Quark Bilinear Operators Research Articles

Non-perturbative renormalization of lattice operators in coordinate space

We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute the renormalization constants of bilinear quark operators for the non-perturbative O(a)-improved Wilson action in the quenched approximation. The matching with perturbative schemes, such as MS¯, is computed at the next-to-leading order in continuum perturbation theory. A feasibility study of this technique with Neuberger fermions is also presented.

Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action

We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)-improved Wilson action. The results are obtained in the quenched approximation at four values of the lattice coupling by using the non-perturbative RI/MOM renormalization method. Several sources of systematic uncertainties, including discretization errors and final volume effects, are examined. The contribution of the Goldstone pole, which in some cases may affect the extrapolation of the renormalization constants to the chiral limit, is non-perturbatively subtracted. The scale independent renormalization constants of bilinear quark operators have been also computed by using the lattice chiral Ward identities approach and compared with those obtained with the RI-MOM method. For those renormalization constants the non-perturbative estimates of which have been already presented in the literature we find an agreement which is typically at the level of 1%.

Renormalization of bilinear quark operators for the chirally improved lattice Dirac operator

We compute non-perturbative renormalization constants of fermionic bilinears for the chirally improved lattice fermions in the quenched approximation of QCD. We address finite size effects and the influence of Gribov copies. Our results are presented in the RI′ and MS schemes as well as in RGI form and we discuss relations between the renormalization constants implied by chiral symmetry.

One-loop renormalisation of quark bilinears for overlap fermions with improved gauge actions

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.

Quark spectra and light hadron phenomenology from overlap fermions with improved gauge field action

We present first results from a simulation of quenched overlap fermions with improved gauge field action. Among the quantities we study are the spectral properties of the overlap operator, the chiral condensate and topological charge, quark and hadron masses, and selected nucleon matrix elements. To make contact with continuum physics, we compute the renormalization constants of quark bilinear operators in perturbation theory and beyond.

Perturbative renormalization factors in domain-wall QCD with improved gauge actions

We evaluate renormalization factors of the domain-wall fermion system with various improved gauge actions at one loop level. The renormalization factors are calculated for quark wave function, quark mass, bilinear quark operators, three- and four-quark operators in modified minimal subtraction (MS-bar) scheme with the dimensional reduction(DRED) as well as the naive dimensional regularization(NDR). We also present detailed results in the mean field improved perturbation theory.

Non-perturbative renormalization constants and light quark masses

We present the results of an extensive non-perturbative calculation of the renormalization constants of bilinear quark operators for the non-perturbativelyO(a)-improved Wilson action. The results are obtained at four values of the lattice coupling, by using the RI/MOM and the Ward identities methods. A new non-perturbative renormalization technique, which is based on the study of the lattice correlation functions at short distance in x-space, is also numerically investigated. We then use our non-perturbative determination of the quark mass renormalization constants to compute the values of the strange and the average up/down quark masses. After performing an extrapolation to the continuum limit, we obtain M s MS¯(2GeV= (106 ± 2 ± 8) MeV and m l MS¯(2 GeV) = (4.4 ± 0.1 ± 0.4) MeV.

Some remarks on O( a) improved twisted mass QCD

Twisted mass QCD (tmQCD) has been introduced as a solution to the problem of unphysical fermion zero modes in lattice QCD with quarks of the Wilson type. We here argue that O( a) improvement of the tmQCD action and simple quark bilinear operators can be more economical than in the standard framework. In particular, an improved and renormalized estimator of the pion decay constant in two-flavour QCD is available, given only the Sheikholeslami-Wohlert coefficient c sw and an estimate of the critical mass m c.

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1, 2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacinga. Based on the generalised transfer matrix, we define the tmQCD Schrödinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.

Non-perturbative renormalisation with domain wall fermions

We present results from a study of the renormalisation of both quark bilinear and four-quark operators for the domain wall fermion action, using the non-perturbative renormalisation technique of the Rome-Southampton group. These results are from a quenched simulation, on a 16 3 × 32 lattice, with β = 6.0 and L s = 16.

Quark masses and renormalization constants from quark propagator and 3-point functions

We have computed the light and strange quark masses and the renormalization constants of the quark bilinear operators, by studying the large- p 2 behaviour of the lattice quark propagator and 3-point functions. The calculation is non-perturbatively improved, at O( a), in the chiral limit. The method used to compute the quark masses has never been applied so far, and it does not require an explicit determination of the quark mass renormalization constant.

Scaling property of domain-wall QCD in perturbation theory

We estimate the lattice artifacts in loop corrections perturbatively for domain-wall QCD with an infinite number of extra flavors. We find that there appear no $\mathcal{O}(a)$ errors in renormalization factors of the quark wave function, mass, and quark bilinear operators at the one- and two-loop levels with off-shell quark momentum. Our proof is based on the even- or oddness of the quantum correction in terms of the quark external momentum and mass, and it can be extended to any loop level.

Perturbative renormalization factors of quark bilinear operators for domain-wall QCD

We calculate one-loop renormalization factors of bilinear operators made of physical quark fields for domain-wall QCD. We find that finite parts of such renormalization factors have reasonable values at 1-loop except an overlap factor between the physical quark field and the zero mode in the theory. We point out that the 1-loop estimate of overall renormalization factors becomes unreliable at the coupling where numerical simulations are currently performed, due to the presence of this overlap factor. We show that this problem disappears if the mean-field improved perturbation theory is employed for renormalization factors.

Non-perturbative renormalization factors of bilinear quark operators for Kogut-Susskind fermions and light quark masses in quenched QCD

Light quark masses are computed for Kogut-Susskind fermions by evaluating non-perturbatively the renormalization factor for bilinear quark operators. Calculations are carried out in the quenched approximation at β = 6.0, 6.2, and 6.4. For the average up and down quark mass we find m MS (2GeV) = 4.15(27)MeV in the continuum limit, which is significantly larger than 3.51(20)MeV ( q * = 1/ a) or 3.40(21)MeV ( q * = π/ a) obtained with the one-loop perturbative renormalization factor.

One-loop renormalization factors and mixing coeffecients of bilinear quark operators for improved gluon and quark actions

We calculate one-loop renormalization factors and mixing coefficients of bilinear quark operators for a class of gluon actions with six-link loops and O(a)-improved quark action. The calculation is carried out by evaluating on-shell Green's functions of quarks and gluons in the standard perturbation theory. We find a general trend that finite parts of one-loop coefficients are reduced approximately by a factor two for the renormalization-group improved gluon actions compared with the case of the standard plaquette gluon action.

Perturbative calculation of improvement coefficients toO(g2a)for bilinear quark operators in lattice QCD

We calculate the ${O(g}^{2}a)$ mixing coefficients of bilinear quark operators in lattice QCD using a standard perturbative evaluation of on-shell Green's functions. Our results for the plaquette gluon action are in agreement with those previously obtained with the Schr\"odinger functional method. The coefficients are also calculated for a class of improved gluon actions having six-link terms.

Perturbative renormalization factors of bilinear quark operators for improved gluon and quark actions in lattice QCD

We calculate one-loop renormalization factors of bilinear quark operators for the gluon action including six-link loops and an $O(a)$-improved quark action in the limit of a massless quark. We find that finite parts of the one-loop coefficients of renormalization factors diminish monotonically as either of the coefficients ${c}_{1}$ or ${c}_{2}{+c}_{3}$ of the six-link terms is decreased below zero. Detailed numerical results are given, for general values of the clover coefficient, for the tree-level improved gluon action in the Symanzik approach ${(c}_{1}=\ensuremath{-}{1/12,c}_{2}{=c}_{3}=0)$ and for the choices suggested by Wilson ${(c}_{1}=\ensuremath{-}{0.252,c}_{2}{=0,c}_{3}=\ensuremath{-}0.17)$ and by Iwasaki ${(c}_{1}=\ensuremath{-}{0.331,c}_{2}{=c}_{3}=0$ and ${c}_{1}=\ensuremath{-}{0.27,c}_{2}{+c}_{3}=\ensuremath{-}0.04)$ from renormalization-group analyses. Compared with the case of the standard plaquette gluon action, the finite parts of the one-loop coefficients are reduced by 10--20 % for the Symanzik action, and approximately by a factor of 2 for the renormalization-group improved gluon actions.

Further one-loop results in O( a) improved lattice QCD

Using the Schrödinger functional we have computed a variety of renormalized on-shell correlation functions to one-loop order of perturbation theory. By studying their approach to the continuum limit we have determined the O( a) counterterms needed to improve the quark mass and a number of isovector quark bilinear operators.

Perturbative renormalisation of bilinear quark and gluon operators

The renormalisation constants for local bilinear quark operators are calculated using the Sheikholeslami-Wohlert improved action. In addition we compute the renormalisation constant of the leading gluon operator for different group representations and discuss the mixing of the operators E 2 and B 2 .

Perturbative renormalization of lattice bilinear quark operators

Our aim is to compute the lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon on the lattice. The theoretical basis of the calculation is the operator product expansion. To construct operators with the appropriate continuum behavior out of the bare lattice operators, one must absorb the effects of momentum scales far greater than any physical scale into a renormalization of the operators. In this work we compute the renormalization constants of all bilinear quark operators of leading twist and spin up to four. The calculation is done for Wilson fermions and in the quenched approximation where dynamical quark loops are neglected.