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The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy. (English) Zbl 1395.81160
Summary: We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the \(2 \rightarrow 5\) amplitude in planar \( \mathcal{N}=4 \) super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop \(N\)-particle MHV amplitude in this region to a function, we specialize to \(N = 7\), and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
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References:
[1] Vecchia, P., The birth of string theory, Lect. Notes Phys., 737, 59, (2008) · Zbl 05353474
[2] Kuraev, EA; Lipatov, LN; Fadin, VS, Multi-Reggeon processes in the Yang-Mills theory, Sov. Phys. JETP, 44, 443, (1976)
[3] Kuraev, EA; Lipatov, LN; Fadin, VS, The pomeranchuk singularity in nonabelian gauge theories, Sov. Phys. JETP, 45, 199, (1977)
[4] Balitsky, II; Lipatov, LN, The pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys., 28, 822, (1978)
[5] Brower, R.; DeTar, C.; Weis, J., Regge theory for multiparticle amplitudes, Phys. Rept., 14, 257, (1974)
[6] P.D.B. Collins, An Introduction to Regge Theory and High-Energy Physics, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2009). · Zbl 1390.81345
[7] Forshaw, JR; Ross, DA, Quantum chromodynamics and the pomeron, Cambridge Lect. Notes Phys., 9, 1, (1997)
[8] V. Del Duca, An introduction to the perturbative QCD Pomeron and to jet physics at large rapidities, hep-ph/9503226 [INSPIRE].
[9] L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories, Nucl. Phys.B 121 (1977) 77 [INSPIRE].
[10] Gliozzi, F.; Scherk, J.; Olive, DI, Supersymmetry, supergravity theories and the dual spinor model, Nucl. Phys., B 122, 253, (1977)
[11] G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys.B 72 (1974) 461 [INSPIRE].
[12] Anastasiou, C.; Bern, Z.; Dixon, LJ; Kosower, DA, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett., 91, 251602, (2003)
[13] Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev.D 72 (2005) 085001 [hep-th/0505205] [INSPIRE].
[14] J. Bartels, L.N. Lipatov and A. Sabio Vera, BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev.D 80 (2009) 045002 [arXiv:0802.2065] [INSPIRE].
[15] Alday, LF; Maldacena, JM, Gluon scattering amplitudes at strong coupling, JHEP, 06, 064, (2007)
[16] Drummond, JM; Korchemsky, GP; Sokatchev, E., Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys., B 795, 385, (2008) · Zbl 1219.81227
[17] A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys.B 794 (2008) 231 [arXiv:0707.1153] [INSPIRE]. · Zbl 1273.81201
[18] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., On planar gluon amplitudes/Wilson loops duality, Nucl. Phys., B 795, 52, (2008) · Zbl 1219.81191
[19] J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys.B 826 (2010) 337 [arXiv:0712.1223] [INSPIRE]. · Zbl 1203.81175
[20] Z. Bern et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev.D 78 (2008) 045007 [arXiv:0803.1465] [INSPIRE].
[21] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys., B 815, 142, (2009) · Zbl 1194.81316
[22] Drummond, JM; Henn, J.; Smirnov, VA; Sokatchev, E., Magic identities for conformal four-point integrals, JHEP, 01, 064, (2007)
[23] Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev.D 75 (2007) 085010 [hep-th/0610248] [INSPIRE].
[24] Z. Bern, J.J.M. Carrasco, H. Johansson and D.A. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev.D 76 (2007) 125020 [arXiv:0705.1864] [INSPIRE].
[25] Alday, LF; Maldacena, J., Comments on gluon scattering amplitudes via AdS/CFT, JHEP, 11, 068, (2007) · Zbl 1245.81256
[26] J. Bartels, L.N. Lipatov and A. Sabio Vera, \(N\) = 4 supersymmetric Yang-Mills scattering amplitudes at high energies: The Regge cut contribution, Eur. Phys. J.C 65 (2010) 587 [arXiv:0807.0894] [INSPIRE].
[27] Lipatov, LN, Analytic properties of high energy production amplitudes in N = 4 SUSY, Theor. Math. Phys., 170, 166, (2012)
[28] V.S. Fadin and L.N. Lipatov, BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N = 4 SUSY, Phys. Lett.B 706 (2012) 470 [arXiv:1111.0782] [INSPIRE].
[29] L. Lipatov, A. Prygarin and H.J. Schnitzer, The Multi-Regge limit of NMHV Amplitudes in N = 4 SYM Theory, JHEP01 (2013) 068 [arXiv:1205.0186] [INSPIRE].
[30] Dixon, LJ; Hippel, M., Bootstrapping an NMHV amplitude through three loops, JHEP, 10, 065, (2014)
[31] L.N. Lipatov and A. Prygarin, Mandelstam cuts and light-like Wilson loops in N = 4 SUSY, Phys. Rev.D 83 (2011) 045020 [arXiv:1008.1016] [INSPIRE].
[32] L.N. Lipatov and A. Prygarin, BFKL approach and six-particle MHV amplitude in N = 4 super Yang-Mills, Phys. Rev.D 83 (2011) 125001 [arXiv:1011.2673] [INSPIRE].
[33] J. Bartels, L.N. Lipatov and A. Prygarin, MHV amplitude for 3 → 3 gluon scattering in Regge limit, Phys. Lett.B 705 (2011) 507 [arXiv:1012.3178] [INSPIRE]. · Zbl 1270.81131
[34] Duca, V.; Duhr, C.; Smirnov, VA, An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM, JHEP, 03, 099, (2010) · Zbl 1271.81104
[35] V. Del Duca, C. Duhr and V.A. Smirnov, The Two-Loop Hexagon Wilson Loop in N = 4 SYM, JHEP05 (2010) 084 [arXiv:1003.1702] [INSPIRE]. · Zbl 1287.81080
[36] Goncharov, AB; Spradlin, M.; Vergu, C.; Volovich, A., Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett., 105, 151605, (2010)
[37] J. Bartels, J. Kotanski and V. Schomerus, Excited Hexagon Wilson Loops for Strongly Coupled N = 4 SYM, JHEP01 (2011) 096 [arXiv:1009.3938] [INSPIRE]. · Zbl 1214.81290
[38] J. Bartels, J. Kotanski, V. Schomerus and M. Sprenger, The Excited Hexagon Reloaded, arXiv:1311.1512 [INSPIRE].
[39] Basso, B.; Caron-Huot, S.; Sever, A., Adjoint BFKL at finite coupling: a short-cut from the collinear limit, JHEP, 01, 027, (2015)
[40] Alday, LF; Gaiotto, D.; Maldacena, J.; Sever, A.; Vieira, P., An operator product expansion for polygonal null Wilson loops, JHEP, 04, 088, (2011) · Zbl 1250.81071
[41] Gaiotto, D.; Maldacena, J.; Sever, A.; Vieira, P., Bootstrapping null polygon Wilson loops, JHEP, 03, 092, (2011) · Zbl 1301.81125
[42] Gaiotto, D.; Maldacena, J.; Sever, A.; Vieira, P., Pulling the straps of polygons, JHEP, 12, 011, (2011) · Zbl 1306.81153
[43] Sever, A.; Vieira, P.; Wang, T., OPE for super loops, JHEP, 11, 051, (2011) · Zbl 1306.81362
[44] B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett.111 (2013) 091602 [arXiv:1303.1396] [INSPIRE].
[45] B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data, JHEP01 (2014) 008 [arXiv:1306.2058] [INSPIRE].
[46] B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions, JHEP08 (2014) 085 [arXiv:1402.3307] [INSPIRE]. · Zbl 1342.81159
[47] Basso, B.; Sever, A.; Vieira, P., Collinear limit of scattering amplitudes at strong coupling, Phys. Rev. Lett., 113, 261604, (2014)
[48] B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion, JHEP09 (2014) 149 [arXiv:1407.1736] [INSPIRE].
[49] Basso, B.; Caetano, J.; Cordova, L.; Sever, A.; Vieira, P., OPE for all helicity amplitudes, JHEP, 08, 018, (2015) · Zbl 1388.81277
[50] B. Basso, J. Caetano, L. Cordova, A. Sever and P. Vieira, OPE for all Helicity Amplitudes II. Form Factors and Data Analysis, JHEP12 (2015) 088 [arXiv:1508.02987] [INSPIRE]. · Zbl 1388.81278
[51] B. Basso, A. Sever and P. Vieira, Hexagonal Wilson loops in planar\( \mathcal{N}=4 \)SYM theory at finite coupling, J. Phys.A 49 (2016) 41LT01 [arXiv:1508.03045] [INSPIRE]. · Zbl 1349.81170
[52] J. Bartels, L.N. Lipatov and A. Prygarin, Collinear and Regge behavior of 2 → 4 MHV amplitude in N = 4 super Yang-Mills theory, arXiv:1104.4709 [INSPIRE].
[53] Hatsuda, Y., Wilson loop OPE, analytic continuation and multi-Regge limit, JHEP, 10, 38, (2014)
[54] Drummond, JM; Papathanasiou, G., Hexagon OPE resummation and multi-Regge kinematics, JHEP, 02, 185, (2016)
[55] Dixon, LJ; Duhr, C.; Pennington, J., Single-valued harmonic polylogarithms and the multi-Regge limit, JHEP, 10, 074, (2012)
[56] Pennington, J., The six-point remainder function to all loop orders in the multi-Regge limit, JHEP, 01, 059, (2013)
[57] Broedel, J.; Sprenger, M., Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space, JHEP, 05, 055, (2016) · Zbl 1388.81202
[58] Dixon, LJ; Drummond, JM; Henn, JM, Bootstrapping the three-loop hexagon, JHEP, 11, 023, (2011) · Zbl 1306.81092
[59] Dixon, LJ; Drummond, JM; Hippel, M.; Pennington, J., Hexagon functions and the three-loop remainder function, JHEP, 12, 049, (2013) · Zbl 1342.81159
[60] L.J. Dixon, J.M. Drummond, C. Duhr and J. Pennington, The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory, JHEP06 (2014) 116 [arXiv:1402.3300] [INSPIRE]. · Zbl 1333.81238
[61] Dixon, LJ; Hippel, M.; McLeod, AJ, The four-loop six-gluon NMHV ratio function, JHEP, 01, 053, (2016)
[62] Caron-Huot, S.; Dixon, LJ; McLeod, A.; Hippel, M., Bootstrapping a five-loop amplitude using steinmann relations, Phys. Rev. Lett., 117, 241601, (2016)
[63] Drummond, JM; Papathanasiou, G.; Spradlin, M., A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon, JHEP, 03, 072, (2015)
[64] Dixon, LJ; Drummond, J.; Harrington, T.; McLeod, AJ; Papathanasiou, G.; Spradlin, M., Heptagons from the steinmann cluster bootstrap, JHEP, 02, 137, (2017) · Zbl 1377.81197
[65] N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A.B. Goncharov, A. Postnikov and J. Trnka, Scattering Amplitudes and the Positive Grassmannian, Cambridge University Press, Cambridge U.K. (2012). · Zbl 1365.81004
[66] Golden, J.; Goncharov, AB; Spradlin, M.; Vergu, C.; Volovich, A., Motivic amplitudes and cluster coordinates, JHEP, 01, 091, (2014)
[67] Caron-Huot, S.; Larsen, KJ, Uniqueness of two-loop master contours, JHEP, 10, 026, (2012)
[68] Prlina, I.; Spradlin, M.; Stankowicz, J.; Stanojevic, S., Boundaries of amplituhedra and NMHV symbol alphabets at two loops, JHEP, 04, 049, (2018) · Zbl 1390.81345
[69] Duca, V.; etal., Multi-Regge kinematics and the moduli space of Riemann spheres with marked points, JHEP, 08, 152, (2016) · Zbl 1390.81627
[70] J. Bartels, A. Kormilitzin, L.N. Lipatov and A. Prygarin, BFKL approach and 2 → 5 maximally helicity violating amplitude in\( \mathcal{N}=4 \)super-Yang-Mills theory, Phys. Rev.D 86 (2012) 065026 [arXiv:1112.6366] [INSPIRE].
[71] J. Bartels, A. Kormilitzin and L. Lipatov, Analytic structure of the N = 7 scattering amplitude in\( \mathcal{N}=4 \)SYM theory in the multi-Regge kinematics: Conformal Regge pole contribution, Phys. Rev.D 89 (2014) 065002 [arXiv:1311.2061] [INSPIRE].
[72] J. Bartels, A. Kormilitzin and L.N. Lipatov, Analytic structure of the N = 7 scattering amplitude in\( \mathcal{N}=4 \)theory in multi-Regge kinematics: Conformal Regge cut contribution, Phys. Rev.D 91 (2015) 045005 [arXiv:1411.2294] [INSPIRE].
[73] Caron-Huot, S., When does the gluon reggeize?, JHEP, 05, 093, (2015)
[74] Bargheer, T.; Papathanasiou, G.; Schomerus, V., The two-loop symbol of all multi-Regge regions, JHEP, 05, 012, (2016)
[75] A. Prygarin, M. Spradlin, C. Vergu and A. Volovich, All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology, Phys. Rev.D 85 (2012) 085019 [arXiv:1112.6365] [INSPIRE].
[76] Bartels, J.; Schomerus, V.; Sprenger, M., Multi-Regge limit of the n-gluon bubble ansatz, JHEP, 11, 145, (2012)
[77] J. Bartels, V. Schomerus and M. Sprenger, The Bethe roots of Regge cuts in strongly coupled\( \mathcal{N}=4 \)SYM theory, JHEP07 (2015) 098 [arXiv:1411.2594] [INSPIRE]. · Zbl 1388.81907
[78] Duca, V.; Duhr, C.; Glover, EWN, Iterated amplitudes in the high-energy limit, JHEP, 12, 097, (2008) · Zbl 1329.81282
[79] F.C.S. Brown, Single-valued hyperlogarithms and unipotent differential equations, http://www.ihes.fr/ brown/RHpaper5.pdf.
[80] F.C.S. Brown, Notes on motivic periods, arXiv:1512.06410. · Zbl 1390.14024
[81] L. Freyhult, Review of AdS/CFT Integrability, Chapter III.4: Twist States and the cusp Anomalous Dimension, Lett. Math. Phys.99 (2012) 255 [arXiv:1012.3993] [INSPIRE].
[82] B. Basso, On the Regge Limit of Polygonal Wilson Loops, talk at Amplitudes 2016, Stockholm Sweden (2016), http://agenda.albanova.se/contributionDisplay.py?contribId=272&confId=5285. · Zbl 1194.81316
[83] F.C.S. Brown, Multiple zeta values and periods of moduli spaces M_{0,\(n\)}(\(R\)), Annales Sci. Ecole Norm. Sup.42 (2009) 371 [math/0606419] [INSPIRE]. · Zbl 1216.11079
[84] Papathanasiou, G., Hexagon Wilson loop OPE and harmonic polylogarithms, JHEP, 11, 150, (2013) · Zbl 1342.81610
[85] L.J. Dixon, J. Drummond, A.J. McLeod, G. Papathanasiou and M. Spradlin, to appear.
[86] S. Moch, P. Uwer and S. Weinzierl, Nested sums, expansion of transcendental functions and multiscale multiloop integrals, J. Math. Phys.43 (2002) 3363 [hep-ph/0110083] [INSPIRE]. · Zbl 1060.33007
[87] Bauer, C.; Frink, A.; Kreckel, R., Introduction to the ginac framework for symbolic computation within the c++ programming language, J. Symb. Comput., 33, 1, (2002) · Zbl 1017.68163
[88] J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE]. · Zbl 1219.81227
[89] S. Weinzierl, Symbolic expansion of transcendental functions, Comput. Phys. Commun.145 (2002) 357 [math-ph/0201011] [INSPIRE]. · Zbl 1001.65025
[90] S. Moch and P. Uwer, -xsummer- transcendental functions and symbolic summation in form, Comput. Phys. Commun.174 (2006) 759 [math-ph/0508008]. · Zbl 1196.68332
[91] Schnetz, O., Graphical functions and single-valued multiple polylogarithms, Commun. Num. Theor. Phys., 08, 589, (2014) · Zbl 1320.81075
[92] Bargheer, T., Systematics of the multi-Regge three-loop symbol, JHEP, 11, 077, (2017) · Zbl 1383.81276
[93] L.N. Lipatov, Integrability of scattering amplitudes in N = 4 SUSY, J. Phys.A 42 (2009) 304020 [arXiv:0902.1444] [INSPIRE]. · Zbl 1176.81062
[94] G. Chachamis and A. Sabio Vera, Open Spin Chains and Complexity in the High Energy Limit, arXiv:1801.04872 [INSPIRE]. · Zbl 1215.81122
[95] K.T. Chen, Iterated path integrals, Bull. Amer. Math. Soc.83 (1977) 831. · Zbl 0389.58001
[96] C. Bogner and F. Brown, Symbolic integration and multiple polylogarithms, arXiv:1209.6524 [INSPIRE].
[97] Duhr, C., Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, JHEP, 08, 043, (2012) · Zbl 1397.16028
[98] Anastasiou, C.; Duhr, C.; Dulat, F.; Mistlberger, B., Soft triple-real radiation for Higgs production at N3LO, JHEP, 07, 003, (2013)
[99] C. Duhr, Mathematical aspects of scattering amplitudes, in Proceedings of Theoretical Advanced Study Institute in Elementary Particle Physics: Journeys Through the Precision Frontier: Amplitudes for Colliders (TASI 2014), Boulder U.S.A. (2014), pg. 419 [arXiv:1411.7538] [INSPIRE].
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