Abstract
In this paper we encode the perturbative BFKL leading logarithmic resummation, relevant for the Regge limit behavior of QCD scattering amplitudes, in the IR-regulated effective action which satisfies exact functional renormalization group equations. This is obtained using a truncation with a specific infinite set of non local vertices describing the multi-Regge kinematics (MRK). The goal is to use this framework to study, in the high energy limit and at larger transverse distances the transition to a much simpler effective local reggeon field theory, whose critical properties were recently investigated in the same framework. We perform a numerical analysis of the spectrum of the BFKL Pomeron deformed by the introduction of a Wilsonian infrared regulator to understand the properties of the leading poles (states) contributing to the high energy scattering.
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J. Bartels, C. Contreras and G.P. Vacca, Could reggeon field theory be an effective theory for QCD in the Regge limit?, JHEP 03 (2016) 201 [arXiv:1512.07182] [INSPIRE].
J. Bartels, C. Contreras and G.P. Vacca, Pomeron-Odderon interactions in a reggeon field theory, Phys. Rev. D 95 (2017) 014013 [arXiv:1608.08836] [INSPIRE].
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [arXiv:1710.05815] [INSPIRE].
T.R. Morris, Derivative expansion of the exact renormalization group, Phys. Lett. B 329 (1994) 241 [hep-ph/9403340] [INSPIRE].
V.N. Gribov and A.A. Migdal, Strong coupling in the Pomeranchuk pole problem, Sov. Phys. JETP 28 (1969) 784 [Zh. Eksp. Teor. Fiz. 55 (1968) 1498] [INSPIRE].
V.N. Gribov and A.A. Migdal, Properties of the Pomeranchuk pole and the branch cuts related to it at low momentum transfer, Sov. J. Nucl. Phys. 8 (1969) 583 [Yad. Fiz. 8 (1968) 1002] [INSPIRE].
H.D.I. Abarbanel and J.B. Bronzan, Structure of the Pomeranchuk singularity in reggeon field theory, Phys. Rev. D 9 (1974) 2397 [INSPIRE].
A.A. Migdal, A.M. Polyakov and K.A. Ter-Martirosian, Theory of interacting Pomerons, Phys. Lett. B 48 (1974) 239 [Pisma Zh. Eksp. Teor. Fiz. 68 (1975) 817] [INSPIRE].
V.A. Abramovsky, V.N. Gribov and O.V. Kancheli, Character of inclusive spectra and fluctuations produced in inelastic processes by multi-Pomeron exchange, Yad. Fiz. 18 (1973) 595 [Sov. J. Nucl. Phys. 18 (1974) 308] [INSPIRE].
J. Bartels, M. Salvadore and G.P. Vacca, AGK cutting rules and multiple scattering in hadronic collisions, Eur. Phys. J. C 42 (2005) 53 [hep-ph/0503049] [INSPIRE].
L.N. Lipatov, Gauge invariant effective action for high-energy processes in QCD, Nucl. Phys. B 452 (1995) 369 [hep-ph/9502308] [INSPIRE].
L.N. Lipatov, Reggeization of the vector meson and the vacuum singularity in non-Abelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [Yad. Fiz. 23 (1976) 642] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-reggeon processes in the Yang-Mills theory, Sov. Phys. JETP 44 (1976) 443 [Zh. Eksp. Teor. Fiz. 71 (1976) 840] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk singularity in non-Abelian gauge theories, Sov. Phys. JETP 45 (1977) 199 [Zh. Eksp. Teor. Fiz. 72 (1977) 377] [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [Yad. Fiz. 28 (1978) 1597] [INSPIRE].
J. Bartels and M. Wusthoff, The triple Regge limit of diffractive dissociation in deep inelastic scattering, Z. Phys. C 66 (1995) 157 [INSPIRE].
J. Bartels, L.N. Lipatov and M. Wusthoff, Conformal invariance of the transition vertex 2 → 4 gluons, Nucl. Phys. B 464 (1996) 298 [hep-ph/9509303] [INSPIRE].
M.A. Braun and G.P. Vacca, Triple Pomeron vertex in the limit N c → ∞, Eur. Phys. J. C 6 (1999) 147 [hep-ph/9711486] [INSPIRE].
J. Bartels, M.G. Ryskin and G.P. Vacca, On the triple Pomeron vertex in perturbative QCD, Eur. Phys. J. C 27 (2003) 101 [hep-ph/0207173] [INSPIRE].
J. Bartels, L.N. Lipatov and G.P. Vacca, Interactions of reggeized gluons in the Mobius representation, Nucl. Phys. B 706 (2005) 391 [hep-ph/0404110] [INSPIRE].
J. Bartels, L.N. Lipatov and G.P. Vacca, A new odderon solution in perturbative QCD, Phys. Lett. B 477 (2000) 178 [hep-ph/9912423] [INSPIRE].
R.A. Janik and J. Wosiek, Solution of the odderon problem, Phys. Rev. Lett. 82 (1999) 1092 [hep-th/9802100] [INSPIRE].
M. Braun, G.P. Vacca and G. Venturi, Properties of the hard Pomeron with a running coupling constant and the high-energy scattering, Phys. Lett. B 388 (1996) 823 [hep-ph/9605304] [INSPIRE].
E. Levin, L. Lipatov and M. Siddikov, BFKL Pomeron with massive gluons and running coupling, Phys. Rev. D 94 (2016) 096004 [arXiv:1608.03816] [INSPIRE].
E. Levin, L. Lipatov and M. Siddikov, Semiclassical solution to the BFKL equation with massive gluons, Eur. Phys. J. C 75 (2015) 558 [arXiv:1508.04118] [INSPIRE].
E. Levin, L. Lipatov and M. Siddikov, BFKL Pomeron with massive gluons, Phys. Rev. D 89 (2014) 074002 [arXiv:1401.4671] [INSPIRE].
L.N. Lipatov, The bare Pomeron in quantum chromodynamics, Sov. Phys. JETP 63 (1986) 904 [Zh. Eksp. Teor. Fiz. 90 (1986) 1536] [INSPIRE].
H. Kowalski, L.N. Lipatov, D.A. Ross and O. Schulz, Decoupling of the leading contribution in the discrete BFKL analysis of high-precision HERA data, Eur. Phys. J. C 77 (2017) 777 [arXiv:1707.01460] [INSPIRE].
H. Kowalski, L.N. Lipatov and D.A. Ross, The behaviour of the Green function for the BFKL Pomeron with running coupling, Eur. Phys. J. C 76 (2016) 23 [arXiv:1508.05744] [INSPIRE].
H. Kowalski, L. Lipatov and D. Ross, The Green function for the BFKL Pomeron and the transition to DGLAP evolution, Eur. Phys. J. C 74 (2014) 2919 [arXiv:1401.6298] [INSPIRE].
R. Kirschner and L.n. Lipatov, Doubly logarithmic asymptotic of the quark scattering amplitude with nonvacuum exchange in the T channel, Sov. Phys. JETP 56 (1982) 266 [Zh. Eksp. Teor. Fiz. 83 (1982) 488] [INSPIRE].
R. Kirschner and L.N. Lipatov, Double logarithmic asymptotics of quark scattering amplitudes with flavor exchange, Phys. Rev. D 26 (1982) 1202 [INSPIRE].
R. Kirschner and L.n. Lipatov, Double logarithmic asymptotics and Regge singularities of quark amplitudes with flavor exchange, Nucl. Phys. B 213 (1983) 122 [INSPIRE].
D.F. Litim, Optimized renormalization group flows, Phys. Rev. D 64 (2001) 105007 [hep-th/0103195] [INSPIRE].
M. Hentschinski, The high energy behavior of QCD: the effective action and the triple-Pomeron-vertex, Ph.D. thesis, Hamburg U., Hamburg, Germany, (2009) [arXiv:0908.2576] [INSPIRE].
M. Siddikov, private communication.
J. Bartels, M.A. Braun, D. Colferai and G.P. Vacca, Diffractive η c photoproduction and electroproduction with the perturbative QCD odderon, Eur. Phys. J. C 20 (2001) 323 [hep-ph/0102221] [INSPIRE].
J. Bartels, High-energy behavior in a non-Abelian gauge theory (II), Nucl. Phys. B 175 (1980) 365 [INSPIRE].
J. Kwiecinski and M. Praszalowicz, Three gluon integral equation and odd c singlet Regge singularities in QCD, Phys. Lett. B 94 (1980) 413 [INSPIRE].
J. Bartels and C. Ewerz, Unitarity corrections in high-energy QCD, JHEP 09 (1999) 026 [hep-ph/9908454] [INSPIRE].
J. Bartels, M. Braun and G.P. Vacca, Pomeron vertices in perturbative QCD in diffractive scattering, Eur. Phys. J. C 40 (2005) 419 [hep-ph/0412218] [INSPIRE].
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Bartels, J., Contreras, C. & Vacca, G.P. A functional RG approach for the BFKL Pomeron. J. High Energ. Phys. 2019, 4 (2019). https://doi.org/10.1007/JHEP01(2019)004
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DOI: https://doi.org/10.1007/JHEP01(2019)004