High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents

We present a high order perturbative computation of the renormalization constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The computational setup is the one provided by the RI'-MOM scheme. Three- and four-loop expansions are made possible by Numerical Stochastic Perturbation Theory. Results are given for various numbers of flavours and/or (within a finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also present four-loop results. Finite size effects are well under control and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with convergence properties of the series. The latter is best discussed in the framework of Boosted Perturbation Theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of Lattice QCD RC's are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, also for which results are for generic n_f up to three loops, while a four-loop result is obtained for n_f=2

Understanding stochastic perturbation theory: toy models and statistical analysis

The numerical stochastic perturbation method based on Parisi-Wu quantisationis applied to a suite of simple models to test its validity at high orders.Large deviations from normal distribution for the basic estimators aresystematically found in all cases (``Pepe effect''). As a consequence oneshould be very careful in estimating statistical errors. We present someresults obtained on Weingarten's ``pathological'' model where reliable resultscan be obtained by an application of the bootstrap method. We also present someevidence that in the far less trivial application to Lattice Gauge Theory asimilar problem should not arise at moderately high loops (up toO(\alpha^{10}))

Inverse Renormalization Group in Quantum Field Theory

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional φ4 scalar field theory on sizes as small as V=82, we apply the inverse transformations to produce rescaled systems of size up to V′=5122 which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group

Transplantation activity in the Organizzazione Centro-Sud Trapianti: A retrospective study from 1999 to March 2004

Background. The Organizzazione Centro-Sud Trapianti (OCST) was set up in 1998 to coordinate the organ procurement and transplantation activity of 9 Italian regions (Abruzzo, Basilicata, Calabria, Campania, Lazio, Molise, Sardinia, Sicily, and Umbria), each referring to a local Regional Transplant Center. The aim of the present study was to estimate organ donation and transplantation rates in the OCST from 1999 to March 2004. Materials and Methods. A retrospective study of organ donors and transplantation activity in the OCST during the study period was performed, pointing out donor epidemiological data, such as age and sex ratio, causes of death, reasons for discarding, and transplantation rate. Donors reported to the OCST were divided into 6 groups: A (October 1998-December 1999), B (2000), C (2001), D (2002), E (2003), and F (January-March 2004). Results. From 1999 to March 2004, 2272 potential donors were reported to the OCST. The nonharvested donors rate increased up to 52% (Group F), which was lower than the previous period (Group E, 64%), but higher than in 1999 (Group A, 43%). The major contributing factor was family opposition, which was 38% in 2002 and 41% in 2003. Conclusions. The introduction of the OCST into the field of organ transplantation has yielded an increase in organ donation and transplantation activity within the regions that set it up from 1999-2003. This trend is a consequence of the growth of reported donors from the intensive care unit, which grew 12.7% from 2002 to 2003. From the data analysis of the first months of 2004, we expect confirmation of this trend

apeNEXT: A multi-TFlops Computer for Simulations in Lattice Gauge Theory

We present the APE (Array Processor Experiment) project for the development of dedicated parallel computers for numerical simulations in lattice gauge theories. While APEmille is a production machine in today's physics simulations at various sites in Europe, a new machine, apeNEXT, is currently being developed to provide multi-Tflops computing performance. Like previous APE machines, the new supercomputer is largely custom designed and specifically optimized for simulations of Lattice QCD.Comment: Poster at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 3 pages, Latex. PSN FRAP15. Replaced for adding forgotten autho

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.Comment: 36 pages, 15 figures, REVTEX documen

Large-order NSPT for lattice gauge theories with fermions:the plaquette in massless QCD

Numerical Stochastic Perturbation Theory (NSPT) allows for perturbative computations in quantum field theory. We present an implementation of NSPT that yields results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. The zero-momentum mode is removed by imposing twisted boundary conditions; in turn, twisted boundary conditions require us to introduce a smell degree of freedom in order to include fermions in the fundamental representation. As a first application, we compute the critical mass of two flavours of Wilson fermions up to order $O(\beta^{-7})$ in a ${\mathrm{SU}}(3)$ gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order $O(\beta^{-35})$ in a ${\mathrm{SU}}(3)$ gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.Comment: 49 pages, 28 figures. Revised version, to be published in EPJC. Some references added, typos corrected, and improved discussion on finite-volume effect