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

Abstract

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%.PACS numbers: 11.15.Ha, 12.38.Gc, 11.10.Gh.1 See also ref.[7] for a related study in the context of the lattice non-linear σ-model.• Finite volume effects have been examined by comparing the results of two independent simulations performed, at the same value of the lattice coupling (β = 6.0), on different lattice volumes.• Goldstone pole contributions: power suppressed contributions coming from the Goldstone pole, which may affect the extrapolation to the chiral limit of the RCs of the pseudoscalar density and of the four-fermion operators coupled to the Goldstone boson, have been non-perturbatively subtracted.The scale independent RCs of the vector and axial-vector currents, Z V and Z A , and the ratio Z P /Z S , have also been determined in this study by using the lattice chiral WI approach, and the results are compared with those obtained with the RI/MOM method. We also compare our determinations of these constants with those obtained by the AL-PHA [16,17] and LANL [18] Collaborations by using the WI method, and our determination of Z P with the one obtained by ALPHA [19] within the SF approach. We find an agreement which is typically at the level of 1%. Since the systematics involved in these approaches are different, these comparisons provide additional confidence on the high level of accuracy reached in the implementation of the RI/MOM non-perturbative method.Our final results for the RCs of bilinear quark operators and four-fermion operators are collected in tables 2-7. Preliminary results of the present study have been presented at the Lattice 2002 conference [5,20].The plan of this paper is as follows. In sec. 2 we give the details of the numerical simulation and briefly review the non-perturbative RI/MOM method used to determine lattice RCs. The various sources of systematic errors involved in the calculation are discussed in sec. 3, where we also provide estimates of the corresponding uncertainties. The results for the RCs of bilinear quark operators obtained with the RI/MOM method are summarized i...

Exploring twisted mass lattice QCD with the Clover term

“…Indeed, we find a very good agreement between our result and the non-twisted determination of Z V performed in Ref. [16] with the non-perturbative RI-MOM method.…”

“…For comparison, we also show in these plots the results obtained in [13] by employing Mtm-Wilson fermions with the non-optimal choice of the critical mass, as well as the results obtained with non-twisted Clover fermions (at β = 6.0) using data produced by our collaboration for the studies described in Refs. [16,21]. In the non-twisted case, the quark mass aµ in Figs.…”

“…[16]. With respect to previous quenched determinations of light quark masses, here we benefit from the use of Mtm-LQCD with the Clover term to probe ever lower values of the quark masses, and thereby reduce the errors due to the chiral extrapolation when determining the light up/down quark masses on the lattice.…”

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)Boucaud1, Soto2, Leroy3 et al. 2006Phys. Rev. D390190View full textAdd to dashboardCite

“…Let us recall that a certain flatness Z V p 2 at large p is also observed with the clover quark action, although it is not so good. Let us recall also that this region is the basis for the standard determi-nations of MOM renormalization constants, usually with the clover quark action (see for example [41], which presumes that discretization artifacts are not large there. Let us then recall that we have no theoretical argument supporting the statement that they are not large.…”

Performance of PHMC and HMC algorithms in Nf=4 LQCD with twisted Wilson quarks

“…refs. [6], [7] and [8]), the unquenched simulations with heavy c, "lightish" s and light u and d sea quarks, from which the non-renormalized and/or bare quantities are computed, can not be immediately used for the evaluation of the renormalization constants of the operators with non-vanishing anomalous dimension. Rather one has to perform, for each of the considered lattice resolutions, further dedicated simulations, now with n f = 4 degenerate sea quarks at a few different, not too large mass values.…”