Abstract
We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green’s functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.
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References
A. Cucchieri and T. Mendes, What’s up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices, PoS(LATTICE 2007)297 [arXiv:0710.0412] [SPIRES].
A. Cucchieri and T. Mendes, Landau-gauge propagators in Yang-Mills theories at β = 0: massive solution versus conformal scaling, Phys. Rev. D 81 (2010) 016005 [arXiv:0904.4033] [SPIRES].
I.L. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker and A. Sternbeck, The Landau gauge gluon and ghost propagators in 4D SU(3) gluodynamics in large lattice volumes, PoS(LATTICE 2007)290 [arXiv:0710.1968] [SPIRES].
I.L. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker and A. Sternbeck, Lattice gluodynamics computation of Landau gauge Green’s functions in the deep infrared, Phys. Lett. B 676 (2009) 69 [arXiv:0901.0736] [SPIRES].
O. Oliveira and P.J. Silva, The lattice infrared Landau gauge gluon propagator: the infinite volume limit, arXiv:0910.2897 [SPIRES].
O. Oliveira and P.J. Silva, The lattice infrared Landau gauge gluon propagator: from finite volume to the infinite volume, arXiv:0911.1643 [SPIRES].
J.M. Cornwall, Dynamical Mass Generation in Continuum QCD, Phys. Rev. D 26 (1982) 1453 [SPIRES].
J.M. Cornwall and J. Papavassiliou, Gauge Invariant Three Gluon Vertex in QCD, Phys. Rev. D 40 (1989) 3474 [SPIRES].
D. Binosi and J. Papavassiliou, Pinch Technique: Theory and Applications, Phys. Rept. 479 (2009) 1 [arXiv:0909.2536] [SPIRES].
N.J. Watson, The gauge-independent QCD effective charge, Nucl. Phys. B 494 (1997) 388 [hep-ph/9606381] [SPIRES].
D. Binosi and J. Papavassiliou, The QCD effective charge to all orders, Nucl. Phys. Proc. Suppl. 121 (2003) 281 [hep-ph/0209016] [SPIRES].
A. Pilaftsis, Generalized pinch technique and the background field method in general gauges, Nucl. Phys. B 487 (1997) 467 [hep-ph/9607451] [SPIRES].
A. Denner, G. Weiglein and S. Dittmaier, Gauge invariance of green functions: Background field method versus pinch technique, Phys. Lett. B 333 (1994) 420 [hep-ph/9406204] [SPIRES].
S. Hashimoto, J. Kodaira, Y. Yasui and K. Sasaki, The Background field method: Alternative way of deriving the pinch technique’s results, Phys. Rev. D 50 (1994) 7066 [hep-ph/9406271] [SPIRES].
J. Papavassiliou, On the connection between the pinch technique and the background field method, Phys. Rev. D 51 (1995) 856 [hep-ph/9410385] [SPIRES].
D. Binosi and J. Papavassiliou, The pinch technique to all orders, Phys. Rev. D 66 (2002) 111901 [hep-ph/0208189] [SPIRES].
D. Binosi and J. Papavassiliou, Pinch technique self-energies and vertices to all orders in perturbation theory, J. Phys. G 30 (2004) 203 [hep-ph/0301096] [SPIRES].
L.F. Abbott, The Background Field Method Beyond One Loop, Nucl. Phys. B 185 (1981) 189 [SPIRES].
J.C. Taylor, Ward Identities and Charge Renormalization of the Yang-Mills Field, Nucl. Phys. B 33 (1971) 436 [SPIRES].
W.J. Marciano and H. Pagels, Quantum Chromodynamics: A Review, Phys. Rept. 36 (1978) 137 [SPIRES].
R. Alkofer, C.S. Fischer and F.J. Llanes-Estrada, Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory, Phys. Lett. B 611 (2005) 279 [Erratum ibid. 670 (2009) 460] [hep-th/0412330] [SPIRES].
P.A. Grassi, T. Hurth and M. Steinhauser, Practical algebraic renormalization, Annals Phys. 288 (2001) 197 [hep-ph/9907426] [SPIRES].
D. Binosi and J. Papavassiliou, Pinch technique and the Batalin-Vilkovisky formalism, Phys. Rev. D 66 (2002) 025024 [hep-ph/0204128] [SPIRES].
D. Binosi and J. Papavassiliou, Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD, Phys. Rev. D 77 (2008) 061702 [arXiv:0712.2707] [SPIRES].
D. Binosi and J. Papavassiliou, New Schwinger-Dyson equations for non-Abelian gauge theories, JHEP 11 (2008) 063 [arXiv:0805.3994] [SPIRES].
T. Kugo and I. Ojima, Local Covariant Operator Formalism of Nonabelian Gauge Theories and Quark Confinement Problem, Prog. Theor. Phys. Suppl. 66 (1979) 1 [SPIRES].
A.C. Aguilar, D. Binosi, J. Papavassiliou and J. Rodriguez-Quintero, Non-perturbative comparison of QCD effective charges, Phys. Rev. D 80 (2009) 085018 [arXiv:0906.2633] [SPIRES].
A.C. Mattingly and P.M. Stevenson, Optimization of R(e+ e−) and ’freezing’ of the QCD couplant at low-energies, Phys. Rev. D 49 (1994) 437 [hep-ph/9307266] [SPIRES].
Y.L. Dokshitzer, G. Marchesini and B.R. Webber, Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes, Nucl. Phys. B 469 (1996) 93 [hep-ph/9512336] [SPIRES].
L. von Smekal, R. Alkofer and A. Hauck, The infrared behavior of gluon and ghost propagators in Landau gauge QCD, Phys. Rev. Lett. 79 (1997) 3591 [hep-ph/9705242] [SPIRES].
A.M. Badalian and V.L. Morgunov, Determination of α s (1GeV) from the charmonium fine structure, Phys. Rev. D 60 (1999) 116008 [hep-ph/9901430] [SPIRES].
A.C. Aguilar, A.A. Natale and P.S. Rodrigues da Silva, Relating a gluon mass scale to an infrared fixed point in pure gauge QCD, Phys. Rev. Lett. 90 (2003) 152001 [hep-ph/0212105] [SPIRES].
S.J. Brodsky, S. Menke, C. Merino and J. Rathsman, On the Behavior of the Effective QCD Coupling α τ(s) at Low Scales, Phys. Rev. D 67 (2003) 055008 [hep-ph/0212078] [SPIRES].
S.J. Brodsky, New perspectives for QCD: The novel effects of final-state interactions and near-conformal effective couplings, Fizika B 13 (2004) 91 [hep-ph/0310289] [SPIRES].
M. Baldicchi and G.M. Prosperi, Infrared behavior of the running coupling constant and bound states in QCD, Phys. Rev. D 66 (2002) 074008 [hep-ph/0202172] [SPIRES].
G. Grunberg, Renormalization Scheme Independent QCD and QED: The Method of Effective Charges, Phys. Rev. D 29 (1984) 2315 [SPIRES].
G. Grunberg, Evidence for infrared finite coupling in Sudakov resummation, Phys. Rev. D 73 (2006) 091901 [hep-ph/0603135] [SPIRES].
H. Gies, Running coupling in Yang-Mills theory: A flow equation study, Phys. Rev. D 66 (2002) 025006 [hep-th/0202207] [SPIRES].
D.V. Shirkov and I.L. Solovtsov, Analytic model for the QCD running coupling with universal α s (0) value, Phys. Rev. Lett. 79 (1997) 1209 [hep-ph/9704333] [SPIRES].
J.A. Gracey, One loop gluon form factor and freezing of α s in the Gribov-Zwanziger QCD Lagrangian, JHEP 05 (2006) 052 [Erratum ibid. 1002 (2010) 078] [hep-ph/0605077] [SPIRES].
G.M. Prosperi, M. Raciti and C. Simolo, On the running coupling constant in QCD, Prog. Part. Nucl. Phys. 58 (2007) 387 [hep-ph/0607209] [SPIRES].
S.J. Brodsky and G.F. de Teramond, Light-front hadron dynamics and AdS/CFT correspondence, Phys. Lett. B 582 (2004) 211 [hep-th/0310227] [SPIRES].
S.J. Brodsky, G.F. de Teramond and A. Deur, Nonperturbative QCD Coupling and its β function from Light-Front Holography, Phys. Rev. D 81 (2010) 096010 [arXiv:1002.3948] [SPIRES].
A.C. Aguilar, D. Binosi and J. Papavassiliou, Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations, Phys. Rev. D 78 (2008) 025010 [arXiv:0802.1870] [SPIRES].
F.V. Gubarev, L. Stodolsky and V.I. Zakharov, On the significance of the quantity A 2, Phys. Rev. Lett. 86 (2001) 2220 [hep-ph/0010057] [SPIRES].
P. Boucaud et al., Testing Landau gauge OPE on the lattice with a < A 2 > condensate, Phys. Rev. D 63 (2001) 114003 [hep-ph/0101302] [SPIRES].
F.V. Gubarev and V.I. Zakharov, Emerging phenomenology of < A min 2 >, Phys. Lett. B 501 (2001) 28 [hep-ph/0010096] [SPIRES].
J.A. Gracey, One loop renormalization of the non-local gauge invariant operator min{U}∫d 4 x(A aUμ )2 in QCD, Phys. Lett. B 651 (2007) 253 [arXiv:0706.1440] [SPIRES].
M. Lavelle, Gauge invariant effective gluon mass from the operator product expansion, Phys. Rev. D 44 (1991) 26 [SPIRES].
A.C. Aguilar and J. Papavassiliou, Power-law running of the effective gluon mass, Eur. Phys. J. A 35 (2008) 189 [arXiv:0708.4320] [SPIRES].
D. Dudal, J.A. Gracey, S.P. Sorella, N. Vandersickel and H. Verschelde, A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results, Phys. Rev. D 78 (2008) 065047 [arXiv:0806.4348] [SPIRES].
C.W. Bernard, Monte Carlo Evaluation of the Effective Gluon Mass, Phys. Lett. B 108 (1982) 431 [SPIRES].
C.W. Bernard, Adjoint Wilson lines and the effective gluon mass, Nucl. Phys. B 219 (1983) 341 [SPIRES].
T. Iritani, H. Suganuma and H. Iida, 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 (2009) 114505 [arXiv:0908.1311] [SPIRES].
G. Parisi and R. Petronzio, On Low-Energy Tests of QCD, Phys. Lett. B 94 (1980) 51 [SPIRES].
F. Halzen, G.I. Krein and A.A. Natale, Relating the QCD Pomeron to an effective gluon mass, Phys. Rev. D 47 (1993) 295 [SPIRES].
F.J. Yndurain, Limits on the mass of the gluon, Phys. Lett. B 345 (1995) 524 [SPIRES].
A. Szczepaniak, E.S. Swanson, C.-R. Ji and S.R. Cotanch, Glueball Spectroscopy in a Relativistic Many-Body Approach to Hadron Structure, Phys. Rev. Lett. 76 (1996) 2011 [hep-ph/9511422] [SPIRES].
J.H. Field, A phenomenological analysis of gluon mass effects in inclusive radiative decays of the J/ψ and Upsilon, Phys. Rev. D 66 (2002) 013013 [hep-ph/0101158] [SPIRES].
A.C. Aguilar, A. Mihara and A.A. Natale, Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations, Phys. Rev. D 65 (2002) 054011 [hep-ph/0109223] [SPIRES].
E.G.S. Luna, A.F. Martini, M.J. Menon, A. Mihara and A.A. Natale, Influence of a dynamical gluon mass in the p p and \( \bar{p}p \) forward scattering, Phys. Rev. D 72 (2005) 034019 [hep-ph/0507057] [SPIRES].
E.G.S. Luna, Survival probability of large rapidity gaps in a QCD model with a dynamical infrared mass scale, Phys. Lett. B 641 (2006) 171 [hep-ph/0608091] [SPIRES].
O. Oliveira and P. Bicudo, Running Gluon Mass from Landau Gauge Lattice QCD Propagator, arXiv:1002.4151 [SPIRES].
D. Dudal, O. Oliveira and N. Vandersickel, Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate < A 2 > in the Landau gauge, Phys. Rev. D 81 (2010) 074505 [arXiv:1002.2374] [SPIRES].
J.S. Ball and T.-W. Chiu, Analytic properties of the vertex function in gauge theories. 2, Phys. Rev. D 22 (1980) 2550 [Erratum ibid. D 23 (1981) 3085]. [SPIRES].
T. Kugo, The universal renormalization factors Z(1)/Z(3) and color confinement condition in non-Abelian gauge theory, hep-th/9511033 [SPIRES].
P.A. Grassi, T. Hurth and A. Quadri, On the Landau background gauge fixing and the IR properties of YM Green functions, Phys. Rev. D 70 (2004) 105014 [hep-th/0405104] [SPIRES].
K.-I. Kondo, Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition, Phys. Lett. B 678 (2009) 322 [arXiv:0904.4897] [SPIRES].
H. Nakajima and S. Furui, Test of the Kugo-Ojima confinement criterion in the lattice Landau gauge, Nucl. Phys. Proc. Suppl. 83 (2000) 521 [hep-lat/9909008] [SPIRES].
H. Nakajima and S. Furui, Numerical study of lattice Landau gauge QCD and the Gribov copy problem, Nucl. Phys. Proc. Suppl. 141 (2005) 34 [hep-lat/0408001] [SPIRES].
S. Furui and H. Nakajima, Infrared features of unquenched finite temperature lattice Landau gauge QCD, Phys. Rev. D 76 (2007) 054509 [hep-lat/0612009] [SPIRES].
A. Sternbeck, The infrared behavior of lattice QCD Green’s functions, hep-lat/0609016 [SPIRES].
A.C. Aguilar, D. Binosi and J. Papavassiliou, Indirect determination of the Kugo-Ojima function from lattice data, JHEP 11 (2009) 066 [arXiv:0907.0153] [SPIRES].
A. Cucchieri, T. Mendes and A. Mihara, Numerical study of the ghost-gluon vertex in Landau gauge, JHEP 12 (2004) 012 [hep-lat/0408034] [SPIRES].
E.M. Ilgenfritz, M. Muller-Preussker, A. Sternbeck and A. Schiller, Gauge-variant propagators and the running coupling from lattice QCD, hep-lat/0601027 [SPIRES].
P. Boucaud et al., Artefacts and < A 2 > power corrections: Reexamining Z ψ (p 2) and Z V ,Phys. Rev. D 74 (2006) 034505 [hep-lat/0504017] [SPIRES].
P. Boucaud et al., Ghost-gluon running coupling, power corrections and the determination of \( {\Lambda_{{\bar{M}S}}} \), Phys. Rev. D 79 (2009) 014508 [arXiv:0811.2059] [SPIRES].
P. Boucaud et al., Gribov’s horizon and the ghost dressing function, Phys. Rev. D 80 (2009) 094501 [arXiv:0909.2615] [SPIRES].
J.M. Cornwall, Positivity issues for the pinch-technique gluon propagator and their resolution, Phys. Rev. D 80 (2009) 096001 [arXiv:0904.3758] [SPIRES].
G. Weiglein, Gauge dependence of Green functions and algebraic calculation of general two loop selfenergies, Diploma Thesis, University of Würzburg (1994).
G. Degrassi and A. Sirlin, Gauge invariant selfenergies and vertex parts of the Standard Model in the pinch technique framework, Phys. Rev. D 46 (1992) 3104 [SPIRES].
J. Papavassiliou, Gauge independent transverse and longitudinal self energies and vertices via the pinch technique, Phys. Rev. D 50 (1994) 5958 [hep-ph/9406258] [SPIRES].
A. Cucchieri, T. Mendes and E.M.S. Santos, Covariant gauge on the lattice: a new implementation, Phys. Rev. Lett. 103 (2009) 141602 [arXiv:0907.4138] [SPIRES].
R.F. Dashen and D.J. Gross, The Relationship Between Lattice and Continuum Definitions of the Gauge Theory Coupling, Phys. Rev. D 23 (1981) 2340 [SPIRES].
A.C. Aguilar and J. Papavassiliou, Infrared finite ghost propagator in the Feynman gauge, Phys. Rev. D 77 (2008) 125022 [arXiv:0712.0780] [SPIRES].
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Aguilar, A.C., Binosi, D. & Papavassiliou, J. QCD effective charges from lattice data. J. High Energ. Phys. 2010, 2 (2010). https://doi.org/10.1007/JHEP07(2010)002
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DOI: https://doi.org/10.1007/JHEP07(2010)002