observation of Vohwinkel that the free lattice propagator can be evaluated recursively and is expressible as a linear function of its values near the origin.

hep-lat↗
arXiv1993

A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory

A non-perturbative finite-size scaling technique is used to study the evolution of the running coupling (in a certain adapted scheme) in the SU(3) Yang-Mills theory. At low energies contact is made with the fundamental dynamical scales, such as the string tension K, while at larger energies the coupling is shown to evolve according to perturbation theory. In that regime the coupling in the MS-bar scheme of dimensional regularization is obtained with an estimated total error of a few percent.

hep-lat↗
arXiv1992

The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories

Following Symanzik we argue that the Schrödinger functional in lattice gauge theories without matter fields has a well-defined continuum limit. Due to gauge invariance no extra counter terms are required. The Schrödinger functional is, moreover, accessible to numerical simulations. It may hence be used to study the scaling properties of the theory and in particular the evolution of the renormalized gauge coupling from low to high energies. A concrete proposition along this line is made and the necessary perturbative analysis of the Schrödinger functional is carried through to 1-loop order.

hep-lat↗
arXiv1992

Computation of the Running Coupling in the SU(2) Yang-Mills Theory

A finite-size scaling technique is applied to the SU(2) gauge theory (without matter fields) to compute a non-perturbatively defined running coupling alpha(q) for a range of momenta q given in units of the string tension K. We find that already at rather low q, the evolution of alpha(q) is well described by the 2-loop approximation to the Callan-Symanzik beta-function. At the highest momentum reached, q=20 sqrt(K), we obtain alpha_MSbar(q)=0.187 +/- 0.005 +/- 0.009 for the running coupling in the MSbar scheme of dimensional regularization.

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