The three-loop β-function of QCD with the clover action

Bode, Achim; Panagopoulos, H.

doi:10.1016/s0550-3213(02)00012-3

Cited by 40 publications

(44 citation statements)

References 20 publications

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“…For the relation between the renormalized coupling constant, g R , and the bare one, g: g R =Z −1 g g, we use the two-loop results of Ref. [13] for Z g corresponding to clover fermions and Wilson gluons. R(µ, 2 GeV) is expressed in terms of Λ MS which for N f =3 was estimated to be 339 MeV [14].…”

Section: B Conversion To Msmentioning

confidence: 99%

Renormalization of local quark-bilinear operators forNf=3flavors of stout link nonperturbative clover fermions

et al. 2015

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The renormalization factors of local quark-bilinear operators are computed non-perturbatively for N f = 3 flavors of SLiNC fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing a = 0.074 fm, and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of the local bilinears to one loop in perturbation theory. We investigate lattice artifacts by computing them perturbatively to second order as well as to all orders in the lattice spacing. The renormalization conditions are defined in the RI ′ -MOM scheme, for both the perturbative and non-perturbative results. The renormalization factors, obtained at different values of the renormalization scale, are translated to the MS scheme and are evolved perturbatively to 2 GeV. Any residual dependence on the initial renormalization scale is eliminated by an extrapolation to the continuum limit. We also study the various sources of systematic errors.Particular care is taken in correcting the non-perturbative estimates by subtracting lattice artifacts computed to one loop perturbation theory using the same action. We test two different methods, by subtracting either the O(g 2 a 2 ) contributions, or the complete (all orders in a) oneloop lattice artifacts.

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Section: B Conversion To Msmentioning

confidence: 99%

Renormalization of local quark-bilinear operators forNf=3flavors of stout link nonperturbative clover fermions

et al. 2015

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“…Such groups are formed by diagrams (7-11), (12)(13), (14)(15)(16)(17)(18), (19)(20), (21)(22)(23) in Fig.2, diagrams (3-7), (8)(9), (10)(11)19) in Fig.4 and diagrams (1-2), (3-4) in Fig.5.…”

Section: Computation and Resultsmentioning

confidence: 99%

“…Our 1-loop results, performed in a generic gauge, are in agreement with results found in the literature (see, e.g., Refs. [4,20]). …”

Section: B Definition Of Renormalized Quantitiesmentioning

confidence: 99%

Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice

Skouroupathis

Panagopoulos

2007

Phys. Rev. D

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We compute the two-loop renormalization functions, in the RI ′ scheme, of local bilinear quark operatorsψΓψ, where Γ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, Z m .As a prerequisite for the above, we also compute the quark field renormalization, Z ψ , up to two loops.We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in c SW , in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge.Finally, we present our results in the M S scheme, for easier comparison with calculations in the continuum.The corresponding results, for fermions in an arbitrary representation, are included in an Appendix.

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“…A first case study of this kind, regarding the β-function with clover improvement, has now been completed and is presented in Ref. [6]. …”

Section: (I)mentioning

confidence: 99%

Critical hopping parameter inO(a)improved lattice QCD

Panagopoulos

Proestos

2001

Phys. Rev. D

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We calculate the critical value of the hopping parameter, κ c , in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions.The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory.The dependence of our results on the number of colors N , the number of fermionic flavors N f , and the clover parameter c SW , is shown explicitly. We compare our results to non perturbative evaluations of κ c coming from Monte Carlo simulations.

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The three-loop β-function of QCD with the clover action

Cited by 40 publications

References 20 publications

Renormalization of local quark-bilinear operators forNf=3flavors of stout link nonperturbative clover fermions

Renormalization of local quark-bilinear operators forNf=3flavors of stout link nonperturbative clover fermions

Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice

Critical hopping parameter inO(a)improved lattice QCD

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