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Computing one-loop corrections to effective vertices with two scales in the EFT for Multi-Regge processes in QCD. (English) Zbl 1430.81086
Summary: The computation of one-loop corrections to Reggeon-Particle-Particle effective vertices with two scales of virtuality is considered in the framework of gauge-invariant effective field theory for Multi-Regge processes in QCD. Rapidity divergences arising in loop integrals are regulated by “tilted Wilson lines” prescription. General analysis of rapidity divergences at one loop is given and necessary scalar integrals with one and two scales of virtuality are computed. Two examples of effective vertices at one loop are considered: the effective vertex of interaction of (space-like) virtual photon with one Reggeized and one Yang-Mills quark and the effective vertex of Reggeized gluon to Yang-Mills gluon transition with an insertion of the operator \(\operatorname{tr} [G_{\mu \nu} G^{\mu \nu}]\) carrying the (space-like) off-shell momentum. All terms \(\sim r^{\pm \epsilon}\) in the rapidity-regulator variable \(r\) cancel between diagrams and only \(\log r\)-divergence is left. It is checked on several examples, that obtained results indeed allow one to reproduce Regge limit of one-loop QCD scattering amplitudes.
MSC:
81V05 Strong interaction, including quantum chromodynamics
81V35 Nuclear physics
81T13 Yang-Mills and other gauge theories in quantum field theory
81T18 Feynman diagrams
81T12 Effective quantum field theories
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References:
[1] Lipatov, L. N., Small x physics in perturbative QCD, Phys. Rep., 286, 131-198 (1997)
[2] Del Duca, V., An introduction to the perturbative QCD pomeron and to jet physics at large rapidities, Sci. Acta, 10, 91-139 (1995)
[3] Bartels, J.; Lipatov, L. N.; Sabio Vera, A., BFKL pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev. D, 80, Article 045002 pp. (2009)
[4] Bartels, J.; Lipatov, L. N.; Sabio Vera, A., N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution, Eur. Phys. J. C, 65, 587-605 (2010)
[5] Bartels, J.; Kormilitzin, A.; Lipatov, L. N., Analytic structure of the \(n = 7\) scattering amplitude in \(N = 4\) theory in multi-Regge kinematics: conformal Regge cut contribution, Phys. Rev. D, 91, 4, Article 045005 pp. (2015)
[6] Bern, Z.; Dixon, L. J.; Smirnov, V. A., Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D, 72, Article 085001 pp. (2005)
[7] Del Duca, V.; Duhr, C.; Gardi, E.; Magnea, L.; White, C. D., The infrared structure of gauge theory amplitudes in the high-energy limit, J. High Energy Phys., 12, Article 021 pp. (2011) · Zbl 1306.81333
[8] Caron-Huot, S.; Gardi, E.; Reichel, J.; Vernazza, L., Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders, J. High Energy Phys., 03, Article 098 pp. (2018) · Zbl 1388.81922
[9] Becher, T.; Neubert, M., Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 111, 19, Article 199905 pp. (2013), Erratum:
[10] Gardi, E.; Magnea, L., Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, J. High Energy Phys., 03, Article 079 pp. (2009)
[11] Becher, T.; Neubert, M., On the structure of infrared singularities of gauge-theory amplitudes, J. High Energy Phys.. J. High Energy Phys., J. High Energy Phys., 11, Article 024 pp. (2013), Erratum:
[12] Gardi, E.; Magnea, L., Infrared singularities in QCD amplitudes, Nuovo Cimento C. Nuovo Cimento C, Frascati Phys. Ser., 50, 5-6, 137-157 (2010)
[13] Kuraev, E. A.; Lipatov, L. N.; Fadin, V. S., Multi - reggeon processes in the Yang-Mills theory, Sov. Phys. JETP, 44, 443 (1976)
[14] Kuraev, E. A.; Lipatov, L. N.; Fadin, V. S., The Pomeranchuk singularity in non-Abelian gauge theories, Sov. Phys. JETP, 45, 199 (1977)
[15] Balitsky, Y. Y.; Lipatov, L. N., The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys., 28, 822 (1978)
[16] Fadin, V. S.; Lipatov, L. N., BFKL pomeron in the next-to-leading approximation, Phys. Lett. B, 429, 127-134 (1998)
[17] Camici, G.; Ciafaloni, M., Irreducible part of the next-to-leading BFKL kernel, Phys. Lett. B. Phys. Lett. B, Phys. Lett. B, 417, 390-406 (1998), Erratum:
[18] Camici, G.; Ciafaloni, M., Energy scale(s) and next-to-leading BFKL equation, Phys. Lett. B, 430, 349-354 (1998)
[19] Gribov, V. N.; Lipatov, L. N., \(e^+ e^-\)-annihilation and deep-inelastic ep-scattering in perturbation theory, Sov. J. Nucl. Phys., 15, 438 (1972)
[20] Dokshitzer, Y. L., Calculation of structure functions of deep-inelastic scattering and \(e^+ e^-\)-annihilation in perturbation theory of quantum chromodynamics, Sov. Phys. JETP, 46, 641 (1977)
[21] Altarelli, G.; Parisi, G., Asymptotic freedom in parton language, Nucl. Phys. B, 126, 298 (1977)
[22] Salam, G. P., A resummation of large subleading corrections at small x, J. High Energy Phys., 07, Article 019 pp. (1998)
[23] Brodsky, S. J.; Fadin, V. S.; Kim, V. T.; Lipatov, L. N.; Pivovarov, G. B., The QCD pomeron with optimal renormalization, JETP Lett., 70, 155-160 (1999)
[24] Ciafaloni, M.; Colferai, D.; Salam, G. P.; Stasto, A. M., Renormalization group improved small x green’s function, Phys. Rev. D, 68, Article 114003 pp. (2003)
[25] Hentschinski, M.; Sabio Vera, A.; Salas, C., \(F_2\) and \(F_L\) at small \(x\) using a collinearly improved BFKL resummation, Phys. Rev. D, 87, Article 076005 pp. (2013)
[26] Ball, R. D.; Bertone, V.; Bonvini, M.; Marzani, S.; Rojo, J.; Rottoli, L., Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data, Eur. Phys. J. C, 78, 4, 321 (2018)
[27] Marzani, S.; Ball, R. D.; Falgari, P.; Forte, S., BFKL at next-to-next-to-leading order, Nucl. Phys. B, 783, 143-175 (2007)
[28] Fadin, V. S.; Fiore, R.; Kotsky, M. I.; Papa, A., Strong bootstrap conditions, Phys. Lett. B, 495, 329-337 (2000)
[29] Fadin, V. S.; Kozlov, M. G.; Reznichenko, A. V., Gluon Reggeization in Yang-Mills theories, Phys. Rev. D, 92, 8, Article 085044 pp. (2015)
[30] Bogdan, A. V.; Fadin, V. S., A proof of the reggeized form of amplitudes with quark exchanges, Nucl. Phys. B, 740, 36-57 (2006) · Zbl 1109.81371
[31] Lipatov, L. N., Gauge invariant effective action for high-energy processes in QCD, Nucl. Phys. B, 452, 369-400 (1995)
[32] Lipatov, L. N.; Vyazovsky, M. I., Quasi-multi-Regge processes with a quark exchange in the t-channel, Nucl. Phys. B, 597, 399-409 (2001)
[33] Rothstein, I. Z.; Stewart, I. W., An effective field theory for forward scattering and factorization violation, J. High Energy Phys., 08, Article 025 pp. (2016)
[34] Moult, I.; Solon, M. P.; Stewart, I. W.; Vita, G., Fermionic Glauber operators and quark reggeization, J. High Energy Phys., 02, Article 134 pp. (2018)
[35] Becher, T.; Bell, G., Analytic regularization in soft-collinear effective theory, Phys. Lett. B, 713, 41-46 (2012)
[36] Chiu, J.-Y.; Jain, A.; Neill, D.; Rothstein, I. Z., A formalism for the systematic treatment of rapidity logarithms in quantum field theory, J. High Energy Phys., 05, Article 084 pp. (2012) · Zbl 1348.81437
[37] Collins, J. C., Foundations of Perturbative QCD (2011), Cambridge University Press: Cambridge University Press Cambridge
[38] Collins, J., New definition of TMD parton densities, Int. J. Mod. Phys. Conf. Ser., 4, 85-96 (2011)
[39] Echevarria, M. G.; Scimemi, I.; Vladimirov, A., Universal transverse momentum dependent soft function at NNLO, Phys. Rev. D, 93, 5, Article 054004 pp. (2016)
[40] Hentschinski, M.; Sabio Vera, A., NLO jet vertex from Lipatov’s QCD effective action, Phys. Rev. D, 85, Article 056006 pp. (2012)
[41] Chachamis, G.; Hentschinski, M.; Madrigal Martinez, J. D.; Sabio Vera, A., Next-to-leading order corrections to the gluon-induced forward jet vertex from the high energy effective action, Phys. Rev. D, 87, 7, Article 076009 pp. (2013)
[42] Chachamis, G.; Hentschinski, M.; Madrigal Martinez, J. D.; Sabio Vera, A., Quark contribution to the gluon Regge trajectory at NLO from the high energy effective action, Nucl. Phys. B, 861, 133-144 (2012) · Zbl 1246.81427
[43] Chachamis, G.; Hentschinski, M.; Madrigal Martinez, J. D.; Sabio Vera, A., Gluon Regge trajectory at two loops from Lipatov’s high energy effective action, Nucl. Phys. B, 876, 453-472 (2013) · Zbl 1284.81292
[44] Nefedov, M.; Saleev, V., On the one-loop calculations with reggeized quarks, Mod. Phys. Lett. A, 32, Article 1750207 pp. (2017)
[45] Karpishkov, A. V.; Nefedov, M. A.; Saleev, V. A., \(B \overline{B}\) angular correlations at the LHC in parton Reggeization approach merged with higher-order matrix elements, Phys. Rev. D, 96, 9, Article 096019 pp. (2017)
[46] Nefedov, M.; Saleev, V., DIS structure functions in the NLO approximation of the Parton Reggeization Approach, EPJ Web Conf., 158, Article 03011 pp. (2017)
[47] Nefedov, M.; Saleev, V., From LO to NLO in the parton Reggeization approach, EPJ Web Conf., 191, Article 04007 pp. (2018)
[48] Bondarenko, S.; Zubkov, M. A., The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons, Eur. Phys. J. C, 78, 8, 617 (2018)
[49] Hentschinski, M., Pole prescription of higher order induced vertices in Lipatov’s QCD effective action, Nucl. Phys. B, 859, 129-142 (2012) · Zbl 1246.81431
[50] Del Duca, V.; Glover, E. W.N., The high-energy limit of QCD at two loops, J. High Energy Phys., 10, Article 035 pp. (2001)
[51] Caron-Huot, S.; Gardi, E.; Vernazza, L., Two-parton scattering in the high-energy limit, J. High Energy Phys., 06, Article 016 pp. (2017) · Zbl 1380.81390
[52] Fadin, V. S.; Lipatov, L. N., Reggeon cuts in QCD amplitudes with negative signature, Eur. Phys. J. C, 78, 6, 439 (2018)
[53] Hentschinski, M., Color glass condensate formalism, Balitsky-JIMWLK evolution, and Lipatov’s high energy effective action, Phys. Rev. D, 97, 11, Article 114027 pp. (2018)
[54] Fadin, V. S.; Sherman, V. E., Fermion reggeization in non-abelian gauge theories, JETP Lett., 23, 599 (1976)
[55] Fadin, V. S.; Sherman, V. E., Processes with fermion exchange in non-abelian gauge theories, Sov. Phys. JETP, 45, 861 (1977)
[56] van Hameren, A., Calculating off-shell one-loop amplitudes for \(k_T\)-dependent factorization: a proof of concept
[57] Ellis, R. K.; Zanderighi, G., Scalar one-loop integrals for QCD, J. High Energy Phys., 0802, Article 002 pp. (2008)
[58] Smirnov, V. A., Feynman Integral Calculus (2006), Springer-Verlag: Springer-Verlag Berlin, Heidelberg
[59] Heinrich, G., Sector decomposition, Int. J. Mod. Phys. A, 23, 1457-1486 (2008) · Zbl 1153.81522
[60] Hahn, T., CUBA: a library for multidimensional numerical integration, Comput. Phys. Commun., 168, 78-95 (2005) · Zbl 1196.65052
[61] Mertig, R.; Bohm, M.; Denner, A., FEYN CALC: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun., 64, 345-359 (1991)
[62] Kotsky, M. I.; Lipatov, L. N.; Principe, A.; Vyazovsky, M. I., Radiative corrections to the quark gluon Reggeized quark vertex in QCD, Nucl. Phys. B, 648, 277-292 (2003)
[63] Soar, G.; Moch, S.; Vermaseren, J. A.M.; Vogt, A., On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x, Nucl. Phys. B, 832, 152-227 (2010) · Zbl 1204.81177
[64] Daleo, A.; Gehrmann-De Ridder, A.; Gehrmann, T.; Luisoni, G., Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, J. High Energy Phys., 01, Article 118 pp. (2010) · Zbl 1269.81194
[65] Antonov, E. N.; Lipatov, L. N.; Kuraev, E. A.; Cherednikov, I. O., Feynman rules for effective Regge action, Nucl. Phys. B, 721, 111-135 (2005) · Zbl 1128.81314
[66] Hahn, T., Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun., 140, 418-431 (2001) · Zbl 0994.81082
[67] Lee, R. N., Presenting LiteRed: a tool for the Loop InTEgrals REDuction
[68] Lee, R. N., LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser., 523, Article 012059 pp. (2014)
[69] Nefedov, M., One-loop corrections to multiscale effective vertices in the EFT for multi-Regge processes in QCD, (27th International Workshop on Deep Inelastic Scattering and Related Subjects. 27th International Workshop on Deep Inelastic Scattering and Related Subjects, DIS 2019, Torino, Italy, April 8-12, 2019 (2019))
[70] Hentschinski, M., The High Energy Behavior of QCD: The Effective Action and the Triple-Pomeron-Vertex (2009), PhD Thesis
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