Four-loop result in SU(3) lattice gauge theory by a stochastic method: lattice correction to the condensate

Renzo, Francesco Di; Onofri, E.; Marchesini, G.; Marenzoni, Paolo

doi:10.1016/0550-3213(94)90026-4

Cited by 65 publications

(99 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[8][9][10][11] and many attempts followed during the next decades, see, e.g., Refs. [12][13][14][15][16][17][18][19][20][21]. These suffered from insufficiently high perturbative orders and, in some cases, also finite volume effects.…”

mentioning

confidence: 99%

Model Independent Determination of the Gluon Condensate in Four Dimensional SU(3) Gauge Theory

2014

View full text Add to dashboard Cite

We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model-independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition. We also determine the binding energy of a B meson in the heavy quark mass limit.PACS numbers: 12.38. Gc,12.38.Bx,11.55.Hx,12.38.Cy,11.15.Bt The operator product expansion (OPE) [1] is a fundamental tool for theoretical analyses in quantum field theories. Its validity is only proven rigorously within perturbation theory, to arbitrary finite orders [2]. The use of the OPE in a non-perturbative framework was initiated by the ITEP group [3] (see also the discussion in Ref. [4]), which postulated that the OPE of a correlator could be approximated by the following series:where the expectation values of local operators O d are suppressed by inverse powers of a large external momentum Q ≫ Λ QCD , according to their dimensionality d.The Wilson coefficients C d (α) encode the physics at momentum scales larger than Q. These are well approximated by perturbative expansions in the strong coupling parameter α. The large-distance physics is described by the matrix elements O d that usually have to be determined non-perturbatively. Almost all QCD predictions of relevance to particle physics phenomenology are based on factorizations that are generalizations of the above generic OPE.For correlators where O 0 = 1, the first term of the OPE expansion is a perturbative series in α. In pure gluodynamics the first non-trivial gauge invariant local operator has dimension four. Its expectation value is the so-called non-perturbative gluon condensate

show abstract

mentioning

confidence: 99%

Model Independent Determination of the Gluon Condensate in Four Dimensional SU(3) Gauge Theory

2014

View full text Add to dashboard Cite

show abstract

“…Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory M. Pepe have computed the perturbative expansion of Z T (g 2 0 ) at two loops using the method of Numerical Stochastic Perturbation Theory [13] at L = 24 and 48. These latter results, show evidence both for strong finite size effects and for large corrections due to high-order terms and to non-perturbative contributions.…”

Section: Pos(lattice2014)322mentioning

confidence: 99%

Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory

Giusti¹

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

View full text Add to dashboard Cite

We present a strategy for a non-perturbative determination of the finite renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. The computation is performed by imposing on the lattice suitable Ward Identites at finite temperature in presence of shifted boundary conditions. We show accurate preliminary numerical data for values of the bare coupling g 2 0 ranging for 0 to 1.

show abstract

“…Numerical stochastic perturbation theory (NSPT) [1][2][3] is a powerful tool that allows many interesting calculations in QCD and other quantum field theories to be performed to high order in the interactions. For technical reasons, the computations proceed in the framework of lattice field theory, but results for renormalized quantities in the continuum theory can then be obtained through an extrapolation to vanishing lattice spacing.…”

Section: Introductionmentioning

confidence: 99%

SMD-based numerical stochastic perturbation theory

Brida

Lüscher

2017

Eur. Phys. J. C

View full text Add to dashboard Cite

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

show abstract

Four-loop result in SU(3) lattice gauge theory by a stochastic method: lattice correction to the condensate

Cited by 65 publications

References 19 publications

Model Independent Determination of the Gluon Condensate in Four Dimensional SU(3) Gauge Theory

Model Independent Determination of the Gluon Condensate in Four Dimensional SU(3) Gauge Theory

Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory

SMD-based numerical stochastic perturbation theory

Contact Info

Product

Resources

About