Abstract
We present three point form factors (FF) in \( \mathcal{N}=4 \) Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the ‘t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of gϕϕ and ϕλλ, where ϕ, λ, g are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani’s IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for gϕϕ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.
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S.J. Parke and T.R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
D.A. Kosower, Light cone recurrence relations for QCD amplitudes, Nucl. Phys. B 335 (1990) 23 [INSPIRE].
Z. Bern and D.A. Kosower, Efficient calculation of one loop QCD amplitudes, Phys. Rev. Lett. 66 (1991) 1669 [INSPIRE].
Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys. B 379 (1992) 451 [INSPIRE].
Z. Bern, A compact representation of the one loop N gluon amplitude, Phys. Lett. B 296 (1992) 85 [INSPIRE].
G. Cristofano, R. Marotta and K. Roland, Unitarity and normalization of string amplitudes, Nucl. Phys. B 392 (1993) 345 [INSPIRE].
K. Roland, Multiloop gluon amplitudes in pure gauge theories, Phys. Lett. B 289 (1992) 148 [INSPIRE].
Z. Bern, D.C. Dunbar and T. Shimada, String based methods in perturbative gravity, Phys. Lett. B 312 (1993) 277 [hep-th/9307001] [INSPIRE].
G. Mahlon, One loop multi-photon helicity amplitudes, Phys. Rev. D 49 (1994) 2197 [hep-ph/9311213] [INSPIRE].
G. Mahlon, Multi-gluon helicity amplitudes involving a quark loop, Phys. Rev. D 49 (1994) 4438 [hep-ph/9312276] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
A.L. Kataev, Riemann ζ(3)- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N = 4 supersymmetric Yang-Mills theory, Phys. Lett. B 691 (2010) 82 [arXiv:1005.2058] [INSPIRE].
A.L. Kataev and S.V. Mikhailov, New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models, Theor. Math. Phys. 170 (2012) 139 [arXiv:1011.5248] [INSPIRE].
A.L. Kataev, Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules, JHEP 02 (2014) 092 [arXiv:1305.4605] [INSPIRE].
M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S matrix, Phys. Rev. D 15 (1977) 996 [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602 [hep-th/0309040] [INSPIRE].
B. Eden, P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Simplifications of four point functions in N = 4 supersymmetric Yang-Mills theory at two loops, Phys. Lett. B 466 (1999) 20 [hep-th/9906051] [INSPIRE].
B. Eden, C. Schubert and E. Sokatchev, Three loop four point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [INSPIRE].
B. Eden, C. Schubert and E. Sokatchev, Four point functions of chiral primary operators in N = 4 SYM,intheproceedingsofthe Quantization, gauge theory, and strings: International Conference dedicated to the memory of Professor Efim Fradkin ; June 5-10, Moscow, Russia (2000), hep-th/0010005 [INSPIRE].
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].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [INSPIRE].
F. Cachazo, M. Spradlin and A. Volovich, Iterative structure within the five-particle two-loop amplitude, Phys. Rev. D 74 (2006) 045020 [hep-th/0602228] [INSPIRE].
Z. Bern, M. Czakon, D.A. Kosower, R. Roiban and V.A. Smirnov, Two-loop iteration of five-point N = 4 super-Yang-Mills amplitudes, Phys. Rev. Lett. 97 (2006) 181601 [hep-th/0604074] [INSPIRE].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
J.M. Drummond, G.P. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [INSPIRE].
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].
L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].
J. Maldacena and A. Zhiboedov, Form factors at strong coupling via a Y-system, JHEP 11 (2010) 104 [arXiv:1009.1139] [INSPIRE].
Z. Gao and G. Yang, Y-system for form factors at strong coupling in AdS 5 and with multi-operator insertions in AdS 3, JHEP 06 (2013) 105 [arXiv:1303.2668] [INSPIRE].
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].
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].
A. Brandhuber, B. Spence, G. Travaglini and G. Yang, Form factors in N = 4 super Yang-Mills and periodic Wilson loops, JHEP 01 (2011) 134 [arXiv:1011.1899] [INSPIRE].
T. Gehrmann, J.M. Henn and T. Huber, The three-loop form factor in N = 4 super Yang-Mills, JHEP 03 (2012) 101 [arXiv:1112.4524] [INSPIRE].
R. Boels, B.A. Kniehl and G. Yang, Master integrals for the four-loop Sudakov form factor, Nucl. Phys. B 902 (2016) 387 [arXiv:1508.03717] [INSPIRE].
A. Brandhuber, G. Travaglini and G. Yang, Analytic two-loop form factors in N = 4 SYM, JHEP 05 (2012) 082 [arXiv:1201.4170] [INSPIRE].
A. Brandhuber, O. Gurdogan, R. Mooney, G. Travaglini and G. Yang, Harmony of super form factors, JHEP 10 (2011) 046 [arXiv:1107.5067] [INSPIRE].
L.V. Bork, D.I. Kazakov and G.S. Vartanov, On MHV form factors in superspace for \( \mathcal{N}=4 \) SYM theory, JHEP 10(2011) 133 [arXiv:1107.5551] [INSPIRE].
V.K. Dobrev and V.B. Petkova, On the group theoretical approach tol extended conformal supersymmetry: classification of multiplets, Lett. Math. Phys. 9 (1985) 287 [INSPIRE].
S. Ferrara and E. Sokatchev, Short representations of SU(2, 2/N ) and harmonic superspace analyticity, Lett. Math. Phys. 52 (2000) 247 [hep-th/9912168] [INSPIRE].
S. Ferrara, Superspace representations of SU(2, 2/N) superalgebras and multiplet shortening, PoS (TMR99) 016.
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 781 [hep-th/9712074] [INSPIRE].
J. Rasmussen, Comments on N = 4 superconformal algebras, Nucl. Phys. B 593 (2001) 634 [hep-th/0003035] [INSPIRE].
W.L. van Neerven, Infrared behavior of on-shell form-factors in a N = 4 supersymmetric Yang-Mills field theory, Z. Phys. C 30 (1986) 595 [INSPIRE].
K. Konishi, Anomalous supersymmetry transformation of some composite operators in SQCD, Phys. Lett. B 135 (1984) 439 [INSPIRE].
L. Andrianopoli and S. Ferrara, K-K excitations on AdS 5 × S 5 as N = 4 ‘primary’ superfields, Phys. Lett. B 430 (1998) 248 [hep-th/9803171] [INSPIRE].
D. Anselmi, M.T. Grisaru and A. Johansen, A critical behavior of anomalous currents, electric-magnetic universality and CFT in four-dimensions, Nucl. Phys. B 491 (1997) 221 [hep-th/9601023] [INSPIRE].
M. Bianchi, S. Kovacs, G. Rossi and Y.S. Stanev, Anomalous dimensions in N = 4 SYM theory at order g 4, Nucl. Phys. B 584 (2000) 216 [hep-th/0003203] [INSPIRE].
A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754] [hep-th/0404092] [INSPIRE].
B. Eden, C. Jarczak and E. Sokatchev, A three-loop test of the dilatation operator in N = 4 SYM, Nucl. Phys. B 712 (2005) 157 [hep-th/0409009] [INSPIRE].
Z. Bajnok and R.A. Janik, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys. B 807 (2009) 625 [arXiv:0807.0399] [INSPIRE].
Z. Bajnok, A. Hegedus, R.A. Janik and T. Lukowski, Five loop Konishi from AdS/CFT, Nucl. Phys. B 827 (2010) 426 [arXiv:0906.4062] [INSPIRE].
F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Wrapping at four loops in N = 4 SYM, Phys. Lett. B 666 (2008) 100 [arXiv:0712.3522] [INSPIRE].
F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Anomalous dimension with wrapping at four loops in N = 4 SYM, Nucl. Phys. B 805 (2008) 231 [arXiv:0806.2095] [INSPIRE].
V.N. Velizhanin, The four-loop anomalous dimension of the Konishi operator in N = 4 supersymmetric Yang-Mills theory, JETP Lett. 89 (2009) 6 [arXiv:0808.3832] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky, V.A. Smirnov and E. Sokatchev, Five-loop Konishi in N = 4 SYM, Nucl. Phys. B 862 (2012) 123 [arXiv:1202.5733] [INSPIRE].
M. Wilhelm, Amplitudes, form factors and the dilatation operator in \( \mathcal{N}=4 \) SYM theory, JHEP 02 (2015) 149 [arXiv:1410.6309] [INSPIRE].
F. Loebbert, D. Nandan, C. Sieg, M. Wilhelm and G. Yang, On-shell methods for the two-loop dilatation operator and finite remainders, JHEP 10 (2015) 012 [arXiv:1504.06323] [INSPIRE].
A. Brandhuber, M. Kostacinska, B. Penante, G. Travaglini and D. Young, The SU(2|3) dynamic two-loop form factors, JHEP 08 (2016) 134 [arXiv:1606.08682] [INSPIRE].
F. Loebbert, C. Sieg, M. Wilhelm and G. Yang, Two-loop SL(2) form factors and maximal transcendentality, JHEP 12 (2016) 090 [arXiv:1610.06567] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-shell methods in perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].
D. Nandan, C. Sieg, M. Wilhelm and G. Yang, Cutting through form factors and cross sections of non-protected operators in \( \mathcal{N}=4 \) SYM, JHEP 06 (2015) 156 [arXiv:1410.8485] [INSPIRE].
T. Ahmed, P. Banerjee, P.K. Dhani, N. Rana, V. Ravindran and S. Seth, Konishi form factor at three loops in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 95 (2017) 085019 [arXiv:1610.05317] [INSPIRE].
V.V. Sudakov, Vertex parts at very high-energies in quantum electrodynamics, Sov. Phys. JETP 3 (1956) 65 [Zh. Eksp. Teor. Fiz. 30 (1956) 87] [INSPIRE].
A.H. Mueller, On the asymptotic behavior of the Sudakov form-factor, Phys. Rev. D 20 (1979)2037 [INSPIRE].
J.C. Collins, Algorithm to compute corrections to the Sudakov form-factor, Phys. Rev. D 22 (1980) 1478 [INSPIRE].
A. Sen, Asymptotic behavior of the Sudakov form-factor in QCD, Phys. Rev. D 24 (1981) 3281 [INSPIRE].
S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [arXiv:0901.0722] [INSPIRE].
E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [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].
L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills theories, Nucl. Phys. B 121 (1977) 77 [INSPIRE].
F. Gliozzi, J. Scherk and D.I. Olive, Supersymmetry, supergravity theories and the dual spinor model, Nucl. Phys. B 122 (1977) 253 [INSPIRE].
D.R.T. Jones, Charge renormalization in a supersymmetric Yang-Mills theory, Phys. Lett. 72B (1977) 199 [INSPIRE].
E.C. Poggio and H.N. Pendleton, Vanishing of Charge Renormalization and Anomalies in a Supersymmetric Gauge Theory, Phys. Lett. B 72 (1977) 200 [INSPIRE].
W. Siegel, Supersymmetric dimensional regularization via dimensional reduction, Phys. Lett. B 84 (1979) 193 [INSPIRE].
D.M. Capper, D.R.T. Jones and P. van Nieuwenhuizen, Regularization by dimensional reduction of supersymmetric and nonsupersymmetric gauge theories, Nucl. Phys. B 167 (1980) 479 [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
T. Gehrmann and E. Remiddi, Two loop master integrals for γ ∗ → 3 jets: the planar topologies, Nucl. Phys. B 601 (2001) 248 [hep-ph/0008287] [INSPIRE].
T. Gehrmann and E. Remiddi, Two loop master integrals for γ ∗ → 3 jets: the nonplanar topologies, Nucl. Phys. B 601 (2001) 287 [hep-ph/0101124] [INSPIRE].
L.W. Garland, T. Gehrmann, E.W.N. Glover, A. Koukoutsakis and E. Remiddi, Two loop QCD helicity amplitudes for e + e − → three jets, Nucl. Phys. B 642 (2002) 227 [hep-ph/0206067] [INSPIRE].
T. Gehrmann, M. Jaquier, E.W.N. Glover and A. Koukoutsakis, Two-Loop QCD corrections to the helicity amplitudes for H → 3 partons, JHEP 02 (2012) 056 [arXiv:1112.3554] [INSPIRE].
T. Ahmed, M. Mahakhud, P. Mathews, N. Rana and V. Ravindran, Two-loop QCD corrections to \( Higgs\to b+\overline{b}+g \) amplitude, JHEP 08 (2014) 075 [arXiv:1405.2324] [INSPIRE].
T. Ahmed, M. Mahakhud, P. Mathews, N. Rana and V. Ravindran, Two-loop QCD correction to massive spin-2 resonance → 3 gluons, JHEP 05 (2014) 107 [arXiv:1404.0028] [INSPIRE].
T. Ahmed, G. Das, P. Mathews, N. Rana and V. Ravindran, The two-loop QCD correction to massive spin-2 \( resonance\to q\overline{q}g \), Eur. Phys. J. C 76 (2016) 667 [arXiv:1608.05906] [INSPIRE].
T. Ahmed et al., NNLO QCD corrections to the Drell-Yan cross section in models of TeV-scale gravity, Eur. Phys. J. C 77 (2017) 22 [arXiv:1606.08454] [INSPIRE].
T. Ahmed, P. Banerjee, P.K. Dhani, P. Mathews, N. Rana and V. Ravindran, Three loop form factors of a massive spin-2 particle with nonuniversal coupling, Phys. Rev. D 95 (2017) 034035 [arXiv:1612.00024] [INSPIRE].
T. Gehrmann, L. Tancredi and E. Weihs, Two-loop QCD helicity amplitudes for g g → Z g and g g → Z γ, JHEP 04 (2013) 101 [arXiv:1302.2630] [INSPIRE].
T. Ahmed, P. Banerjee, P. K. Dhani, N. Rana and V. Ravindran, Two loop QCD corrections for pseudoscalar + jet production, in preparation.
F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
L.V. Bork, D.I. Kazakov and G.S. Vartanov, On form factors in N = 4 SYM, JHEP 02 (2011) 063 [arXiv:1011.2440] [INSPIRE].
B. Penante, B. Spence, G. Travaglini and C. Wen, On super form factors of half-BPS operators in N = 4 super Yang-Mills, JHEP 04 (2014) 083 [arXiv:1402.1300] [INSPIRE].
A. Brandhuber, B. Penante, G. Travaglini and C. Wen, The last of the simple remainders, JHEP 08 (2014) 100 [arXiv:1406.1443] [INSPIRE].
L.V. Bork, On NMHV form factors in N = 4 SYM theory from generalized unitarity, JHEP 01 (2013) 049 [arXiv:1203.2596] [INSPIRE].
O.T. Engelund and R. Roiban, Correlation functions of local composite operators from generalized unitarity, JHEP 03 (2013) 172 [arXiv:1209.0227] [INSPIRE].
L.V. Bork, On form factors in \( \mathcal{N}=4 \) SYM theory and polytopes, JHEP 12 (2014) 111 [arXiv:1407.5568] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279.
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman integral reduction, arXiv:1201.4330 [INSPIRE].
R.N. Lee, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, JHEP 07 (2008) 031 [arXiv:0804.3008] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
R.K. Ellis and J.C. Sexton, QCD radiative corrections to parton parton scattering, Nucl. Phys. B 269 (1986) 445 [INSPIRE].
Z. Bern, A. De Freitas, L.J. Dixon and H.L. Wong, Supersymmetric regularization, two loop QCD amplitudes and coupling shifts, Phys. Rev. D 66 (2002) 085002 [hep-ph/0202271] [INSPIRE].
V. Ravindran, On Sudakov and soft resummations in QCD, Nucl. Phys. B 746 (2006) 58 [hep-ph/0512249] [INSPIRE].
V. Ravindran, Higher-order threshold effects to inclusive processes in QCD, Nucl. Phys. B 752 (2006) 173 [hep-ph/0603041] [INSPIRE].
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
T. D. Lee and M. Nauenberg, Degenerate systems and mass singularities, Phys. Rev. 133 (1964) B1549 [INSPIRE].
S.G. Naculich, H. Nastase and H.J. Schnitzer, Subleading-color contributions to gluon-gluon scattering in N = 4 SYM theory and relations to N = 8 supergravity, JHEP 11 (2008) 018 [arXiv:0809.0376] [INSPIRE].
T. Gehrmann and E. Remiddi, Numerical evaluation of two-dimensional harmonic polylogarithms, Comput. Phys. Commun. 144 (2002) 200 [hep-ph/0111255] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories, Nucl. Phys. B 582 (2000) 19 [hep-ph/0004008] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. B 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory, hep-ph/0112346 [INSPIRE].
A.V. Kotikov and L.N. Lipatov, On the highest transcendentality in N = 4 SUSY, Nucl. Phys. B 769 (2007) 217 [hep-th/0611204] [INSPIRE].
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].
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].
B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
J. Drummond, C. Duhr, B. Eden, P. Heslop, J. Pennington and V.A. Smirnov, Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [INSPIRE].
B. Basso, V. Goncalves, S. Komatsu and P. Vieira, Gluing hexagons at three loops, Nucl. Phys. B 907 (2016) 695 [arXiv:1510.01683] [INSPIRE].
V. Gonçalves, Extracting OPE coefficient of Konishi at four loops, JHEP 03 (2017) 079 [arXiv:1607.02195] [INSPIRE].
A. Koukoutsakis, Higgs bosons and QCD jets at two loops, Ph.D. thesis, Durham University, Durham, U.K. (2003).
V. Ravindran, J. Smith and W.L. van Neerven, Two-loop corrections to Higgs boson production, Nucl. Phys. B 704 (2005) 332 [hep-ph/0408315] [INSPIRE].
A. Vogt, Next-to-next-to-leading logarithmic threshold resummation for deep inelastic scattering and the Drell-Yan process, Phys. Lett. B 497 (2001) 228 [hep-ph/0010146] [INSPIRE].
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Banerjee, P., Dhani, P.K., Mahakhud, M. et al. Finite remainders of the Konishi at two loops in \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2017, 85 (2017). https://doi.org/10.1007/JHEP05(2017)085
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DOI: https://doi.org/10.1007/JHEP05(2017)085