Lattice and renormalons in heavy quark physics

Czechoslovak Journal of Physics, 1986

Recent results of lattice Monte-Carlo calculations in QCD are used to estimate the value of Ax/~. Special attention is paid to the role played by the light quarks in the construction of the continuum limit in QCD. The resulting value of A~ 9 S turns out to be strongly dependent on nf, the number of light quarks taken into account.

Nuclear Physics B, 2006

We present results for the light quark masses obtained from a lattice QCD simulation with N f = 2 degenerate Wilson dynamical quark flavours. The sea quark masses of our lattice, of spacing a ≃ 0.06 fm, are relatively heavy, i.e., they cover the range corresponding to 0.60 M P /M V 0.75. After implementing the non-perturbative RI-MOM method to renormalise quark masses, we obtain m MS ud (2 GeV) = 4.3 ± 0.4 +1.1

Proceedings of the …, 2001

Lattice-based investigations of two fundamental QCD quantities are described, namely the gluon and quark propagators in Landau gauge. We have studied the Landau gauge gluon propagator using a variety of lattices with spacings from a = 0.17 to 0.41 fm to explore finite volume and discretization effects. We also introduce the general method of "tree-level correction" to minimize the effect of lattice artefacts at large momenta. We demonstrate that it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings and to explore the infinite volume and continuum limits of the Landau-gauge gluon propagator. These results confirm the earlier conclusion that the Landau gauge gluon propagator is infrared finite. We study the Landau gauge quark propagator in quenched QCD using two forms of the O(a)-improved propagator with the Sheikholeslami-Wohlert quark action with the nonperturbative value for the clover coefficient csw and mean-field improvement coefficients in our improved quark propagators. We again implement an appropriate form of tree-level correction. We find good agreement between our improved quark propagators. The extracted value of infrared quark mass in the chiral limit is found to be 300 ± 30 MeV. We conclude that the momentum regime where the transition from nonperturbative to perturbative QCD occurs is Q 2 ≃ 4 GeV 2 .

Physical Review D, 2006

We study the scaling behavior of the quark propagator on two lattices with similar physical volume in Landau gauge with 2+1 flavors of dynamical quarks in order to test whether we are close to the continuum limit for these lattices. We use configurations generated with an improved staggered ("Asqtad") action by the MILC collaboration. The calculations are performed on 28 3 × 96 lattices with lattice spacing a = 0.09 fm and on 20 3 × 64 lattices with lattice spacing a = 0.12 fm. We calculate the quark mass function, M (q 2 ), and the wave-function renormalization function, Z(q 2 ), for a variety of bare quark masses. Comparing the behavior of these functions on the two sets of lattices we find that both Z(q 2 ) and M (q 2 ) show little sensitivity to the ultraviolet cutoff.

2008

Dependence of a/r c (inverse Sommer parameter in units of lattice spacing a) on am q (quark mass in lattice unit) has been observed in all lattice QCD simulations with sea quarks including the ones with improved actions. How much of this dependence is a scaling violation has remained an intriguing question. Our approach has been to investigate the issue with an action with known lattice artifacts, i.e., the standard Wilson quark and gauge action with β = 5.6 and 2 degenerate flavors of sea quarks on 16 3 × 32 lattices. In order to study in detail the sea quark mass dependence, measurements are carried out at eight values of the PCAC quark mass values am q from about 0.07 to below 0.015. Though scaling violations may indeed be present for relatively large am q , a consistent scenario at sufficiently small am q seems to emerge in the mass-independent scheme where for a fixed β , 1/r 0 and √ σ have linear dependence on m q as physical effects similar to the quark mass dependence of the rho mass. We present evidence for this scenario and accordingly extract the lattice scale (a = 0.0805(7) fm, a −1 = 2.45(2) GeV) by chiral extrapolation to the physical point.

In this paper we extend the estimate of the value of the lattice spacing a in units of the r 0 scale at values of the bare coupling larger than those available. By using results from the computation of the renormalised coupling in the Schrödinger functional formalism we find that from β ≃ 7 onward the behaviour predicted by asymptotic freedom at tree loop describes very well the data if a value of r 0 Λ slightly lower then the latest available is used. We also show that, by sticking to the current value, an effective four loop term can describe as well the data. The systematic relative error on the lattice spacing induced by the choice of the procedure is between 1% and 3% for 6.92 < β < 8.5.

Nuclear Physics B - Proceedings Supplements, 1998

We have technically improved the non-perturbative renormalization method, proposed by Martinelli et al., by using quark momentum sources and sinks. Composite two-fermion operators up to three derivatives have been measured for Wilson fermions and Sheikholeslami-Wohlert improved fermions in the quenched approximation. The calculations are performed in the Landau gauge on 16 3 32 lattices at β = 6.0 for 3 κ values in each case. The improved sources greatly decrease the statistical noise. We extract and discuss here renormalization factors for local operators and moments of the structure functions for Wilson fermions.

Arxiv preprint hep-lat/0012011, 2000

Arxiv preprint hep-ph/0301138, 2003

Heavy-light mesons, heavy quarkonium and doubly heavy baryons are briefly discussed. Effective field theories (EFTs) of QCD based on the heavy quark mass expansion 1/mQ provide a unified frame-work to describe all three systems. They produce a number of model-independent ...

Physical Review D, 2010

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.