QCD lattice simulations yield hadron masses as functions of the quark masses. From the gradients of the hadron masses the sigma terms can then be determined. We consider here dynamical 2+1 flavour simulations, in which we start from a point of the fl
avour symmetric line and then keep the singlet or average quark mass fixed as we approach the physical point. This leads to highly constrained fits for hadron masses in a multiplet. The gradient of this path for a hadron mass then gives a relation between the light and strange sigma terms. A further relation can be found from the change in the singlet quark mass along the flavour symmetric line. This enables light and strange sigma terms to be estimated for the baryon octet.
QCD lattice simulations determine hadron masses as functions of the quark masses. From the gradients of these masses and using the Feynman-Hellmann theorem the hadron sigma terms can then be determined. We use here a novel approach of keeping the sin
glet quark mass constant in our simulations which upon using an SU(3) flavour symmetry breaking expansion gives highly constrained (i.e. few parameter) fits for hadron masses in a multiplet. This is a highly advantageous procedure for determining the hadron mass gradient as it avoids the use of delicate chiral perturbation theory. We illustrate the procedure here by estimating the light and strange sigma terms for the baryon octet.
We summarize the higher-loop perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with results from lattice simulations in order to expose the genuinely non-perturbative content of the
latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost and gluon propagators in Landau gauge up to three and four loops. We present results in the infinite volume and $a to 0$ limits, based on a general fitting strategy.
This is the second of two papers devoted to the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Such a computation should enable a comparison with results from lattice simulations in order to reveal the genu
inely non-perturbative content of the latter. The gluon propagator is computed by means of Numerical Stochastic Perturbation Theory: results range from two up to four loops, depending on the different lattice sizes. The non-logarithmic constants for one, two and three loops are extrapolated to the lattice spacing $a to 0$ continuum and infinite volume $V to infty$ limits.
This is the first of a series of two papers on the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to eventually compare with results from lattice simulations in order to enlight the genuine
ly non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost propagator in Landau gauge up to three loops. We present results in the infinite volume and $a to 0$ limits, based on a general strategy that we discuss in detail.
We complete our high-accuracy studies of the lattice ghost propagator in Landau gauge in Numerical Stochastic Perturbation Theory up to three loops. We present a systematic strategy which allows to extract with sufficient precision the non-logarithmi
c parts of logarithmically divergent quantities as a function of the propagator momentum squared in the infinite-volume and $ato 0$ limits. We find accurate coincidence with the one-loop result for the ghost self-energy known from standard Lattice Perturbation Theory and improve our previous estimate for the two-loop constant contribution to the ghost self-energy in Landau gauge. Our results for the perturbative ghost propagator are compared with Monte Carlo measurements of the ghost propagator performed by the Berlin Humboldt university group which has used the exponential relation between potentials and gauge links.
We calculate Wilson loops of various sizes up to loop order $n=20$ for lattice sizes of $L^4 (L=4, 6, 8, 12)$ using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the perturbativ
e series at high orders. We discuss three models to estimate the perturbative series: a renormalon inspired fit, a heuristic fit based on an assumed power-law singularity and boosted perturbation theory. We have found differences in the behavior of the perturbative series for smaller and larger Wilson loops at moderate $n$. A factorial growth of the coefficients could not be confirmed up to $n=20$. From Monte Carlo measured plaquette data and our perturbative result we estimate a value of the gluon condensate $<frac{alpha}{pi}GG>$.
We present higher loop results for the gluon and ghost propagator in Landau gauge on the lattice calculated in numerical stochastic perturbation theory. We make predictions for the perturbative content of those propagators as function of the lattice
momenta for finite lattices. To find out their nonperturbative contributions, the logarithmic definition of the gauge fields and the corresponding Faddeev-Popov operator have to be implemented in the Monte Carlo simulations.
For the Stout Link Non-perturbative Clover (SLiNC) action we determine in one-loop lattice perturbation theory the critical hopping parameter $kappa_c$ and the clover parameter $c_{SW}$ which is needed for $mathcal{O}(a)$ improvement. Performing this
calculation off-shell we are also able to compute the non gauge invariant quark field improvement coefficient $c_{NGI}$. Additionally, we present first results for the renormalization factors of the scalar, pseudoscalar, vector and axial vector currents. We discuss mean field improvement for the SLiNC action.
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume
limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.
