Renormalization and running of quark mass and field in the regularization invariant and schemes at three and four loops

Abstract

We derive explicit transformation formulae relating the renormalized quark mass and field as defined in the MS-scheme with the corresponding quantities defined in any other scheme. By analytically computing the three-loop quark propagator in the high-energy limit (that is keeping only massless terms and terms of first order in the quark mass) we find the NNNLO conversion factors transforming the MS quark mass and the renormalized quark field to those defined in a "Regularization Invariant" (RI) scheme which is more suitable for lattice QCD calculations. The NNNLO contribution in the mass conversion factor turns out to be large and comparable to the previous NNLO contribution at a scale of 2 GeV -the typical normalization scale employed in lattice simulations. Thus, in order to get a precise prediction for the MS masses of the light quarks from lattice calculations the latter should use a somewhat higher scale of around, say, 3 GeV where the (apparent) convergence of the perturbative series for the mass conversion factor is better.We also compute two more terms in the high-energy expansion of the MS renormalized quark propagator. The result is then used to discuss the uncertainty caused by the use of the high energy limit in determining the MS mass of the charmed quark. As a by-product of our calculations we determine the four-loop anomalous dimensions of the quark mass and field in the Regularization Invariant scheme. Finally, we discuss some physical reasons lying behind the striking absence of ζ(4) in these computed anomalous dimensions.

Renormalization of quark propagators from twisted-mass lattice QCD atNf=2

“…The discrepancy is anyhow only affecting the conversion of Z RI q to Z MS pert q at 2 GeV. In Table 6 of [28] one finds results for Z MS q obtained at 2 GeV by applying the standard perturbative conversion formulae [13]. Indeed, they turn out to be in between our results in Eq.…”

“…its running starts at O(α 2 ). The perturbative running has been computed up to four loops [13] and references therein. The needed formulae are accessible on the web site also indicated in ref.…”

“…We use µ = µ = 10 GeV as the renormalisation scale ; c RI 0Zq (p 2 , µ 2 ) is computed from the four loop perturbative running of Z q [13]: was obtained in appendix A. We express the lattice spacing (cut-off) dependence as a dependence in g 2 bare .…”

Kaon mixing beyond the SM from Nf = 2 tmQCD and model independent constraints from the UTA

“…Results are obtained with methods M1 and M2 [18] at each value of the gauge coupling in MS and RI-MOM at 2 GeV. We have used the three-loop conversion formula from RI-MOM to MS [56].…”

Lattice QCD determination of m b , f B and f Bs with twisted mass Wilson fermions

“…known up to N 3 LO in perturbation theory [19][20][21][22][23][24][25]. The NLO expression reads used for N f = 2 in the present analysis.…”