Two-loop relation between the bare lattice coupling and the coupling in pure SU(N) gauge theories

We compute the Schrödinger functional (SF) for the case of lattice QCD with Wilson fermions (with and without SW improvement) at two-loop order in lattice perturbation theory. This allows us to extract the three-loop β-function in the SF-scheme. These results are required to compute the running coupling, the Λ-parameter and quark masses by finite size techniques with negligible systematic errors. In addition our results enable the implementation of two-loop O(a) improvement in SF-simulations. This article is based on the revised version of ref. [11].

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“…The coefficients k i which have been computed in [9] and checked by the authors of ref. [10] are given by…”

Section: The Step Scaling Functionmentioning

confidence: 99%

“…The first step, the computation of the relationship of α MS to the bare lattice coupling α 0 , has been completed in refs. [9], [10] and [11]. In this paper we perform the second step, the relationship of α SF to α 0 for N f > 0 flavors (the case N f = 0 has already been presented in [12]- [14]).…”

Section: Introductionmentioning

confidence: 99%

Two-loop computation of the Schrödinger functional in lattice QCD

2000

Self Cite

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“…(4.1) and (4.2) hold is a consequence of the invariance of L toy under parity, P. Furthermore we note that η cr ¼ η cr ðg 2 s ; ρ; λ 0 Þ does not depend on the scalar field (squared) mass. 10 In conclusion, if one sets η ¼ η cr in (3.1), the transformationsχ L ×χ R are promoted to symmetries of the action up to irrelevant Oðb 2 Þ cutoff effects. Recalling the form of the exact symmetries χ L [Eq.…”

Section: Ivχ L ×χ R Symmetry Enhancement and Naturally Light Fermionmentioning

confidence: 90%

“…[9] and plotted as a function of a=r 0 after determining the relation between g 2 0 and aΛ QCD =r 0 Λ QCD combining results from Refs. [10][11][12][13][14]. Simulation data are extracted from measurements carried out in a number of LQCD studies employing Wilson fermions.…”

Section: A Some Numericsmentioning

confidence: 99%

Nonperturbative mechanism for elementary particle mass generation

Frezzotti

Rossi

2015

Phys. Rev. D

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Taking inspiration from lattice QCD data, we argue that a finite nonperturbative contribution to the quark mass is generated as a consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn triggered by the explicit breaking of chiral symmetry induced by the critical Wilson term in the action. In pure lattice QCD this mass term cannot be separated from the unavoidably associated linearly divergent contribution. However, if QCD is enlarged to a theory where also a scalar field is present, coupled to an SU(2) doublet of fermions via a Yukawa and a Wilson-like term, then in the phase where the scalar field takes a nonvanishing expectation value, a dynamically generated and "naturally" light fermion mass (numerically unrelated to the expectation value of the scalar field) is conjectured to emerge at a critical value of the Yukawa coupling where the symmetry of the model is maximally enhanced. Masses dynamically generated in this way display a natural hierarchy according to which the stronger is the strongest of the interactions the fermion is subjected to, the larger will be its mass.

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“…To be precise, 2-loop accuracy here means that we truncate the β-function at 2 loops and integrate the resulting renormalization group equation exactly. Thanks to the recent work (Bode (1997), Lüscher and Weisz (1995)), we can also compare to the 3-loop evolution of the coupling. It is surprising that the perturbative evolution is so precise down to very low energy scales.…”

Section: The Running Of the Couplingmentioning

confidence: 99%

Non-perturbative renormalization of QCD

Sommer¹

Lecture Notes in Physics

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Abstract. In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the scale-dependence of renormalized quantities is explained. An important ingredient in the practical applications is the Schrödinger functional. It is introduced and its renormalization properties are discussed. Concerning applications, the computation of the running coupling and the running quark mass are covered in detail and it is shown how the Λ-parameter and renormalization group invariant quark mass can be obtained. Further topics are the renormalization of isovector currents and non-perturbative Symanzik improvement. Contents IntroductionBasic

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Two-loop relation between the bare lattice coupling and the coupling in pure SU(N) gauge theories

Cited by 57 publications

References 30 publications

Two-loop computation of the Schrödinger functional in lattice QCD

Two-loop computation of the Schrödinger functional in lattice QCD

Nonperturbative mechanism for elementary particle mass generation

Non-perturbative renormalization of QCD

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