18 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
Structure functions from the Compton amplitude
We have initiated a program to compute the Compton amplitude from lattice QCD with the Feynman-Hellman method. This amplitude is related to the structure function via a Fredholm integral equation of the first kind. It is known that these types of equations are inherently ill--posed - they are, e.g., extremely sensitive to perturbations of the system. We discuss two methods which are candidates to handle these problems: the model free inversion based on singular value decomposition and one Bayesian type approach. We apply the Bayesian method to currently available lattice data for the Compton amplitude
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
Anomalous magnetic moment of the muon with dynamical QCD+QED
There exists a long standing discrepancy of around 3.5Ï between experimental measurements and standard model calculations of the magnetic moment of the muon. Current experiments aim to reduce the experimental uncertainty by a factor of 4, and Standard Model calculations must also be improved by a similar factor. The largest uncertainty in the Standard Model calculation comes from the QCD contribution, in particular the leading order hadronic vacuum polarisation (HVP). To calculate the HVP contribution, we use lattice gauge theory, which allows us to study QCD at low energies. In order to better understand this quantity, we investigate the effect of QED corrections to the leading order HVP term by including QED in our lattice calculations, and investigate flavour breaking effects. This is done using fully dynamical QCD+QED gauge configurations generated by the QCDSF collaboration and a novel method of quark tuning
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