Non-perturbative renormalization in lattice field theory

Sint, Stefan

doi:10.1016/s0920-5632(01)00941-0

Cited by 30 publications

(25 citation statements)

References 69 publications

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“…Recently it is recognized that an essential step toward the precise determination of B K is to control the systematic error associated with the renormalization, and for the precision now required, the non-perturbative renormalization seems necessary [3,11,12,13]. Among several non-perturbative schemes on the lattice the Schrödinger functional (SF) scheme [14,15,16,17] has an advantage that systematic errors can be unambiguously controlled: A unique renormalization scale is introduced through the box size to reduce the lattice artifact and a large range of the renormalization scale can be covered by the step scaling function (SSF) technique. A few years ago the CP-PACS collaboration has calculated B K using the quenched domain-wall QCD (DWQCD) with the Iwasaki gauge action [6], and a good scaling behavior with small statistical errors has been observed.…”

Section: Introductionmentioning

confidence: 99%

Precise determination ofBKand light quark masses in quenched domain-wall QCD

et al. 2008

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We calculate non-perturbative renormalization factors at hadronic scale for ∆S = 2 four-quark operators in quenched domain-wall QCD using the Schrödinger functional method. Combining them with the non-perturbative renormalization group running by the Alpha collaboration, our result yields the fully non-perturbative renormalization factor, which converts the lattice bare B K to the renormalization group invariant (RGI) B K . Applying this to the bare B K previously obtained by the CP-PACS collaboration at a −1 ≃ 2, 3, 4 GeV, we obtain B K = 0.782(5)(7) (equivalent to B MS K (NDR, 2GeV) = 0.565(4)(5) by 2-loop running) in the continuum limit, where the first error is statistical and the second is systematic due to the continuum extrapolation. Except the quenching error, the total error we have achieved is less than 2%, which is much smaller than the previous ones. Taking the same procedure, we obtain m

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Section: Introductionmentioning

confidence: 99%

Precise determination ofBKand light quark masses in quenched domain-wall QCD

et al. 2008

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“…3 Implementing this programme may be non-trivial and CPU-time demanding, e.g. in the theory with nondegenerate and/or dynamical quarks, as well as for operators with complicated mixings [ 12]. 4 At the non-perturbative level, csw and amc are uniquely defined only up to O(a) and O(a 3 ) corrections [ 11], respectively.…”

Section: Exceptional Configurationsmentioning

confidence: 99%

“…It is understood that the continuum limit must be approached at fixed values of the renormalized parameters, including α. In this way, the cutoff effects inherent to any determination of α at finite lattice spacing have no impact on the (extrapolated) continuum limit results 13 12 The definitions (15) are special cases of those in eq. (17).…”

Section: Continuum Limit and Cutoff Effectsmentioning

confidence: 99%

Wilson fermions with chirally twisted mass

Frezzotti¹

2003

Nuclear Physics B - Proceedings Supplements

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Lattice formulations of QCD with Wilson fermions and a chirally twisted quark mass matrix provide an attractive framework for non-perturbative numerical studies. Owing to reparameterization invariance, the limiting continuum theory is just QCD. No spurious quark zero modes, which are responsible for the problem with exceptional configurations, can occur at finite values of the quark mass. Moreover, the details of the lattice formulation can be adjusted so as to simplify the renormalization and the O(a) improvement of several quantities of phenomenological relevance. The first exploratory studies in the quenched approximation yield very encouraging results.

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“…All necessary renormalization constants and improvement coefficients are known with non-perturbative accuracy in the relevant range of bare couplings. We refer to [4] for a review and further references.…”

Section: Strategymentioning

confidence: 99%

The charm quark's mass in quenched QCD

Rolf

Sint

2002

Nuclear Physics B - Proceedings Supplements

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We present our preliminary result for the charmed quark mass, which follows from taking the Ds and K meson masses from experiment and r0 = 0.5 fm (or, equivalently FK = 160 MeV) to set the scale. For the renormalization group invariant quark mass we obtain Mc = 1684(64) MeV, which translates to mc(mc) = 1314(40)(20)(7) MeV for the running mass in the MS scheme. Renormalization is treated non-perturbatively, and the continuum limit has been taken, so that the only uncontrolled systematic error consists in the use of the quenched approximation.

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Non-perturbative renormalization in lattice field theory

Cited by 30 publications

References 69 publications

Precise determination ofBKand light quark masses in quenched domain-wall QCD

Precise determination ofBKand light quark masses in quenched domain-wall QCD

Wilson fermions with chirally twisted mass

The charm quark's mass in quenched QCD

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