Non-perturbative determination of the axial current normalization constant in 0(a) improved lattice QCD

Lüscher, Martin; Sint, Stefan; Sommer, Rainer; Wittig, Hartmut

doi:10.1016/s0550-3213(97)00087-4

Cited by 294 publications

(421 citation statements)

References 25 publications

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“…Indeed, at a 2 p 2 = 1, with this subtraction and using again Z ψ = 0.85 near the chiral limit, we find Z Subtr P = 1/1.88 = 0.53 which corresponds to the fully resummed short-distance contribution determined directly from the lattice data 11 . To get an estimate of the consequences on the light quark masses, we use [22] (which uses the notation am for ρ) where one finds ρ ∼ am q , with am u,d = 0.001836, and we take Z A = 0.79 [23]. We then find:…”

Section: Calculation Of the M S Massmentioning

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: Calculation Of the M S Massmentioning

confidence: 99%

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

Cudell

Yaouanc²,

Pittori

1999

Physics Letters B

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“…The function Z A (g 0 ) [1] currently used by the ALPHA collaboration was obtained by requiring that certain chiral Ward identities are satisfied in the O(a) on-shell improved lattice theory up to O(a 2 ) cutoff effects. This normalization condition is evaluated at zero quark mass and hence the mass term in the PCAC relation was dropped.…”

Section: Introductionmentioning

confidence: 99%

Non-perturbative renormalization of the axial current with improved Wilson quarks

Hoffmann

Knechtli

Rolf

et al. 2004

Nuclear Physics B - Proceedings Supplements

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We present a new normalization condition for the axial current, which is derived from the PCAC relation with non-vanishing mass. Using this condition reduces the O(r0m) corrections to the axial current normalization constant ZA for an easier chiral extrapolation in the cases, where simulations at zero quark-mass are not possible. The method described here also serves as a preparation for a determination of ZA in the full two-flavor theory. IntroductionDue to the explicit breaking of chiral symmetry in a lattice theory with Wilson quarks a finite renormalization constant Z A for the isovector axial current is needed so that Ward identities take their canonical form up to small lattice corrections. Otherwise a safe extrapolation to the continuum can not be achieved for physical quantities involving this current.The function Z A (g 0 ) [1] currently used by the ALPHA collaboration was obtained by requiring that certain chiral Ward identities are satisfied in the O(a) on-shell improved lattice theory up to O(a 2 ) cutoff effects. This normalization condition is evaluated at zero quark mass and hence the mass term in the PCAC relation was dropped.However, even in the framework of the Schrödinger functional simulations at vanishing quark mass are not possible if the physical volume, or equivalently the renormalized coupling, is too large. For the large couplings one therefore evaluates the normalization condition at finite quark mass and extrapolates to the chiral point. Since the mass term was ignored in the derivation of the normalization condition this introduces an error of O(r 0 m) in Z A . The Sommer scale r 0 [2] is used as a typical hadronic scale.Here we present a normalization condition for the axial current, which is derived using the full PCAC relation. This reduces the O(r 0 m) errors in Z A to O(am) and therefore results in a much flatter chiral extrapolation.

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“…Here, Z A renormalizes the axial current and the term linear in b A subtracts O(a)-artefacts proportional to the bare subtracted quark mass m q . Both coefficients were obtained non-perturbatively on the lattice [10,9]. Some simulation parameters are summarized in table 1.…”

Section: Strategy and Simulationmentioning

confidence: 99%

“…The systematic errors can be kept under control by using non-perturbative O(a)-improvement [8,9] and renormalization [10] together with a well controlled approach to the continuum. In particular, we simulated at four different values of the lattice spacing between a = 0.1, .…”

Section: Introductionmentioning

confidence: 99%

A precise determination of the decay constant of the Ds-meson in quenched QCD

Juettner

Rolf

2004

Nuclear Physics B - Proceedings Supplements

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We present a precise determination of the leptonic decay constant FD s of the Ds-meson in quenched lattice QCD. This work is particularly focused on the analysis and discussion of all sources of systematic errors. We simulate directly at the physical quark masses for five different lattice spacings between 0.1 fm and 0.03 fm using O(a)-improvement. The finest lattice is still work in progress. After taking the continuum limit and setting the scale with the Kaon decay constant FK = 160 MeV we arrive at a value of FD s = 252(9) MeV. Setting the scale with the nucleon mass instead leads to a decrease of about 20 MeV of FD s .

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Non-perturbative determination of the axial current normalization constant in 0(a) improved lattice QCD

Cited by 294 publications

References 25 publications

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

Pseudoscalar vertex, Goldstone boson and quark masses on the lattice

Non-perturbative renormalization of the axial current with improved Wilson quarks

A precise determination of the decay constant of the Ds-meson in quenched QCD

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