Peter Weisz

The Schrodinger Functional — a Renormalizable Probe for Non-Abelian Gauge Theories

Following Symanzik we argue that the Schrodinger 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 Schrodinger 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 Schrodinger functional is carried through to 1-loop order.

Chiral symmetry and O(a) improvement in lattice QCD

Abstract 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.

Leading and Next-to-leading {QCD} Corrections to

Abstract We present a complete calculation of leading and next-to-leading QCD corrections to the QCD factors η2K and η ¯ 2 B , relevant for the CP-violating ɛ-parameter and B 0 − B ¯ 0 mixing in the presence of a heavy top quark. We demonstrate explicitly that the resulting η2s are gauge as well as renormalization prescription independent. We also show that they do not depend on the infrared structure of the theory. We emphasize that these results only follow after correct factorization of short and long distance contributions, which has not been done properly in many recent QCD analyses present in the literature. We stress however that η2(xt) with xt = mt2/MW2 depends sensitively on the definition of the top quark mass and only the product η2(xt)S(xt) (S(xt) being the function resulting from the lowest order box diagram) is free from this dependence. For m t = m ¯ t ( M w ) the corresponding η2s decrease strongly with mt, whereas for m t * = m ¯ t ( m t ) they show only a weak mt*-dependence: 0.58 ⩾ η2K* ⩾ 0.56 and 0.88 ≥ η ¯ 2 B * ≥ 0.84 for GeV ⩽m*t⩽300 GeV and Λ M S ¯ = 200 M e V . A critical discussion of the existing literature on QCD calculations in the presence of a large mt is presented.

\epsilon

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 g0 i range 0 ⩽ g0 ⩽ 1. A finite-size method based on the Schrodinger functional is employed, which enables us to perform all calculations at z nearly zero quark mass. As a by-product the critical hopping parameter κc is obtained at all couplings considered.

Parameter and

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 scheme of dimensional regularization is obtained with an estimated total error of a few percent.

B^0 - \bar{B}^0

Abstract We propose to compute the running coupling g 2 in lattice gauge theories and non-linear σ-models through a finite-size scaling analysis. The idea is shown to work well in the O(3) σ-model, where we succeed to determine g 2 (in, say, a momentum subtraction scheme) at energies up to about 30 times the mass of the particles in the theory.

Mixing in the Presence of a Heavy Top Quark

Lattice QCD with Wilson quarks and a chirally twisted mass term represents a promising alternative regularization of QCD, which does not suffer from unphysical fermion zero modes. We show how the correlation functions of the renormalized theory are related to the theory with a standard parameterization of the mass term. In particular we discuss the conditions under which these relations take the same form as obtained from naive continuum considerations. We discuss in detail some applications and comment on potential benefits and problems of this framework.

Non-perturbative O(a) improvement of lattice QCD

The gradient flow in non-abelian gauge theories on

A precise determination of the running coupling in the SU(3) Yang-Mills theory

{\mathbb{R}^4}

A Numerical method to compute the running coupling in asymptotically free theories

is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the correlation functions of the time-dependent field can be expanded in perturbation theory, the Feynman rules being those of a renormalizable field theory on