Non-perturbative O(a) improvement of lattice QCD

Lüscher, Martin; Sint, Stefan; Sommer, Rainer; Weisz, Peter; Wolff, Ulli

doi:10.1016/s0550-3213(97)00080-1

Cited by 511 publications

(817 citation statements)

References 29 publications

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“…in Eqs. (2.1) and (2.2) of [38], and ∂ 0 , ∂ * 0 are the forward and backward lattice time derivatives, respectively. Finally, the improvement coefficient, c A , is set to its perturbative 1-loop value [39,40], since a non-perturbative estimate is not available for N f = 3 and our choice of gauge action.…”

Section: Lattice Observablesmentioning

confidence: 99%

“…Using a combination of simulations and perturbation theory we have produced a model for the sensitivity of our data to a variation of c t andc t . The details are deferred to Appendix A, where we obtain linearized shifts of the data, for instance, 38) and analogously for a shiftc t =c t + c t . Hence, the model yields an estimate of the data that would have been obtained if the simulations had been performed at slightly different values c t andc t .…”

Section: Treatment Of Statistical Errorsmentioning

confidence: 99%

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A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

et al. 2018

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Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale 1 MS , a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of α s =ḡ 2 /(4π). In the present work we reach this precision by studying scales that vary by a factor 2 5 = 32, reaching down to α s ≈ 0.1. We here provide the details of our analysis and an extended discussion. a

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Section: Lattice Observablesmentioning

confidence: 99%

Section: Treatment Of Statistical Errorsmentioning

confidence: 99%

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

et al. 2018

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“…The ALPHA collaboration developed a method to do so within the Schrödinger functional framework [2]. For quenched QCD the nonperturbative clover coefficient is now known for gauge coupling 6/g 2 ≥ 5.7, corresponding to lattice spacings a ∼ < 0.17 fm [2,3]. A substantial reduction of scaling violations in this region from O(a) to O(a 2 ) has been verified nicely in [3].…”

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confidence: 95%

Thermodynamics with dynamical clover fermions

Edwards

Heller

1999

Physics Letters B

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We investigate the finite temperature behavior of nonperturbatively improved clover fermions on lattices with temporal extent N t = 4 and 6. Unfortunately in the gauge coupling range, where the clover coefficient has been determined nonperturbatively, the finite temperature crossover/transition occurs at heavy pseudoscalar masses and large pseudoscalar to vector meson mass ratios. However, on an N t = 6 lattice the thermal crossover for the improved fermions is much smoother than for unimproved Wilson fermions and no strange metastable behavior is observed.Simulations with Wilson fermions suffer O(a) scaling violations due to the dimension five operator that Wilson introduced to give the unwanted fermion doublers masses of order the cutoff, 1/a. These scaling violations are much larger than those in the glue sector, which are O(a 2 ), and they can be numerically quite large, necessitating use of small lattice spacings at large simulation cost to get results that can be reliably extrapolated to the continuum limit.The O(a) scaling violations can be reduced to O(a 2 ) by introducing another dimension five operator into the fermion action, the so called clover term,where F µν (x) is a lattice transcription of the field strength tensor F µν (x), usually taken from four open plaquettes looking like a clover leaf, as proposed by Sheikholeslami and Wohlert [1]. For the reduction of scaling violations to work the clover coefficient, c sw , needs to be determined nonperturbatively as a function of the gauge coupling. The ALPHA collaboration developed a method to do so within the Schrödinger functional framework [2]. For quenched QCD the nonperturbative clover coefficient is now known for gauge coupling

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“…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 O(a) improvement of lattice QCD

Cited by 511 publications

References 29 publications

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

Thermodynamics with dynamical clover fermions

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

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