Empirical central limit theorems for ergodic automorphisms of the torus

Let T be an ergodic automorphism of the d-dimensional torus T^d, and f be a continuous function from T^d to R^l. On the probability space T^d equipped with the Lebesgue-Haar measure, we prove the weak convergence of the sequential empirical process of the sequence (f o T^i)_{i \geq 1} under some mild conditions on the modulus of continuity of f. The proofs are based on new limit theorems and new inequalities for non-adapted sequences, and on new estimates of the conditional expectations of f with respect to a natural filtration.Comment: 32 page

Ghost-gluon coupling, power corrections and ΛMSˉ\Lambda_{\bar{MS}} from twisted-mass lattice QCD at Nf=2N_f=2

A non-perturbative calculation of the ghost-gluon running QCD coupling constant is performed using $N_f=2$ twisted-mass dynamical fermions. The extraction of $\Lambda_{\bar{MS}}$ in the chiral limit reveals the presence of a non-perturbative OPE contribution that is assumed to be dominated by a dimension-two \VEV{A^2} condensate. In this contest a novel method for calibrating the lattice spacing in lattice simulations is presented.Comment: 7 pages, 4 figures, XXVIII International Symposium on Lattice Field Theory 201

Modified instanton profile effects from lattice Green functions

We trace here instantons through the analysis of pure Yang-Mills gluon Green functions in the Landau gauge for a window of IR momenta (0.4 GeV $< k < 0.9$ GeV). We present lattice results that can be fitted only after substituting the BPST profile in the Instanton liquid model (ILM) by one based on the Diakonov and Petrov variational methods. This also leads us to gain information on the parameters of ILM.Comment: 32 pagex, 6 figure

A Ghost Story II: Ghosts, Gluons and the Gluon condensate beyond the IR of QCD

Beyond the deep IR, the analysis of ghost and gluon propagators still keeps very interesting non-perturbative information. The Taylor-scheme coupling can be computed and applied to obtain the $\Lambda_{\rm QCD}$ parameter from Landau gauge lattice simulations. Furthermore, a dimension-two gluon condensate, that can be understood in the instanton liquid model, plays an important role in the game.Comment: 12 pp., 3 fig

Yukawa model on a lattice: two body states

We present first results of the solutions of the Yukawa model as a Quantum Field Theory (QFT) solved non perturbatively with the help of lattice calculations. In particular we will focus on the possibility of binding two nucleons in the QFT, compared to the non relativistic result.Comment: 3 pages, talk at "IVth International Conference on Quarks and Nuclear Physics" (Madrid, June 2006

Two body scattering length of Yukawa model on a lattice

The extraction of scattering parameters from Euclidean simulations of a Yukawa model in a finite volume with periodic boundary conditions is analyzed both in non relativistic quantum mechanics and in quantum field theory.Comment: 4 pages, talk at "18th International IUPAP conference on Few Body Problems in Physics" (Sao Paulo, August 2006

Renormalisation of quark propagators from twisted-mass lattice QCD at NfN_f=2

We present results concerning the non-perturbative evaluation of the renormalisation constant for the quark field, $Z_q$, from lattice simulations with twisted mass quarks and three values of the lattice spacing. We use the RI'-MOM scheme. $Z_q$ has very large lattice spacing artefacts; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalisation constants. We recall and develop the non-perturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice spacing artefacts scale indeed as $a^2p^2$. We then study the running of $Z_q$ with particular attention to the non-perturbative effects, presumably dominated by the dimension-two gluon condensate \VEV{A^2} in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units confirming that it is a continuum effect. It gives a $\sim 4$ contribution at 2 GeV. Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties. Finally combining all our results and using the known Wilson coefficient of \VEV{A^2} we find g^2(\mu^2) \VEV{A^2}_{\mu^2\; CM} = 2.01(11)(^{+0.61}_{- 0.73}) \;\mathrm {GeV}^2 at $\mu=10\, \mathrm{GeV}$, in fair agreement within uncertainties with the value indepently extracted from the strong coupling constant.Comment: 38 pages, 8 tables, 8 figure