Abstract
The structure constants of twist-two operators with spin j in the BFKL limit g2 → 0, j → 1 and \( \frac{g^2}{j-1} \) ∼ 1 are found from the calculation of the three-point correlator of twist-two light-ray operators in the triple Regge limit. It is well known that the anomalous dimensions of twist-two operators in this limit are determined by the BFKL intercept. Similarly, the obtained structure constants are determined by an analytic function of three BFKL intercepts.
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S. Moch, J.A.M. Vermaseren and A. Vogt, The Three loop splitting functions in QCD: The Nonsinglet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [INSPIRE].
A. Vogt, S. Moch and J.A.M. Vermaseren, The Three-loop splitting functions in QCD: The Singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, Three Loop Cusp Anomalous Dimension in QCD, Phys. Rev. Lett. 114 (2015) 062006 [arXiv:1409.0023] [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions, JHEP 01 (2016) 140 [arXiv:1510.07803] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N} \) = 4 Super-Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5 /CFT 4, JHEP 09 (2015) 187 [arXiv:1405.4857] [INSPIRE].
C. Marboe and V. Velizhanin, Twist-2 at seven loops in planar \( \mathcal{N} \) = 4 SYM theory: full result and analytic properties, JHEP 11 (2016) 013 [arXiv:1607.06047] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in \( \mathcal{N} \) = 4 SYM, JHEP 07 (2014) 156 [arXiv:1402.0871] [INSPIRE].
V. Kazakov and E. Sobko, Three-point correlators of twist-2 operators in N = 4 SYM at Born approximation, JHEP 06 (2013) 061 [arXiv:1212.6563] [INSPIRE].
E. Sobko, A new representation for two- and three-point correlators of operators from sl(2) sector, JHEP 12 (2014) 101 [arXiv:1311.6957] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure Constants and Integrable Bootstrap in Planar N = 4 SYM Theory, arXiv:1505.06745 [INSPIRE].
B. Eden and F. Paul, Half-BPS half-BPS twist two at four loops in N = 4 SYM, arXiv:1608.04222 [INSPIRE].
D. Chicherin, A. Georgoudis, V. Gonçalves and R. Pereira, All five-loop planar four-point functions of half-BPS operators in \( \mathcal{N} \) = 4 SYM, JHEP 11 (2018) 069 [arXiv:1809.00551] [INSPIRE].
A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in \( \mathcal{N} \) = 4 SYM: cusps in the ladder limit, JHEP 10 (2018) 060 [arXiv:1802.04237] [INSPIRE].
J. Collins, Foundations of perturbative QCD, Cambridge University Press (2013) [INSPIRE].
I.I. Balitsky and V.M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989) 541 [INSPIRE].
I. Balitsky, V. Kazakov and E. Sobko, Two-point correlator of twist-2 light-ray operators in N = 4 SYM in BFKL approximation, arXiv:1310.3752 [INSPIRE].
A.V. Belitsky, S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Superconformal operators in N = 4 superYang-Mills theory, Phys. Rev. D 70 (2004) 045021 [hep-th/0311104] [INSPIRE].
V.S. Fadin and L.N. Lipatov, BFKL Pomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Pomeron Eigenvalue at Three Loops in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 115 (2015) 251601 [arXiv:1507.04010] [INSPIRE].
V.N. Velizhanin, BFKL Pomeron in the next-to-next-to-leading approximation in the planar N = 4 SYM theory, arXiv:1508.02857 [INSPIRE].
S. Caron-Huot and M. Herranen, High-energy evolution to three loops, JHEP 02 (2018) 058 [arXiv:1604.07417] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, Pomeron in the N = 4 supersymmetric gauge model at strong couplings, Nucl. Phys. B 874 (2013) 889 [arXiv:1301.0882] [INSPIRE].
R.C. Brower, M.S. Costa, M. Djurić, T. Raben and C.-I. Tan, Strong Coupling Expansion for the Conformal Pomeron/Odderon Trajectories, JHEP 02 (2015) 104 [arXiv:1409.2730] [INSPIRE].
I. Balitsky, V. Kazakov and E. Sobko, Structure constant of twist-2 light-ray operators in the Regge limit, Phys. Rev. D 93 (2016) 061701 [arXiv:1506.02038] [INSPIRE].
I. Balitsky, V. Kazakov and E. Sobko, Three-point correlator of twist-2 light-ray operators in N = 4 SYM in BFKL approximation, arXiv:1511.03625 [INSPIRE].
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
Y.V. Kovchegov, Unitarization of the BFKL Pomeron on a nucleus, Phys. Rev. D 61 (2000) 074018 [hep-ph/9905214] [INSPIRE].
Y.V. Kovchegov, Small x F(2) structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].
G.P. Korchemsky, Conformal bootstrap for the BFKL Pomeron, Nucl. Phys. B 550 (1999) 397 [hep-ph/9711277] [INSPIRE].
L.N. Lipatov, The Bare Pomeron in Quantum Chromodynamics, Sov. Phys. JETP 63 (1986) 904 [INSPIRE].
A.R. White, The Triangle anomaly in triple Regge limits, Phys. Rev. D 63 (2001) 016007 [hep-ph/9910458] [INSPIRE].
M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].
I. Balitsky, NLO BFKL and anomalous dimensions of light-ray operators, Int. J. Mod. Phys. Conf. Ser. 25 (2014) 1460024 [INSPIRE].
I. Balitsky and G.A. Chirilli, High-energy amplitudes in N = 4 SYM in the next-to-leading order, Phys. Lett. B 687 (2010) 204 [arXiv:0911.5192] [INSPIRE].
I. Balitsky and G.A. Chirilli, NLO evolution of color dipoles in N = 4 SYM, Nucl. Phys. B 822 (2009) 45 [arXiv:0903.5326] [INSPIRE].
M. Alfimov, N. Gromov and V. Kazakov, QCD Pomeron from AdS/CFT Quantum Spectral Curve, JHEP 07 (2015) 164 [arXiv:1408.2530] [INSPIRE].
L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].
I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60 (1999) 014020 [hep-ph/9812311] [INSPIRE].
I. Balitsky, High-energy QCD and Wilson lines, hep-ph/0101042 [INSPIRE].
G.A. Chirilli and Y.V. Kovchegov, Solution of the NLO BFKL Equation and a Strategy for Solving the All-Order BFKL Equation, JHEP 06 (2013) 055 [arXiv:1305.1924] [INSPIRE].
G.A. Chirilli and Y.V. Kovchegov, γ * γ * Cross Section at NLO and Properties of the BFKL Evolution at Higher Orders, JHEP 05 (2014) 099 [Erratum ibid. 08 (2015) 075] [arXiv:1403.3384] [INSPIRE].
I.I. Balitsky and V.M. Braun, Nonlocal Operator Expansion for Structure Functions of e + e − Annihilation, Phys. Lett. B 222 (1989) 123 [INSPIRE].
I.I. Balitsky and V.M. Braun, The Nonlocal operator expansion for inclusive particle production in e + e − annihilation, Nucl. Phys. B 361 (1991) 93 [INSPIRE].
I.I. Balitsky and V.M. Braun, Valleys in Minkowski space and instanton induced cross-sections, Nucl. Phys. B 380 (1992) 51 [INSPIRE].
A. Babansky and I. Balitsky, Scattering of color dipoles: From low to high-energies, Phys. Rev. D 67 (2003) 054026 [hep-ph/0212075] [INSPIRE].
I. Balitsky, Operator expansion for diffractive high-energy scattering, AIP Conf. Proc. 407 (1997) 953 [hep-ph/9706411] [INSPIRE].
Y.V. Kovchegov and E. Levin, Quantum chromodynamics at high energy, vol. 33, Cambridge University Press (2012) [INSPIRE].
V.A. Smirnov, Feynman integral calculus, Springer (2006) [INSPIRE].
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Balitsky, I. Structure constants of twist-two light-ray operators in the triple Regge limit. J. High Energ. Phys. 2019, 42 (2019). https://doi.org/10.1007/JHEP04(2019)042
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DOI: https://doi.org/10.1007/JHEP04(2019)042