Determining fundamental parameters of QCD on the lattice

Sommer, Rainer

doi:10.1016/j.nuclphysbps.2006.09.099

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…The authors of [10] report on an SU(2)-study on a 52 4 -lattice, whereas in [11] results from an SU(3) calculation on a 56 4 -lattice are discussed with larger lattices on their way. 7 The physical volumes of both these studies are comparable. The resulting propagators are very similar with small deviations for the first few points in the infrared.…”

Section: Comparison To Lattice Resultsmentioning

confidence: 84%

“…E.g., Λ M S ≈ 240 MeV for N f = 0 from the lattice determination by the ALPHA Collaboration[7] 2. This is different in Coulomb gauge and interpolating gauges, where a stronger suppression is expected from the Gribov-Zwanziger scenario, and where this infrared suppression of the gluon propagator is observed on the lattice already in rather small volumes[12,13].…”

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confidence: 86%

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Large volume behaviour of Yang-Mills propagators

et al. 2007

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We investigate finite volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. In particular, we demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. This solves an important open problem of previous studies where the infinite volume limit led to an apparent mismatch, especially of the infrared behaviour, between torus extrapolations and the existing infinite volume solutions obtained in 4-dimensional Euclidean space-time. However, the correct infinite volume limit is approached rather slowly. The typical scales necessary to see the onset of the leading infrared behaviour emerging already imply volumes of at least 10 to 15 fm in lengths. To reliably extract the infrared exponents of the infinite volume solutions requires even much larger ones. While the volumes in the Monte-Carlo simulations available at present are far too small to facilitate that, we obtain a good qualitative agreement of our torus solutions with recent lattice data in comparable volumes.Comment: 34 pages, 8 figures; v2: typos corrected, refs. added, version accepted by Annals of Physic

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Section: Comparison To Lattice Resultsmentioning

confidence: 84%

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confidence: 86%

Large volume behaviour of Yang-Mills propagators

et al. 2007

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“…For the SU(3) theory with two flavours of Wilson fermions, the perturbative prediction is obtained using the Λ parameter computed in Ref. [37,38]; it can be compared to the value of the lattice spacing recently computed for two values of β in Ref. [39].…”

Section: Perturbative and Nonperturbative Scalingmentioning

confidence: 99%

Higher representations on the lattice: perturbative studies

Debbio

Frandsen

Panagopoulos

et al. 2008

J. High Energy Phys.

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We present analytical results to guide numerical simulations with Wilson fermions in higher representations of the colour group. The ratio of Λ parameters, the additive renormalization of the fermion mass, and the renormalization of fermion bilinears are computed in perturbation theory, including cactus resummation. We recall the chiral Lagrangian for the different patterns of symmetry breaking that can take place with fermions in higher representations, and discuss the possibility of an Aoki phase as the fermion mass is reduced at finite lattice spacing.

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“…Due to translation invariance in space the spatial eigenfunctions are plane waves with momentum values that are integer multiples of 2π/L in the range −π/a < p k ≤ π/a. 3 For c = 1 the operator (2.1) is diagonal in Dirac space, so its eigenvalues are 2 (d+1)/2 -fold degenerated. Its eigenfunctions (in space-time) are then given by…”

Section: Free Fermionsmentioning

confidence: 99%

“…If the temporal extension is a multiple of the spatial extension, say T = 2L, the inverse of the spatial extension 1/L provides an infrared cutoff and is the natural energy scale in the massless theory. In fact this has enabled a fully non-perturbative determination of the scale dependence of the fundamental parameters of N f = 2 QCD, see [3] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Test of the Schrödinger functional with chiral fermions in the Gross-Neveu model

Leder

2008

J. High Energy Phys.

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The recently proposed construction of chiral fermions on lattices with boundaries is tested in an interacting theory up to first order of perturbation theory. We confirm that, in the bulk of the lattice, the chiral Ward identities take their continuum value up to cutoff effects without any tuning. Universal quantities are defined that have an expansion in the renormalised couplings with coefficients that are functions of the physical size and the periodicity in the spatial direction. These coefficient functions have to be identical for different discretisations. We find agreement with the standard Wilson fermions. The computation is done in the asymptotically free Gross-Neveu model with continuous chiral symmetry.

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Determining fundamental parameters of QCD on the lattice

Abstract: We summarize the status of determinations of fundamental parameters of QCD by the ALPHA Collaboration.Comment: 5 pages, talk at "Loops and Legs 2006

Cited by 4 publications

References 20 publications

Large volume behaviour of Yang-Mills propagators

Large volume behaviour of Yang-Mills propagators

Higher representations on the lattice: perturbative studies

Test of the Schrödinger functional with chiral fermions in the Gross-Neveu model

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