19 research outputs found
Using NSPT for the Removal of Hypercubic Lattice Artifacts
The treatment of hypercubic lattice artifacts is essential for the
calculation of non-perturbative renormalization constants of RI-MOM schemes. It
has been shown that for the RI'-MOM scheme a large part of these artifacts can
be calculated and subtracted with the help of diagrammatic Lattice Perturbation
Theory (LPT). Such calculations are typically restricted to 1-loop order, but
one may overcome this limitation and calculate hypercubic corrections for any
operator and action beyond the 1-loop order using Numerical Stochastic
Perturbation Theory (NSPT). In this study, we explore the practicability of
such an approach and consider, as a first test, the case of Wilson fermion
bilinear operators in a quenched theory. Our results allow us to compare
boosted and unboosted perturbative corrections up to the 3-loop order.Comment: 7 pages, 6 figures, talk presented at the 32nd International
Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York,
USA; PoS(LATTICE2014)29
Discretization Errors for the Gluon and Ghost Propagators in Landau Gauge using NSPT
The subtraction of hypercubic lattice corrections, calculated at 1-loop order
in lattice perturbation theory (LPT), is common practice, e.g., for
determinations of renormalization constants in lattice hadron physics.
Providing such corrections beyond 1-loop order is however very demanding in
LPT, and numerical stochastic perturbation theory (NSPT) might be the better
candidate for this. Here we report on a first feasibility check of this method
and provide (in a parametrization valid for arbitrary lattice couplings) the
lattice corrections up to 3-loop order for the SU(3) gluon and ghost
propagators in Landau gauge. These propagators are ideal candidates for such a
check, as they are available from lattice simulations to high precision and can
be combined to a renormalization group invariant product (Minimal MOM coupling)
for which a 1-loop LPT correction was found to be insufficient to remove the
bulk of the hypercubic lattice artifacts from the data. As a bonus, we also
compare our results with the ever popular H(4) method.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on
Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German
SU(3) Landau gauge gluon and ghost propagators using the logarithmic lattice gluon field definition
We study the Landau gauge gluon and ghost propagators of SU(3) gauge theory,
employing the logarithmic definition for the lattice gluon fields and
implementing the corresponding form of the Faddeev-Popov matrix. This is
necessary in order to consistently compare lattice data for the bare
propagators with that of higher-loop numerical stochastic perturbation theory
(NSPT). In this paper we provide such a comparison, and introduce what is
needed for an efficient lattice study. When comparing our data for the
logarithmic definition to that of the standard lattice Landau gauge we clearly
see the propagators to be multiplicatively related. The data of the associated
ghost-gluon coupling matches up almost completely. For the explored lattice
spacings and sizes discretization artifacts, finite-size and Gribov-copy
effects are small. At weak coupling and large momentum, the bare propagators
and the ghost-gluon coupling are seen to be approached by those of higher-order
NSPT.Comment: 18 pages, 19 figures, 5 table
Exploring the Nucleon Structure from First Principles of QCD
Quantum Chromodynamics (QCD) is generally assumed to be the fundamental
theory underlying nuclear physics. In recent years there is progress towards investigating the
nucleon structure from first principles of QCD. Although this structure is best revealed in Deep
Inelastic Scattering, a consistent analysis has to be performed in a fully non-perturbative scheme.
The only known method for this purpose are lattice simulations. We first sketch the ideas of
Monte Carlo simulations in lattice gauge theory. Then we comment in particular on the issues
of chiral symmetry and operator mixing. Finally we present our results for the Bjorken variable
of a single quark, and for the second Nachtmann moment of the nucleon structure functions
Lattice studies at zero and finite temperature in the SU(2) Higgs model at small couplings
Bunk B, Ilgenfritz E-M, Kripfganz J, Schiller A. Lattice studies at zero and finite temperature in the SU(2) Higgs model at small couplings. Physics Letters B. 1992;284(3-4):371-376.In the weak coupling region (beta=8, lambda=0.0017235 and 0.023705) the Higgs transition is determined on symmetrical (16(4)) as well as thermal (16(3)xN(tau)) lattices. This transition is weakly first order and becomes weaker for larger lambda. Higgs and vector boson masses are obtained near to the phase transition, consistent with a mass ratio depending on lambda only. The transition temperature is obtained as a function of the Higgs mass. The results are compared with perturbative relations