By introducing an additional operator into the action and using the Feynman–Hellmann theorem we describe a method to determine both the quark line connected and disconnected terms of matrix elements. ...As an illustration of the method we calculate the gluon contribution (chromo-electric and chromo-magnetic components) to the nucleon mass.
The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion ...decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann–Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.
QCD lattice simulations with 2+1 flavours typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass to its physical value and then the up-down ...quark mass. An alternative method of tuning the quark masses is discussed here in which the singlet quark mass is kept fixed, which ensures that the kaon always has mass less than the physical kaon mass. It can also take into account the different renormalisations (for singlet and non-singlet quark masses) occurring for non-chirally invariant lattice fermions and so allows a smooth extrapolation to the physical quark masses. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Results show the correct order for the baryon octet and decuplet spectrum and an extrapolation to the physical pion mass gives mass values to within a few percent of their experimental values.
A novel method for nonperturbative renormalization of lattice operators is introduced, which lends itself to the calculation of renormalization factors for nonsinglet as well as singlet operators. ...The method is based on the Feynman–Hellmann relation, and involves computing two-point correlators in the presence of generalized background fields arising from introducing additional operators into the action. As a first application, and test of the method, we compute the renormalization factors of the axial vector current Aμ and the scalar density S for both nonsinglet and singlet operators for Nf=3 flavors of SLiNC fermions. For nonsinglet operators, where a meaningful comparison is possible, perfect agreement with recent calculations using standard three-point function techniques is found.
We are investigating the direct determination and non-perturbative renormalisation of gluon matrix elements. Such quantities are sensitive to ultra– violet fluctuations, and are in general ...statistically noisy. To obtain statistically significant results, we extend an earlier application of the Feynman–Hellmann theorem to gluonic matrix elements to calculate a renormalisation factor in the
RI – MOM
scheme, in the quenched case. This work demonstrates that the Feynman–Hellmann method is capable of providing a feasible option for calculating gluon quantities.
A major objective of lattice QCD is the computation of hadronic
matrix elements. The standard method is to use three-point and
four-point correlation functions. An alternative approach,
requiring ...only the computation of two-point correlation functions
is to use the Feynman-Hellmann theorem. In this talk we develop this
method up to second order in perturbation theory, in a context appropriate
for lattice QCD. This encompasses the Compton Amplitude (which forms the
basis for deep inelastic scattering) and hadron scattering.
Some numerical results are presented showing results indicating what
this approach might achieve.
We investigate the non-perturbative renormalisation of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are ...relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.
We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. ...Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami–Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary
m
2/p
2
, in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg–Wilson relation, and show how to remove
O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.
We compute lattice renormalisation constants of local bilinear quark operators for overlap fermions and improved gauge actions. Among the actions we consider are the Symanzik, Lüscher–Weisz, Iwasaki ...and DBW2 gauge actions. The results are given for a variety of
ρ parameters. We show how to apply mean field (tadpole) improvement to overlap fermions. The question, what is a good gauge action, is discussed from the perturbative point of view. Finally, we show analytically that the gauge dependent part of the self-energy and the amputated Green functions are independent of the lattice fermion representation, using either Wilson or overlap fermions.
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