Non-perturbative renormalization of two-quark operators with an improved lattice fermion action

Martinelli, G.; Petrarca, S.; Sachrajda, Christopher; Vladikas, A.

doi:10.1016/0370-2693(93)90562-v

Cited by 82 publications

(80 citation statements)

References 9 publications

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“…But one requires a gluon exchange at lowest order, which gives an additional αs factor. This was shown by Politzer [6] for the correspondinḡ ψψ contribution to the propagator 4 Let us also recall that in the context of the lattice, this relation has been discussed and used by the Rome group to fix ZA on quark states [7]. defined in [10] so that the numbers in r.h.s.…”

Section: Fit Of Lattice Data For γ 5 As Function Of the Hopping Parammentioning

confidence: 99%

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

Cudell

Yaouanc²,

Pittori

1999

Physics Letters B

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We analyse the Structure Function collaboration data on the quark pseudoscalar vertex and extract the Goldstone boson pole contribution, in 1/p 2 . The strength of the pole is found to be quite large at presently accessible scales. We draw the important consequences of this finding for the various definitions of quark masses (short distance and Georgi-Politzer), and point out problems with the operator product expansion and with the non-perturbative renormalisation method. Continuum model for the quark pseudoscalar vertexIt is well known that the quark pseudoscalar (PS) vertex contains a non-perturbative contribution from the Goldstone boson, in the continuum. On the lattice, the use of a non perturbative renormalisation scheme [2] makes this contribution manifest, although it should go to zero for large momentum transfers. The purpose of this letter is to extract it from lattice simulation data, and to show that it is not negligible for presently accessible scales. In particular, it must be subtracted when evaluating the short distance quark masses from the lattice through the non perturbative method of ref. [1]. This method uses the off-shell axial Ward identity (AWI) and renormalises the mass in the momentum subtraction (MOM) scheme of ref.[2], which can afterwards be related to the MS scheme. The MOM renormalisation involves the pseudoscalar vertex, whence the necessity of the subtraction of the Goldstone contribution to extract the short distance quantity 2 . For physical u, d quarks, the Goldstone contribution becomes very large, larger than the perturbative part; this corresponds to a very large dynamical u, d mass, larger than the usual current mass at the scales accessible to standard lattice calculations.The expected behaviour of the pseudoscalar vertex in the continuum has been described as follows in the 70's in the works of Lane and Pagels [4,5] and others. Near the chiral limit, the one-particle-irreducible PS quark vertex Λ 5 can be described through a perturbative contribution plus a non-perturbative Goldstone boson contribution.The perturbative contribution is of course 1 × γ 5 , with QCD radiative corrections, which according to the renormalisation group lead to a logarithmic behaviour [α s (p 2 )] 4/11 for N F = 0.As to the non-perturbative contribution, firstly, according to PCAC, the Goldstone boson must dominate other pole contributions in the PS vertex near the chiral limit: the coupling of the pion to the PS vertex indeed gives a pole ∼ 1/(q 2 + m 2 π ), where q is the momentum transferred at the vertex; other poles (radial excitations) contributions are suppressed in the chiral limit. At q = 0, in terms of the quark mass m, this gives a 1/m pole contribution. We emphasize that this pole contribution explodes at q = 0 in the chiral limit, i.e. it is singular 1 Laboratoire associe au CNRS-URA D00063. 2 The problem would be quite different if other methods are used to extract quark masses, see e.g. ref.[3].

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Section: Fit Of Lattice Data For γ 5 As Function Of the Hopping Parammentioning

confidence: 99%

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

Cudell

Yaouanc²,

Pittori

1999

Physics Letters B

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“…Non-perturbative renormalization is, hence, required for the non-ratio quantities to reduce the large uncertainty. The renormalization would be accomplished by RI/MOM scheme [63,64], in which an additional renormalization condition is required to manage the 1/a power divergence.…”

Section: Physical Light Quark Mass Point Simulationmentioning

confidence: 99%

NeutralBmeson mixings andBmeson decay constants with static heavy and domain-wall light quarks

et al. 2015

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Neutral B meson mixing matrix elements and B meson decay constants are calculated. Static approximation is used for b quark and domain-wall fermion formalism is employed for light quarks. The calculations are carried out on 2 + 1 flavor dynamical ensembles generated by RBC/UKQCD Collaborations with lattice spacings 0.086 fm (a −1 ∼ 2.3 GeV) and 0.11 fm (1.7 GeV), and a fixed physical spatial volume of about (2.7 fm) 3 . In the static quark action, link-smearings are used to improve the signal-to-noise ratio. We employ two kinds of link-smearings, HYP1 and HYP2, and their results are combined in taking the continuum limit. For the matching between the lattice and the continuum theory, one-loop perturbative O(a) improvements are made to reduce discretization errors. As the most important quantity of this work, we obtain SU (3)

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“…[1,3] has been successfully applied to compute renormalization constants of composite fermion operators in many lattice regularizations: Wilson fermions [1], [3]- [10], Kogut-Susskind fermions [11], domain-wall fermions [12] and overlap fermions [13]. The method imposes RI/MOM renormalization conditions on conveniently defined amputated Green functions computed non-perturbatively between off-shell quark states at large virtuality in a fixed gauge.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the gauge dependence of the RI/MOM renormalization procedure

et al. 2002

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The RI/MOM non-perturbative renormalization scheme is studied on the lattice in SU(3) quenched QCD with Wilson fermions. The gauge dependence of some fermion bilinear renormalization constants is discussed by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is moderate and below the statistical errors.

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Non-perturbative renormalization of two-quark operators with an improved lattice fermion action

Cited by 82 publications

References 9 publications

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

NeutralBmeson mixings andBmeson decay constants with static heavy and domain-wall light quarks

Remarks on the gauge dependence of the RI/MOM renormalization procedure

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