Abstract
We review the infrared properties of the pure Yang–Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature, i.e. decoupling and scaling solutions. We will mainly focus on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson–Schwinger equations of the theory and from “quenched” lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.
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References
Wilson K.G.: Confinement of quarks. Phys. Rev. D 10, 2445–2459 (1974)
Cornwall J.M.: Quark confinement and vortices in massive gauge invariant QCD. Nucl.Phys. B 157, 392 (1979)
Greensite J.: An introduction to the confinement problem. Lect. Notes Phys. 821, 1–211 (2011)
Chetyrkin, K.G., Retey, A.: Three loop three linear vertices and four loop similar to MOM β functions in massless QCD. arXiv:hep-ph/0007088 (2000)
Sheikholeslami B., Wohlert R.: Improved continuum limit lattice action for QCD with Wilson fermions. Nucl. Phys. B 259, 572 (1985)
Iwasaki Y., Yoshie T.: Renormalization group improved action for SU(3) lattice gauge theory and the string tension. Phys. Lett. B 143, 449 (1984)
Luscher M., Weisz P.: On-shell improved lattice gauge theories. Commun. Math. Phys. 97, 59 (1985)
Luscher M., Weisz P.: Computation of the action for on-shell improved lattice gauge theories at weak coupling. Phys. Lett. B 158, 250 (1985)
Bowman P.O., Heller U.M., Leinweber D.B., Parappilly M.B., Williams A.G.: Unquenched gluon propagator in Landau gauge. Phys. Rev. D 70, 034509 (2004)
Bowman P.O., Heller U.M., Leinweber D.B., Parappilly M.B., Williams A.G. et al.: Unquenched quark propagator in Landau gauge. Phys. Rev. D 71, 054507 (2005)
Parappilly M.B., Bowman P.O., Heller U.M., Leinweber D.B., Williams A.G. et al.: Effects of dynamical sea-quarks on quark and gluon propagators. AIP Conf. Proc. 842, 237–239 (2006)
Silva, P.J., Oliveira, O.: Unquenching the Landau gauge lattice propagators and the Gribov problem. PoS LATTICE2010:287 (2010)
Dyson F.J.: The S matrix in quantum electrodynamics. Phys. Rev. 75, 1736–1755 (1949)
Schwinger J.S.: On the Green’s functions of quantized fields 1. Proc. Natl. Acad. Sci. 37, 452–455 (1951)
Alkofer R., von Smekal L.: The infrared behavior of QCD Green’s functions: confinement dynamical symmetry breaking, and hadrons as relativistic bound states. Phys. Rept. 353, 281 (2001)
Mandelstam S.: Approximation Scheme for QCD. Phys. Rev. D 20, 3223 (1979)
Mandelstam S.: General introduction to confinement. Phys. Rept. 67, 109 (1980)
Brown N., Pennington M.R.: Studies of confinement: how the gluon propagates. Phys. Rev. D 39, 2723 (1989)
Aguilar A.C., Papavassiliou J.: Gluon mass generation in the PT-BFM scheme. JHEP 0612, 012 (2006)
Aguilar A.C., Binosi D., Papavassiliou J.: Gluon and ghost propagators in the Landau gauge: deriving lattice results from Schwinger-Dyson equations. Phys. Rev. D 78, 025010 (2008)
Cucchieri, A., Mendes, T.: What’s up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices. PoS LAT2007:297 (2007)
Bogolubsky, I.L., Ilgenfritz, E.M., Muller-Preussker, M., Sternbeck, A.: The Landau gauge gluon and ghost propagators in 4D SU(3) gluodynamics in large lattice volumes. PoS LAT2007:290 (2007)
Sternbeck A., Ilgenfritz E.-M., Muller-Preussker M., Schiller A.: The Gluon and ghost propagator and the influence of Gribov copies. Nucl. Phys. Proc. Suppl. 140, 653–655 (2005)
Boucaud, P., Leroy, J.P., Le Yaouanc, A., Lokhov, A.Y., Micheli, J., et al.: The infrared behaviour of the pure Yang–Mills green functions. arXiv:hep-ph/0507104, 205
Sternbeck, A., von Smekal, L., Leinweber, D.B., Williams, A.G.: Comparing SU(2) to SU(3) gluodynamics on large lattices. PoS LAT2007:340 (2007)
Boucaud P., Leroy J.-P., Le Yaouanc A., Micheli J., Pène O. et al.: IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation. JHEP 0806, 012 (2008)
Boucaud P., Leroy J.P., Le Yaouanc A., Micheli J., Pène O. et al.: On the IR behaviour of the Landau-gauge ghost propagator. JHEP 0806, 099 (2008)
Fischer C.S., Maas A., Pawlowski J.M.: On the infrared behavior of Landau gauge Yang–Mills theory. Ann. Phys. 324, 2408–2437 (2009)
Aguilar A.C., Binosi D., Papavassiliou J., Rodriguez-Quintero J.: Non-perturbative comparison of QCD effective charges. Phys. Rev. D 80, 085018 (2009)
Fischer C.S., Pawlowski J.M.: Uniqueness of infrared asymptotics in Landau gauge Yang–Mills theory. Phys. Rev. D 75, 025012 (2007)
Watson P., Reinhardt H.: The Coulomb gauge ghost Dyson-Schwinger equation. Phys. Rev. D 82, 125010 (2010)
Epple D., Reinhardt H., Schleifenbaum W., Szczepaniak A.P.: Subcritical solution of the Yang–Mills Schroedinger equation in the Coulomb gauge. Phys. Rev. D 77, 085007 (2008)
Leder M., Pawlowski J.M., Reinhardt H., Weber A.: Hamiltonian flow in Coulomb gauge Yang–Mills theory. Phys. Rev. D 83, 025010 (2011)
Cornwall J.M.: Positivity issues for the pinch-technique gluon propagator and their resolution. Phys. Rev. D 80, 096001 (2009)
Boucaud Ph., Gomez M.E., Leroy J.P., Le Yaouanc A., Micheli J. et al.: The low-momentum ghost dressing function and the gluon mass. Phys. Rev. D 82, 054007 (2010)
Gribov V.N.: Quantization of nonabelian gauge theories. Nucl. Phys. B 139, 1 (1978)
Dell’Antonio G., Zwanziger D.: Every gauge orbit passes inside the Gribov horizon. Commun. Math. Phys. 138, 291–299 (1991)
Zwanziger D.: Action from the Gribov horizon. Nucl. Phys. B 321, 591 (1989)
Zwanziger D.: Renormalizability of the critical limit of lattice gauge theory by BRS invariance. Nucl. Phys. B 399, 477–513 (1993)
Kondo K.-I.: Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition. Phys. Lett. B 678, 322–330 (2009)
Dudal D., Sobreiro R.F., Sorella S.P., Verschelde H.: The Gribov parameter and the dimension two gluon condensate in Euclidean Yang–Mills theories in the Landau gauge. Phys. Rev. D 72, 014016 (2005)
Dudal D., Sorella S.P., Vandersickel N., Verschelde H.: New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach. Phys. Rev. D 77, 071501 (2008)
Dudal D., Gracey J.A., Paolo Sorella S., Vandersickel N., Verschelde H.: A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results. Phys. Rev. D 78, 065047 (2008)
Zwanziger D.: Local and renormalizable action from the Gribov horizon. Nucl. Phys. B 323, 513–544 (1989)
Dudal D., Oliveira O., Vandersickel N.: Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate \({\langle A^{2}\rangle }\) in the Landau gauge. Phys. Rev. D 81, 074505 (2010)
Dudal, D., Sorella, S.P., Vandersickel, N.: The dynamical origin of the refinement of the Gribov-Zwanziger theory. arXiv:1105.3371 (2011)
Ellwanger U., Hirsch M., Weber A.: Flow equations for the relevant part of the pure Yang–Mills action. Z. Phys. C 69, 687–698 (1996)
Ellwanger U., Hirsch M., Weber A.: The heavy quark potential from Wilson’s exact renormalization group. Eur. Phys. J. C 1, 563–578 (1998)
Fischer C.S., Gies H.: Renormalization flow of Yang–Mills propagators. JHEP 10, 048 (2004)
Pawlowski J.M., Litim D.F., Nedelko S., von Smekal L.: Infrared behaviour and fixed points in Landau gauge QCD. Phys. Rev. Lett. 93, 152002 (2004)
Pawlowski J.M.: Aspects of the functional renormalisation group. Ann. Phys. 322, 2831–2915 (2007)
Fischer C.S., Pawlowski J.M.: Uniqueness of infrared asymptotics in Landau gauge Yang- Mills theory II. Phys. Rev. D 80, 025023 (2009)
Frasca M.: Infrared gluon and ghost propagators. Phys. Lett. B 670, 73–77 (2008)
Frasca M.: Yang–Mills propagators and QCD. Nucl. Phys. Proc. Suppl. 186, 260–263 (2009)
Frasca M.: Mapping a massless scalar field theory on a Yang–Mills theory: classical case. Mod. Phys. Lett. A 24, 2425–2432 (2009)
Tissier M., Wschebor N.: Infrared propagators of Yang–Mills theory from perturbation theory. Phys. Rev. D 82, 101701 (2010)
Tissier, M., Wschebor, N.: An infrared safe perturbative approach to Yang–Mills correlators. arXiv:1105.2475 (2011)
Zwanziger D.: Non-perturbative Faddeev-Popov formula and infrared limit of QCD. Phys. Rev. D 69, 016002 (2004)
Zwanziger D.: Nonperturbative Landau gauge and infrared critical exponents in QCD. Phys. Rev. D 65, 094039 (2002)
Kugo, T., Ojima, I.: Prog. Theor. Phys. Supp. pp. 1–130 (1979)
Kugo, T.: The universal renormalization factors Z(1)/Z(3) and color confinement condition in nonAbelian gauge theory. In: International Symposium on BRS Symmetry, pp. 107–119, Kyoto (1995)
Boucaud P., Leroy J.P., Le Yaouanc A., Micheli J., Pène O. et al.: Gribov’s horizon and the ghost dressing function. Phys. Rev. D 80, 094501 (2009)
Greensite J., Olejnik S.: Coulomb energy, vortices, and confinement. Phys. Rev. D 67, 094503 (2003)
Greensite J., Olejnik S., Zwanziger D.: Center vortices and the Gribov horizon. JHEP 0505, 070 (2005)
Pennington M.R.: Strong coupling continuum QCD. AIP Conf. Proc. 1343, 63–68 (2011)
Lerche C., von Smekal L.: On the infrared exponent for gluon and ghost propagation in Landau gauge QCD. Phys. Rev. D 65, 125006 (2002)
Chetyrkin K.G.: Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions. Nucl. Phys. B 710, 499–510 (2005)
Bloch J.C.R.: Two-loop improved truncation of the ghost-gluon Dyson-Schwinger equations: multiplicatively renormalizable propagators and nonperturbative running coupling. Few-Body Syst. 33, 111–152 (2003)
Schwinger J.S.: Gauge invariance and mass. Phys. Rev. 125, 397–398 (1962)
Cornwall J.M.: Dynamical mass generation in continuum QCD. Phys. Rev. D 26, 1453 (1982)
Aguilar A.C., Papavassiliou J.: Power-law running of the effective gluon mass. Eur. Phys. J. A 35, 189–205 (2008)
Lavelle M.: Gauge invariant effective gluon mass from the operator product expansion. Phys. Rev. D 44, 26–28 (1991)
Boucaud P., De Soto F., Leroy J.P., Le Yaouanc A., Micheli J., Pène O., Rodríguez-Quintero J.: Ghost-gluon running coupling, power corrections and the determination of \({\Lambda_{\overline{\rm MS}}}\) . Phys. Rev. D 79, 014508 (2009)
Aguilar, A.C., Binosi, D., Papavassiliou, J.: Infrared finite effective charge of QCD. PoS LC2008:050 (2008)
Taylor J.C.: Ward identities and charge renormalization of the Yang–Mills field. Nucl. Phys. B 33, 436–444 (1971)
Itzykson C., Zuber J.-B.: Quantum Field Theory. McGraw-Hill, New York (1980)
Boucaud P., Leroy J.P., Le Yaouanc A., Lokhov A.Y., Micheli J. et al.: Divergent IR gluon propagator from Ward-Slavnov-Taylor identities?. JHEP 0703, 076 (2007)
Davydychev A.I., Osland P., Tarasov O.V.: Three gluon vertex in arbitrary gauge and dimension. Phys. Rev. D 54, 4087–4113 (1996)
Ball J.S., Chiu T.-W.: Analytic properties of the vertex function in gauge theories 2. Phys. Rev. D 22, 2550 (1980)
Boucaud P., Leroy J.P., Le Yaouanc A., Lokhov A.Y., Micheli J. et al.: Constraints on the IR behaviour of gluon and ghost propagator from Ward-Slavnov-Taylor identities. Eur. Phys. J. A 31, 750–753 (2007)
Alkofer R., Huber M.Q., Schwenzer K.: Infrared singularities in Landau gauge Yang–Mills theory. Phys. Rev. D 81, 105010 (2010)
Zwanziger D.: Vanishing of zero momentum lattice gluon propagator and color confinement. Nucl. Phys. B 364, 127–161 (1991)
Mandula J.E., Ogilvie M.: The gluon is massive: a lattice calculation of the gluon propagator in the Landau gauge. Phys. Lett. B 185, 127–132 (1987)
Gupta R., Guralnik G., Kilcup G., Patel A., Sharpe S.R. et al.: The hadron spectrum on a 183 × 42 lattice. Phys. Rev. D 36, 2813 (1987)
Bernard C.W., Parrinello C., Soni A.: The Gluon propagator in momentum space. Nucl. Phys. Proc. Suppl. 30, 535–538 (1993)
Suman H., Schilling K.: First lattice study of ghost propagators in SU(2) and SU(3) gauge theories. Phys. Lett. B 373, 314–318 (1996)
Cucchieri A.: Gribov copies in the minimal Landau gauge: the influence on gluon and ghost propagators. Nucl. Phys. B 508, 353–370 (1997)
Nakajima H., Furui Sadataka: Test of the Kugo–Ojima confinement criterion in the lattice Landau gauge. Nucl. Phys. Proc. Suppl. 83, 521–523 (2000)
Cucchieri, A., Mendes, T.: Numerical test of the Gribov-Zwanziger scenario in Landau gauge. PoS QCD-TNT09:026 (2009)
Sternbeck, A., Ilgenfritz, E.M., Muller-Preussker, M., Schiller, A.: Studying the infrared region in Landau gauge QCD. PoS LAT2005:333 (2006)
Bonnet F.D.R., Bowman P.O., Leinweber D.B., Williams A.G.: Infrared behavior of the gluon propagator on a large volume lattice. Phys. Rev. D 62, 051501 (2000)
Bonnet F.D.R., Bowman P.O., Leinweber D.B., Williams A.G., Zanotti J.M.: Infinite volume and continuum limits of the Landau gauge gluon propagator. Phys. Rev. D 64, 034501 (2001)
Sternbeck A., Ilgenfritz E.-M., Mueller-Preussker M., Schiller A.: Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics. Phys. Rev. D 72, 014507 (2005)
Boucaud P., Leroy J.P., Le Yaouanc A., Lokhov A.Y., Micheli J. et al.: Asymptotic behavior of the ghost propagator in SU3 lattice gauge theory. Phys. Rev. D 72, 114503 (2005)
Silva P.J., Oliveira O.: Infrared gluon propagator from lattice QCD: results from large asymmetric lattices. Phys. Rev. D 74, 034513 (2006)
Silva P.J., Oliveira O.: Studying the infrared behaviour of gluon and ghost propagators using large asymmetric lattices. AIP Conf. Proc. 892, 220–222 (2007)
Sternbeck, A., Ilgenfritz, E.-M., Muller-Preussker, M., Schiller, A., Bogolubsky, I.L.: Lattice study of the infrared behavior of QCD Green’s functions in Landau gauge. PoS LAT2006:076 (2006)
Oliveira O., Silva P.J.: Infrared gluon and ghost propagators exponents from lattice QCD. Eur. Phys. J. C 62, 525–534 (2009)
Oliveira O., Silva P.J.: Does the lattice zero momentum gluon propagator for pure gauge SU(3) Yang–Mills theory vanish in the infinite volume limit?. Phys. Rev. D 79, 031501 (2009)
Oliveira, O., Silva, P.J.: The lattice infrared Landau gauge gluon propagator: the infinite volume limit. PoS LAT2009:226 (2009)
Oliveira O., Silva, P.J.: The lattice infrared Landau gauge gluon propagator: from finite volume to the infinite volume. PoS QCD-TNT09:033 (2009)
Iritani T., Suganuma H., Iida H.: Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function. Phys. Rev. D 80, 114505 (2009)
Suganuma, H., Iritani, T., Yamamoto, A., Iida, H.: Lattice QCD analysis for gluons. PoS QCD-TNT09:044 (2009)
Suganuma, H., Iritani, T., Yamamoto, A., Iida, H.: Lattice QCD study for gluon propagator and gluon spectral function. PoS LAT2010:289 (2010)
Bogolubsky I.L., Ilgenfritz E.M., Muller-Preussker M., Sternbeck A.: Lattice gluodynamics computation of Landau gauge Green’s functions in the deep infrared. Phys. Lett. B 676, 69–73 (2009)
Halzen F., Krein G.I., Natale A.A.: Relating the QCD pomeron to an effective gluon mass. Phys. Rev. D 47, 295–298 (1993)
Oliveira O., Bicudo P.: Running gluon mass from Landau gauge lattice QCD propagator. J. Phys. G G38, 045003 (2011)
von Smekal L., Alkofer R., Hauck A.: The Infrared behavior of gluon and ghost propagators in Landau gauge QCD. Phys. Rev. Lett. 79, 3591–3594 (1997)
Sternbeck A., Ilgenfritz E.-M., Muller-Preussker M., Schiller A.: Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum. Nucl. Phys. Proc. Suppl. 153, 185–190 (2006)
Cucchieri A., Mendes T., Mihara A.: Numerical study of the ghost-gluon vertex in Landau gauge. JHEP 0412, 012 (2004)
Cucchieri A., Maas A., Mendes T.: Three-point vertices in Landau-gauge Yang–Mills theory. Phys. Rev. D 77, 094510 (2008)
Alles B., Henty D., Panagopoulos H., Parrinello C., Pittori C. et al.: α s from the nonperturbatively renormalised lattice three gluon vertex. Nucl. Phys. B 502, 325–342 (1997)
Boucaud P., Leroy J.P., Micheli J., Pène O., Roiesnel C.: Lattice calculation of α s in momentum scheme. JHEP 9810, 017 (1998)
Boucaud P., De Soto F., Le Yaouanc A., Leroy J.P., Micheli J. et al.: The strong coupling constant at small momentum as an instanton detector. JHEP 0304, 005 (2003)
Bowman P.O. et al.: Scaling behavior and positivity violation of the gluon propagator in full QCD. Phys. Rev. D 76, 094505 (2007)
Cucchieri A., Mendes T.: Landau-gauge propagators in Yang–Mills theories at β = 0: massive solution versus conformal scaling. Phys. Rev. D 81, 016005 (2010)
Becirevic D. et al.: Asymptotic behaviour of the gluon propagator from lattice QCD. Phys. Rev. D 60, 094509 (1999)
Becirevic D. et al.: Asymptotic scaling of the gluon propagator on the lattice. Phys. Rev. D 61, 114508 (2000)
de Soto F., Roiesnel C.: On the reduction of hypercubic lattice artifacts. JHEP 0709, 007 (2007)
Fischer C.S., Axel M., Pawlowski J.M., von Smekal L.: Large volume behaviour of Yang–Mills propagators. Ann. Phys. 322, 2916–2944 (2007)
Cucchieri A., Mendes T.: Constraints on the IR behavior of the gluon propagator in Yang–Mills theories. Phys. Rev. Lett. 100, 241601 (2008)
Cucchieri A., Mendes T.: Infrared behavior of gluon and ghost propagators from asymmetric lattices. Phys. Rev. D 73, 071502 (2006)
Oliveira, O., Silva, P.J., Ilgenfritz, E.M., Sternbeck, A.: The Gluon propagator from large asymmetric lattices. PoS LAT2007:323 (2007)
Bowman P.O., Heller U.M., Leinweber D.B., Parappilly M.B., Williams A.G.: QCD propagators: some results from the lattice. Nucl. Phys. Proc. Suppl. 161, 27–33 (2006)
Giusti L., Paciello M.L., Parrinello C., Petrarca S., Taglienti B.: Problems on lattice gauge fixing. Int. J. Mod. Phys. A 16, 3487–3534 (2001)
Bogolubsky I.L., Bornyakov V.G., Burgio G., Ilgenfritz E.M., Muller-Preussker M. et al.: Improved Landau gauge fixing and the suppression of finite-volume effects of the lattice gluon propagator. Phys. Rev. D 77, 014504 (2008)
Maas A.: Constructing non-perturbative gauges using correlation functions. Phys. Lett. B 689, 107–111 (2010)
Bogolubsky, I.L., Ilgenfritz, E.-M., Muller-Preussker, M., Sternbeck, A.: The Landau gauge gluon propagator in 4D SU(2) lattice gauge theory revisited: Gribov copies and scaling properties. PoS LAT2009:237 (2009)
Bornyakov V.G., Mitrjushkin V.K., Muller-Preussker M.: SU(2) lattice gluon propagator: continuum limit, finite-volume effects and infrared mass scale m IR . Phys. Rev. D 81, 054503 (2010)
Lokhov, A.Y., Pène, O., Roiesnel, C.: Scaling properties of the probability distribution of lattice Gribov copies. arXiv:hep-lat/0511049 (2005)
Christ N.H., Lee T.D.: Operator ordering and Feynman rules in gauge theories. Phys. Rev. D 22, 939 (1980)
Zwanziger D.: No confinement without Coulomb confinement. Phys. Rev. Lett. 90, 102001 (2003)
Cucchieri, A., Mendes, T.: Gauge fixing and gluon propagator in lambda gauges (1998)
Maas, A., Cucchieri, A., Mendes, T.: Propagators in Yang–Mills theory for different gauges. PoS CONFINEMENT8:181 (2008)
Iritani T., Suganuma H.: Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: a linkage between the Landau and the Coulomb gauges. Phys. Rev. D 83, 054502 (2011)
Maas, A., Mendes, T., Olejnik, S.: Yang–Mills Theory in lambda-gauges. arXiv:1108.2621 (2011)
Burgio G., Quandt M., Reinhardt H.: BRST symmetry versus horizon condition in Yang–Mills theory. Phys. Rev. D 81, 074502 (2010)
Quandt, M., Burgio, G., Chimchinda, S., Reinhardt, H.: Coulomb gauge ghost propagator and the Coulomb potential. PoS CONFINEMENT8:066 (2008)
Langfeld K., Moyaerts L.: Propagators in Coulomb gauge from SU(2) lattice gauge theory. Phys. Rev. D 70, 074507 (2004)
Cucchieri A., Zwanziger D.: Numerical study of gluon propagator and confinement scenario in minimal Coulomb gauge. Phys. Rev. D 65, 014001 (2001)
Quandt, M., Burgio, G., Chimchinda, S., Reinhardt, H.: Coulomb gauge Green functions and Gribov copies in SU(2) lattice gauge theory. PoS LAT2007:325 (2007)
Burgio, G., Quandt, M., Reinhardt, H.: The gluon propagator in Coulomb gauge from the lattice. PoS CONFINEMENT8:051 (2008)
Burgio, G., Quandt, M., Schrock, M., Reinhardt, H.: Propagators in lattice Coulomb gauge and confinement mechanisms. PoS, LATTICE2010:272 (2010)
Burgio G., Quandt M., Reinhardt H.: Coulomb gauge gluon propagator and the Gribov formula. Phys. Rev. Lett. 102, 032002 (2009)
Nakagawa Y., Nakamura A., Saito T., Toki T.: The Coulomb gauge confinement scenario and the color-dependent quark potentials in lattice QCD simulations. Mod. Phys. Lett. A 23, 2348–2351 (2008)
Nakagawa Y., Nakamura A., Saito T., Toki H.: The volume dependence of the long-range two-body potentials in various color channels by lattice QCD. Phys. Rev. D 77, 034015 (2008)
Nakagawa Y., Voigt A., Ilgenfritz E.-M., Muller-Preussker M., Nakamura A. et al.: Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang–Mills theory. Phys. Rev. D 79, 114504 (2009)
Greensite, J., Olejnik, S.: Gluon chains and the quark-antiquark potential. PoS LAT2009:240 (2009)
Greensite, J.: Aspects of confinement in Coulomb gauge. PoS QCD-TNT09:017 (2009)
Greensite J., Olejnik S.: Constituent gluon content of the static quark-antiquark state in Coulomb gauge. Phys. Rev. D 79, 114501 (2009)
Nakagawa, Y., Nakamura, A., Saito, T., Toki, H.: Coulomb gauge gluon propagator on anisotropic lattices. PoS LAT2009:230 (2009)
Nakagawa Y., Nakamura A., Saito T., Toki H.: Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang–Mills theory. Phys. Rev. D 81, 054509 (2010)
Nakagawa Y., Nakamura A., Saito T., Toki H.: Scaling study of the gluon propagator in Coulomb gauge QCD on isotropic and anisotropic lattices. Phys. Rev. D 83, 114503 (2011)
Rodriguez-Quintero J.: A brief comment on the similarities of the IR solutions for the ghost propagator DSE in Landau and Coulomb gauges. Phys. Rev. D 83, 097501 (2011)
Boucaud P., Le Yaouanc A., Leroy J.P., Micheli J., Pène O. et al.: Consistent OPE description of gluon two point and three point Green function?. Phys. Lett. B 493, 315–324 (2000)
Boucaud P., Le Yaouanc A., Leroy J.P., Micheli J., Pène O., Rodríguez-Quintero J.: Testing Landau gauge OPE on the lattice with a \({\langle A^{2}\rangle}\) condensate. Phys. Rev. D 63, 114003 (2001)
De Soto F., Rodriguez-Quintero J.: Remarks on the determination of the Landau gauge OPE for the asymmetric three gluon vertex. Phys. Rev. D 64, 114003 (2001)
Boucaud P., Leroy J.P., Le Yaouanc A., Lokhov A.Y., Micheli J. et al.: Non-perturbative power corrections to ghost and gluon propagators. JHEP 0601, 037 (2006)
Shifman M.A., Vainshtein A.I., Zakharov V.I.(1979) QCD and resonance physics. Sum rules. Nucl. Phys. B 147, 385, 448, 519 (1979)
Lavelle M., Oleszczuk M.: The operator product expansion of the QCD propagators. Mod. Phys. Lett. A 7, 3617–3630 (1992)
Martinelli G., Sachrajda C.T.: On the difficulty of computing higher twist corrections. Nucl. Phys. B 478, 660–686 (1996)
Pène, O., Blossier, B., Boucaud, Ph., Le Yaouanc, A., Leroy, J.P. et al.: Vacuum expectation value of \({\langle A^{2}\rangle}\) from LQCD. PoS FACESQCD:010 (2011)
Chetyrkin K.G., Maier A.: Wilson expansion of QCD propagators at three loops: operators of dimension two and three. JHEP 1001, 092 (2010)
Boucaud P., de Soto F., Leroy J.P., Le Yaouanc A., Micheli J. et al.: Quark propagator and vertex: systematic corrections of hypercubic artifacts from lattice simulations. Phys. Lett. B 575, 256–267 (2003)
Boucaud, Ph., Dudal, D., Leroy, J.P., Pene, O., Rodriguez-Quintero, J.: On the leading OPE corrections to the ghost-gluon vertex and the Taylor theorem. arXiv:1109.3803 (2011)
Aguilar A.C., Papavassiliou J.: Chiral symmetry breaking with lattice propagators. Phys. Rev. D 83, 014013 (2011)
Fischer C.S.: Infrared properties of QCD from Dyson-Schwinger equations. J. Phys. G G32, R253–R291 (2006)
Burgio G., Quandt M., Reinhardt H.: Coulomb gauge gluon propagator and the Gribov formula. Phys. Rev. Lett. 102, 032002 (2009)
Watson P., Reinhardt H.: Propagator Dyson-Schwinger equations of Coulomb Gauge Yang–Mills theory within the first order formalism. Phys. Rev. D 75, 045021 (2007)
Watson P., Reinhardt H.: Two-point functions of Coulomb gauge Yang–Mills theory. Phys. Rev. D 77, 025030 (2008)
Popovici C., Watson P., Reinhardt H.: Quarks in Coulomb gauge perturbation theory. Phys. Rev. D 79, 045006 (2009)
Popovici C., Watson P., Reinhardt H.: Coulomb gauge confinement in the heavy quark limit. Phys. Rev. D 81, 105011 (2010)
Szczepaniak A.P., Swanson E.S.: Coulomb gauge QCD, confinement, and the constituent representation. Phys. Rev. D 65, 025012 (2002)
Reinhardt H., Feuchter C.: On the Yang–Mills wave functional in Coulomb gauge. Phys. Rev. D 71, 105002 (2005)
Schleifenbaum W., Leder M., Reinhardt H.: Infrared analysis of propagators and vertices of Yang–Mills theory in Landau and Coulomb gauge. Phys. Rev. D 73, 125019 (2006)
Epple D., Reinhardt H., Schleifenbaum W.: Confining solution of the Dyson-Schwinger equations in Coulomb gauge. Phys. Rev. D 75, 045011 (2007)
Rodriguez-Quintero J.: On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions. JHEP 1101, 105 (2011)
Binosi D., Papavassiliou J.: Pinch technique: theory and applications. Phys. Rept. 479, 1–152 (2009)
von Smekal L., Hauck A., Alkofer R.: A solution to coupled Dyson-Schwinger equations for gluons and ghosts in Landau gauge. Ann. Phys. 267, 1 (1998)
Fischer C.S., Alkofer R., Reinhardt H.: The elusiveness of infrared critical exponents in Landau gauge Yang–Mills theories. Phys. Rev. D 65, 094008 (2002)
Watson P., Alkofer R.: Verifying the Kugo-Ojima confinement criterion in Landau gauge QCD. Phys. Rev. Lett. 86, 5239 (2001)
Alkofer R., Fischer C.S., Llanes-Estrada F.J.: Vertex functions and infrared fixed point in Landau gauge SU(N) Yang–Mills theory. Phys. Lett. B 611, 279–288 (2005)
Schleifenbaum W., Maas A., Wambach J., Alkofer R.: Infrared behaviour of the ghost gluon vertex in Landau gauge Yang–Mills theory. Phys. Rev. D 72, 014017 (2005)
Huber M.Q., Schwenzer K., Alkofer R.: On the infrared scaling solution of SU(N) Yang–Mills theories in the maximally Abelian gauge. Eur. Phys. J. C68, 581–600 (2010)
Aguilar, A.C., Natale, A.A.: A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations. JHEP 0408, 057 (2004). Erratum added online, jan/11/2005
Binosi D., Papavassiliou J.: The Pinch technique to all orders. Phys. Rev. D 66, 111901 (2002)
Aguilar A.C., Binosi D., Papavassiliou J.: QCD effective charges from lattice data. JHEP 1007, 002 (2010)
Grassi P.A., Hurth T., Steinhauser M.: Practical algebraic renormalization. Ann. Phys. 288, 197–248 (2001)
Davies C.T.H. et al.: Update: accurate determinations of α s from realistic lattice QCD. Phys. Rev. D 78, 114507 (2008)
Luscher M., Sommer R., Weisz P., Wolff U.: A precise determination of the running coupling in the SU(3) Yang–Mills theory. Nucl. Phys. B 413, 481–502 (1994)
Maris P., Tandy P.C.: Bethe-Salpeter study of vector meson masses and decay constants. Phys. Rev. C 60, 055214 (1999)
Maris P., Roberts C.D., Tandy P.C.: Pion mass and decay constant. Phys. Lett. B 420, 267–273 (1998)
Roberts H.L.L., Roberts C.D., Bashir A., Gutierrez-Guerrero L.X., Tandy P.C.: Abelian anomaly and neutral pion production. Phys. Rev. C 82, 065202 (2010)
Roberts H.L.L., Bashir A., Gutierrez-Guerrero L.X., Roberts C.D., Wilson D.J.: π- and ρ-mesons, and their diquark partners, from a contact interaction. Phys. Rev. C 83, 065206 (2011)
Iddir F., Semlala L.: The hybrid meson: new results from the updated m g and α s parameters. Int. J. Mod. Phys. A 26, 4101–4110 (2011)
Oliveira, O., de Paula, W., Frederico, T.: Linking dynamical gluon mass to chiral symmetry breaking via a QCD low energy effective field theory. arXiv:1105.4899 (2011)
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Boucaud, P., Leroy, J.P., Le Yaouanc, A. et al. The Infrared Behaviour of the Pure Yang–Mills Green Functions. Few-Body Syst 53, 387–436 (2012). https://doi.org/10.1007/s00601-011-0301-2
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DOI: https://doi.org/10.1007/s00601-011-0301-2