Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-lat/0611013

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

F. Di Renzo·V. Miccio·L. Scorzato·C. Torrero
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

F. Di Renzo, V. Miccio, L. Scorzato, C. Torrero. 2007-05-08. High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents. https://doi.org/10.1140/epjc%2Fs10052-007-0319-2

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exact and Near-Exact Inverse Renormalization Group with Constrained Monte Carlo

We establish conditions for exactness of the inverse renormalization group via constrained Markov processes, a class of Monte Carlo simulations which sample the degrees of freedom within a block on a fine lattice under the constraint that they remain consistent with the corresponding degree of freedom on the coarse lattice according to a forward renormalization group transformation. We show analytically, for an arbitrary transformation, that constrained Markov processes correspond to an exact inversion of the renormalization group at the fixed point action, and to a near-exact inversion in the vicinity of the fixed point. We then optimize renormalization group transformations directly on inversely renormalized configurations to effectively map the action onto itself and ensure computational stability in the generation of configurations for high-dimensional systems. Starting from a set of uncorrelated configurations for the three-dimensional $ϕ^{4}$ quantum field theory at lattice volume $V=16^{3}$, we invert the renormalization group with constrained Monte Carlo to construct a set of uncorrelated, near-equilibrium configurations for $V=128^{3}$ and extract two critical exponents of the system. The inversion exhibits no critical slowing down, with dynamic critical exponent $z=0.03(2)$.

hep-lat↗
arXiv2026

First Overlap Formulation and Perturbative Results for Supersymmetric QCD

We present a lattice formulation of N=1 supersymmetric QCD (SQCD) based on overlap fermions, providing a discretization consistent with the Ginsparg-Wilson relation. Particular emphasis is placed on the construction of Yukawa terms that preserve a lattice-modified chiral symmetry involving overlap quarks and gluinos. To realize this modified chiral symmetry in the Yukawa sector, we follow Lüscher's strategy and introduce auxiliary Dirac and Majorana fermionic fields for the quark and gluino fields, respectively. After functional integration over these auxiliary fields, ultralocal interaction terms arise as additional contributions to the lattice action. Within this framework, and using the Wilson gauge action for gluons, we also carry out one-loop perturbative calculations. In particular, we compute the self-energies of the quark, gluon, gluino, and squark fields in the presence of quark and squark masses, enabling an unambiguous determination of the corresponding field and mass counterterms on the lattice. This work provides a robust foundation for future perturbative determinations of the fine-tunings of the gauge, Yukawa, and quartic couplings, and already shows, as expected, a reduction in the number of required counterterms relative to Wilson-type fermions.

hep-lat↗
arXiv2026

Quark-mass dependence of two-nucleon scattering

Understanding how the properties of the visible Universe depend on the parameters of the Standard Model of particle physics requires \emph{ab initio} theoretical computations. To that end, we investigate the quark-mass dependence of low-energy nucleon-nucleon scattering in the deuteron and dineutron channels. We perform lattice-QCD calculations at pion masses $M_π\approx 200$ and $280$ MeV and compare their results to phenomenology at the physical point and to a previous calculation at $M_π\approx 710$ MeV. Scattering amplitudes, phase shifts, and threshold parameters are determined from finite-volume spectra using quantization conditions that explicitly incorporate long-distance effects from one-pion exchange. We analyze the pion-mass dependence of scattering lengths and effective ranges using chiral effective field theory with Weinberg and Kaplan-Savage-Wise power countings. From this, we estimate the pion-mass derivatives of the inverse scattering lengths and binding momentum, at the physical point. Both power countings indicate that the deuteron unbinds near $M_π\approx 220$ MeV.

hep-lat↗