Abstract
We introduce a generating function for the coefficients of the leading logarithmic BFKL Green’s function in transverse-momentum space, order by order in αS , in terms of single-valued harmonic polylogarithms. As an application, we exhibit fully analytic azimuthal-angle and transverse-momentum distributions for Mueller-Navelet jet cross sections at each order in αS . We also provide a generating function for the total cross section valid to any number of loops.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-Reggeon Processes in the Yang-Mills Theory, Sov. Phys. JETP 44 (1976) 443 [Erratum ibid. 45 (1977) 199] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theories, Sov. Phys. JETP 45 (1977) 199 [INSPIRE].
I. Balitsky and L. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].
L. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys. 23 (1976) 338 [INSPIRE].
V.S. Fadin and L. Lipatov, BFKL Pomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290] [INSPIRE].
G. Camici and M. Ciafaloni, Irreducible part of the next-to-leading BFKL kernel, Phys. Lett. B 412 (1997) 396 [Erratum ibid. B 417 (1998) 390] [hep-ph/9707390] [INSPIRE].
M. Ciafaloni and G. Camici, Energy scale(s) and next-to-leading BFKL equation, Phys. Lett. B 430 (1998) 349 [hep-ph/9803389] [INSPIRE].
A.H. Mueller and H. Navelet, An Inclusive Minijet Cross-Section and the Bare Pomeron in QCD, Nucl. Phys. B 282 (1987) 727 [INSPIRE].
V. Del Duca and C.R. Schmidt, Dijet production at large rapidity intervals, Phys. Rev. D 49 (1994) 4510 [hep-ph/9311290] [INSPIRE].
W.J. Stirling, Production of jet pairs at large relative rapidity in hadron hadron collisions as a probe of the perturbative Pomeron, Nucl. Phys. B 423 (1994) 56 [hep-ph/9401266] [INSPIRE].
V. Del Duca and C.R. Schmidt, BFKL versus \( O\left( {\alpha_s^3} \right) \) corrections to large rapidity dijet production, Phys. Rev. D 51 (1995) 2150 [hep-ph/9407359] [INSPIRE].
V. Del Duca and C.R. Schmidt, Azimuthal angle decorrelation in large rapidity Dijet production at the Tevatron, Nucl. Phys. Proc. Suppl. B 39 (1995) 137 [hep-ph/9408239] [INSPIRE].
L.H. Orr and W.J. Stirling, Dijet production at hadron hadron colliders in the BFKL approach, Phys. Rev. D 56 (1997) 5875 [hep-ph/9706529] [INSPIRE].
C.R. Schmidt, A Monte Carlo solution to the BFKL equation, Phys. Rev. Lett. 78 (1997) 4531 [hep-ph/9612454] [INSPIRE].
J. Andersen, V. Del Duca, S. Frixione, C. Schmidt and W.J. Stirling, Mueller-Navelet jets at hadron colliders, JHEP 02 (2001) 007 [hep-ph/0101180] [INSPIRE].
J.R. Andersen, On the role of NLL corrections and energy conservation in the high energy evolution of QCD, Phys. Lett. B 639 (2006) 290 [hep-ph/0602182] [INSPIRE].
D. Colferai, F. Schwennsen, L. Szymanowski and S. Wallon, Mueller Navelet jets at LHC - complete NLL BFKL calculation, JHEP 12 (2010) 026 [arXiv:1002.1365] [INSPIRE].
B. Ducloue, L. Szymanowski and S. Wallon, Confronting Mueller-Navelet jets in NLL BFKL with LHC experiments at 7 TeV, JHEP 05 (2013) 096 [arXiv:1302.7012] [INSPIRE].
D0 collaboration, B. Abbott et al., Probing BFKL dynamics in the dijet cross section at large rapidity intervals in \( p\overline{p} \) collisions at \( \sqrt{s} \) = 1800 GeV and 630-GeV, Phys. Rev. Lett. 84 (2000) 5722 [hep-ex/9912032] [INSPIRE].
ATLAS collaboration, Measurement of dijet production with a veto on additional central jet activity in pp collisions at \( \sqrt{s} \) = 7 TeV using the ATLAS detector, JHEP 09 (2011) 053 [arXiv:1107.1641] [INSPIRE].
CMS collaboration, Ratios of dijet production cross sections as a function of the absolute difference in rapidity between jets in proton-proton collisions at \( \sqrt{s} \) = 7 TeV, Eur. Phys. J. C 72 (2012) 2216 [arXiv:1204.0696] [INSPIRE].
D0 collaboration, S. Abachi et al., The Azimuthal decorrelation of jets widely separated in rapidity, Phys. Rev. Lett. 77 (1996) 595 [hep-ex/9603010] [INSPIRE].
CMS collaboration, Azimuthal angle decorrelations of jets widely separated in rapidity in pp collisions at \( \sqrt{s} \) = 7 TeV, CMS-PAS-FSQ-12-002 (2013).
L.J. Dixon, C. Duhr and J. Pennington, Single-valued harmonic polylogarithms and the multi-Regge limit, JHEP 10 (2012) 074 [arXiv:1207.0186] [INSPIRE].
J. Pennington, The six-point remainder function to all loop orders in the multi-Regge limit, JHEP 01 (2013) 059 [arXiv:1209.5357] [INSPIRE].
F.C.S. Brown, Single-valued multiple polylogarithms in one variable, C. R. Acad. Sci. Paris, Ser. I 338 (2004) 527.
F. Brown, Single-valued periods and multiple zeta values, arXiv:1309.5309 [INSPIRE].
E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
V. Knizhnik and A. Zamolodchikov, Current Algebra and Wess-Zumino Model in Two-Dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].
K. Ihara, M. Kaneko and D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compositio Math. 142 (2006) 307.
K.T. Chen, Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977) 831.
F.C. Brown, Multiple zeta values and periods of moduli spaces M 0,n , Annales Sci. Ecole Norm. Sup. 42 (2009) 371 [math/0606419] [INSPIRE].
A. Goncharov, A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 [INSPIRE].
A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical Polylogarithms for Amplitudes and Wilson Loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].
C. Duhr, H. Gangl and J.R. Rhodes, From polygons and symbols to polylogarithmic functions, JHEP 10 (2012) 075 [arXiv:1110.0458] [INSPIRE].
J. Blümlein, D. Broadhurst and J. Vermaseren, The Multiple Zeta Value Data Mine, Comput. Phys. Commun. 181 (2010) 582 [arXiv:0907.2557] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1309.6647
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Del Duca, V., Dixon, L.J., Duhr, C. et al. The BFKL equation, Mueller-Navelet jets and single-valued harmonic polylogarithms. J. High Energ. Phys. 2014, 86 (2014). https://doi.org/10.1007/JHEP02(2014)086
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2014)086