Non-perturbative Heavy Quark Effective Theory: a test and its matching to QCD

We give an introduction to the special problems encountered in a treatment of HQET beyond perturbation theory in the gauge coupling constant. In particular, we report on a recent test of HQET as an effective theory for QCD and discuss how HQET can be implemented on the lattice including the non-perturbative matching of the effective theory to QCD.Comment: 12 pages, Late

Non-perturbative Heavy Quark Effective Theory: Introduction and Status

We give an introduction to Heavy Quark Effective Theory (HQET). Our emphasis is on its formulation non-perturbative in the strong coupling, including the non-perturbative determination of the parameters in the HQET Lagrangian. In a second part we review the present status of HQET on the lattice, largely based on work of the ALPHA collaboration in the last few years. We finally discuss opportunities and challenges.Comment: 31 pages, 15 figures, Contribution to the Proceedings of the Final Meeting of DFG SFB-TR-9 (Durbach, Germany, Sept. 2014), to appear in Nucl. Phys. (Proc. Suppl.

New Perspectives for B-Physics from the Lattice

We give an introduction to the problems faced on the way to a reliable lattice QCD computation of B-physics matrix elements. In particular various approaches for dealing with the large scale introduced by the heaviness of the b-quark are mentioned and promising recent achievements are described. We present perspectives for future developments.Comment: Invited talk at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 15 pages LaTeX. PSN FRAT07. Updated references and result of ref.[40

Fundamental parameters of QCD

The theory of strong interactions, QCD, is described in terms of a few parameters, namely the strong coupling constant alpha_s and the quark masses. We show how these parameters can be determined reliably using computer simulations of QCD on a space-time lattice, and by employing a finite-size scaling method, which allows to trace the energy dependence of alpha_s and quark masses over several orders of magnitude. We also discuss methods designed to reduce the effects of finite lattice spacing and address the issue of computer resources required.Comment: Contribution to proceedings of NIC Symposium 2001, 13 pages, 7 figures, uses nic-series.cl

Non-perturbative computation of the strong coupling constant on the lattice

We review the long term project of the ALPHA collaboration to compute in QCD the running coupling constant and quark masses at high energy scales in terms of low energy hadronic quantities. The adapted techniques required to numerically carry out the required multiscale non-perturbative calculation with our special emphasis on the control of systematic errors are summarized. The complete results in the two dynamical flavor approximation are reviewed and an outlook is given on the ongoing three flavor extension of the programme with improved target precision.Comment: 30 pages, 20 figures, Contribution to the Proceedings of the Final Meeting of DFG SFB-TR-9 (Durbach, Germany, Sept. 2014), to appear in Nucl. Phys. (Proc. Suppl.)

Large NN scaling and factorization in SU(N)\mathrm{SU}(N) Yang-Mills theory

We present results for Wilson loops smoothed with the Yang-Mills gradient flow and matched through the scale $t_0$. They provide renormalized and precise operators allowing to test the $1/N^2$ scaling both at finite lattice spacing and in the continuum limit. Our results show an excellent scaling up to $1/N = 1/3$. Additionally, we obtain a very precise non-perturbative confirmation of factorization in the large $N$ limit.Comment: 8 pages, 7 figures. Presented at the 35th International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June 2017 (Lattice 2017

Large NN scaling and factorization in SU(NN) Yang-Mills gauge theory

The large $N$ limit of SU($N$) gauge theories is well understood in perturbation theory. Also non-perturbative lattice studies have yielded important positive evidence that 't Hooft's predictions are valid. We go far beyond the statistical and systematic precision of previous studies by making use of the Yang-Mills gradient flow and detailed Monte Carlo simulations of SU($N$) pure gauge theories in 4 dimensions. With results for $N=3,4,5,6,8$ we study the limit and the approach to it. We pay particular attention to observables which test the expected factorization in the large $N$ limit. The investigations are carried out both in the continuum limit and at finite lattice spacing. Large $N$ scaling is verified non-perturbatively and with high precision; in particular, factorization is confirmed. For quantities which only probe distances below the typical confinement length scale, the coefficients of the $1/N$ expansion are of $\mathrm{O}(1)$, but we found that large (smoothed) Wilson loops have rather large $\mathrm{O}(1/N^2)$ corrections. The exact size of such corrections does, of course, also depend on what is kept fixed when the limit is taken.Comment: 25 pages, 11 figure

Topological susceptibility and the sampling of field space in Nf=2N_f=2 lattice QCD simulations

We present a measurement of the topological susceptibility in two flavor QCD. In this observable, large autocorrelations are present and also sizable cutoff effects have to be faced in the continuum extrapolation. Within the statistical accuracy of the computation, the result agrees with the expectation from leading order chiral perturbation theory.Comment: 22 pages, 7 figures; References added, minor clarifications in the text, results unchange