Stochastic perturbation theory

A collection of links to numerical stochastic perturbation theory results for lattice actions. In contrast to many other lists of references given in this website, multi-loop calculations are not listed separately for stochastic perturbation theory calculations. One of the main advantages of stochastic perturbation theory is the ability to do high order calculations far more efficiently than is possibly in standard lattice perturbation theory. At low orders this advantage is lost and one may as well use standard perturbative techniques, if possible. Thus the results from numerical stochastic perturbation theory are invariably multi-loop and separate listings are not required.

2010s

• M. Lüscher, Instantaneous stochastic perturbation theory, (2014) [arXiv:1412.5311]
• M. Brambilla, F. Di Renzo and M. Hasegawa High-loop perturbative renormalization constants for lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n_f=4 Wilson fermions, [arXiv:1402.6581]
• G.S. Bali, C. Bauer and A. Pineda The perturbative expansion of the plaquette to O(α^35) in four-dimensional SU(3) gauge theory, [arXiv:1401.7999]
• M. Dalla Brida and D. Hesse, Numerical stochastic perturbation theory and the gradient flow, PoS(LATTICE 2013) 459 [arXiv:1311.3936]
• J. Simeth et al., Discretization errors for the gluon and ghost propagators in Landau gauge using NSPT, [arXiv:1311.1934]
• M. Brambilla et al., Numerical stochastic perturbation theory in the Schrödinger gunctional, [arXiv:1310.8536]
• M. Brambilla and F. Di Renzo, High-loop perturbative renormalization constants for lattice QCD (II): three-loop quark currents for tree-level Symanzik improved gauge action and n_f=2 Wilson fermions, [arXiv:1310.4981]
• G. Bali et al. The perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory, Phys. Rev. D 87 (2013) 094517, [arXiv:1303.3279]
• R. Horsley et al., Wilson loops to 20th order numerical stochastic perturbation theory, Phys. Rev. D 86 (2012) 054502 [arXiv:1205.1659]
• C. Bauer, G.S. Bali and A. Pineda, Compelling evidence of renormalons in QCD from high order perturbative expansions, Phys. Rev. Lett. 108 (2012) 242002 [arXiv:1111.3946]
• F. Di Renzo et al., Two-point functions of quenched lattice QCD in numerical stochastic perturbation theory. (II) The gluon propagator in Landau gauge Nucl. Phys. B 842 (2011) 122 [arXiv:1008.2617]
• F. Di Renzo et al., Two-point functions of quenched lattice QCD in numerical stochastic perturbation theory. (I) The ghost propagator in Landau gauge, Nucl. Phys. B 831 (2010) 262 [arXiv:0912.4152]
• F. Di Renzo et al., Two-point functions of quenched lattice QCD in numerical stochastic perturbation theory, AIP Conf. Proc. 1343 (2011) 236 [arXiv:1012.1764]
• G.S. Bali, C. Bauer and A. Pineda, The static quark self-energy at large orders from NSPT, PoS(LATTICE 2011) 222 [arXiv:1111.6158]
• C. Torrero et al., NSPT study of the three-loop lattice gluon propagator in Landau gauge, PoS(LATTICE 2010) 291 [arXiv:1010.5353]
• C. Bauer and G.S. Bali, Hunting the static energy renormalon, PoS(LATTICE 2010) 221 [arXiv:1011.1165]
• R. Horsley et al., Very high order lattice perturbation theory for Wilson loops, (2010) [arXiv:1010.4674]

2005s

• M. Brambilla and F. Di Renzo, The Dirac operator spectrum: a perturbative approach, PoS(LATTICE 2009) 209 [arXiv:1002.0452]
• E.-M. Ilgenfritz et al., Wilson loops in very high order lattice perturbation theory, PoS(LATTICE 2009) 236 [arXiv:0910.2795]
• M. Brambilla, F. Di Renzo and L. Scorzato, High loop renormalization constants for Wilson fermions/Symanzik improved gauge action, PoS LAT2009 (2009) 211 [arXiv:1002.0446]
• C. Torrero and G.S. Bali, NSPT calculations in the Schrodinger Functional formalism, PoS(LATTICE 2009) 203 [arXiv:0910.4138]
• F. Di Renzo et al., The lattice ghost propagator in Landau gauge up to three loops using numerical stochastic perturbation theory, PoS LAT2009. (2009) 234 [arXiv:0910.2905]
• E.-M. Ilgenfritz et al., Wilson loops in very high order lattice perturbation theory, PoS(LATTICE 2009) 236 [arXiv:0910.2795]
• F. Di Renzo et al., The Landau gauge lattice ghost propagator in stochastic perturbation theory, PoS(LATTICE 2008) 217 [arXiv:0809.4950]
• C. Torrero and G.S. Bali, Towards a determination of Csw using numerical stochastic perturbation theory (NSPT), PoS(LATTICE 2008) 2015 [arXiv:0812.1680]
• E.-M. Ilgenfritz, H. Perlt and A. Schiller, The lattice gluon propagator in stochastic perturbation theory, PoS(LATTICE 2007) 251 [arXiv:0710.0560]
• F. Di Renzo, L. Scorzato and C. Torrero, High loop renormalization constants by NSPT: a status report, PoS(LATTICE 2007) 240 [arXiv:0710.0552]
• F. Di Renzo et al., High-loop perturbative renormalization constants for lattice QCD (I): finite constants for Wilson quark currents, Eur. Phys. J. C 51 (2007) 645 [arXiv:hep-lat/0611013]
• F. Di Renzo et al., Renormalization constants for lattice QCD: new results from numerical stochastic perturbation theory, PoS(LATTICE 2006) 156 [arXiv:hep-lat/0609077]
• P.E.L. Rakow, Stochastic perturbation theory and the gluon condensate, PoS(LATTICE 2005) 284 [arXiv:hep-lat/0510046]
• F. Di Renzo et al., Wilson fermions quark bilinears to three loops, PoS(LATTICE 2005) 237 [arXiv:hep-lat/0509158]
• C. Torrero et al., Four-loop plaquette in 3d with a mass regulator, PoS(LATTICE 2005) 189 [arXiv:hep-lat/0509157]
• V. Miccio et al. Fermionic observables in numerical stochastic perturbation theory, PoS(LATTICE 2005) 108 [arXiv:hep-lat/0509141]
• F. Di Renzo, E. Onofri, and G. Marchesini, Renormalons from eight-loop expansion of the gluon condensate in lattice gauge theory, Nucl. Phys. B 457 (1995) 202 [arXiv:hep-th/9502095]
• F. Di Renzo et al., 3-d lattice SU(3) free energy to four loops, Nucl. Phys. B (Proc. Suppl.) 140 (2005) 586 [arXiv:hep-lat/0409150]

2000s

• F. Di Renzo and L. Scorzato, The Nf=2 residual mass in perturbative lattice-HQET for an improved determination of the (MS bar) b-quark mass, JHEP 0411 (2004) 036 [arXiv:hep-lat/0408015]
• F. Di Renzo and L. Scorzato, Numerical stochastic perturbation theory for full QCD, JHEP 0410 (2004) 073 [arXiv:hep-lat/0410010]
• F. Di Renzo and L. Scorzato, The n_f=2 residual mass in lattice HQET to alpha^3 order, PoS LAT2004 (2004) [arXiv:hep-lat/0409151]
• F. Di Renzo et al., Two and three loops computations of renormalization constants for lattice QCD, PoS LAT2004 (2004) [arXiv:hep-lat/0409149]
• F. Di Renzo et al., Preliminary results in unquenched numerical stochastic perturbation theory, PoS LAT2003 (2003) [arXiv:hep-lat/0309108]
• F. Di Renzo, V. Miccio and L. Scorzato, Unquenched numerical stochastic perturbation theory, PoS LAT2002 (2002) [arXiv:hep-lat/0209018]
• F. Di Renzo and L. Scorzato, A consistency check for renormalons in lattice gauge theory: beta^(-10) contributions to the SU(3) plaquette, JHEP 0110 (2001) 038 [arXiv:hep-lat/0011067]
• F. Di Renzo and L. Scorzato, The residual mass in lattice heavy quark effective theory to alpha^3 order, JHEP 0102 (2001) 020 [arXiv:hep-lat/0012011]
• F. Di Renzo and L. Scorzato, Fermionic loops in numerical stochastic perturbation theory, Nucl. Phys. B (Proc. Suppl.) 94 (2000) 567 [arXiv:hep-lat/0010064]
• R. Alfieri et al., Understanding stochastic perturbation theory: toy models and statistical analysis, Nucl. Phys. B 578 (2000) 383 [arXiv:hep-lat/0002018]
• F. Di Renzo and L. Scorzato, Numerical stochastic perturbation theory. Convergence and features of the stochastic process. Computations at fixed (Landau) gauge, Nucl. Phys. B (Proc. Suppl.) 83 (2000) 822 [arXiv:hep-lat/9909168]
• G. Burgio et al., Beta-function, renormalons and the mass term from perturbative wilson loops, Nucl. Phys. B (Proc. Suppl.) 83 (2000) 822 [arXiv:hep-lat/9909169]

1990s

• G. Burgio et al., New issues for numerical stochastic perturbation theory, Nucl. Phys. B (Proc. Suppl.) 73 (1999) 853 [arXiv:hep-lat/9809103]
• G. Burgio et al., Developments and new applications of numerical stochastic perturbation theory, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 808 [arXiv:hep-lat/9709106]
• F. Di Renzo et al., Four-loop result in SU(3) lattice gauge theory by a stochastic method: lattice correction to the condensate, Nucl. Phys. B 426 (1994) 675 [arXiv:hep-lat/9405019]
• F. Di Renzo et al., Lattice perturbation theory on the computer, Nucl. Phys. B (Proc. Suppl.) 34 (1994) 795
• F. Di Renzo et al., Lattice perturbation theory by Langevin dynamics, (1993) [arXiv:hep-lat/9308006]

Applications beyond zero temperature QCD

• F. Di Renzo et al., Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory, JHEP 0809(2008) 61 [arXiv:0808.0557]
• F. Di Renzo et al., Four loop stochastic perturbation theory in 3d SU(3), PoS LAT2003 (2003) [arXiv:hep-lat/0309111]

QCD at non-zero temperature

• C. Torrero et al., Towards 4-loop NSPT result for a 3-dimensional condensate-contribution to hot QCD pressure, PoS LAT2007 (2007) 231 [arXiv:0711.1176]
• F. Di Renzo et al., The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure, JHEP 0607 (2006) 026 [arXiv:0605042]