×

Two-loop doubly massive four-point amplitude involving a half-BPS and Konishi operator. (English) Zbl 1416.81197

Summary: The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no similarity with similar amplitudes in QCD.

MSC:

81U05 \(2\)-body potential quantum scattering theory
81T17 Renormalization group methods applied to problems in quantum field theory
81V05 Strong interaction, including quantum chromodynamics
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Yang, C-N; Mills, RL, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev., 96, 191, (1954) · Zbl 1378.81075
[2] Maldacena, JM, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113, (1999) · Zbl 0969.81047
[3] Bern, Z.; Dixon, LJ; Smirnov, VA, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev., D 72, (2005)
[4] Brandhuber, A.; Spence, B.; Travaglini, G.; Yang, G., Form Factors in N = 4 Super Yang-Mills and Periodic Wilson Loops, JHEP, 01, 134, (2011) · Zbl 1214.81146
[5] L.V. Bork, D.I. Kazakov and G.S. Vartanov, On form factors in N = 4 SYM, JHEP02 (2011) 063 [arXiv:1011.2440] [INSPIRE].
[6] Bork, LV; Kazakov, DI; Vartanov, GS, On MHV Form Factors in Superspace for = 4 SYM Theory, JHEP, 10, 133, (2011) · Zbl 1303.81110
[7] Brandhuber, A.; Gurdogan, O.; Mooney, R.; Travaglini, G.; Yang, G., Harmony of Super Form Factors, JHEP, 10, 046, (2011) · Zbl 1303.81111
[8] Gehrmann, T.; Henn, JM; Huber, T., The three-loop form factor in N = 4 super Yang-Mills, JHEP, 03, 101, (2012) · Zbl 1309.81159
[9] Brandhuber, A.; Travaglini, G.; Yang, G., Analytic two-loop form factors in N = 4 SYM, JHEP, 05, 082, (2012) · Zbl 1348.81400
[10] Boels, R.; Kniehl, BA; Yang, G., Master integrals for the four-loop Sudakov form factor, Nucl. Phys., B 902, 387, (2016) · Zbl 1332.81126
[11] Ahmed, T.; Banerjee, P.; Dhani, PK; Rana, N.; Ravindran, V.; Seth, S., Konishi form factor at three loops in \( \mathcal{N} \) = △ supersymmetric Yang-Mills theory, Phys. Rev., D 95, (2017)
[12] Boels, RH; Huber, T.; Yang, G., The Sudakov form factor at four loops in maximal super Yang-Mills theory, JHEP, 01, 153, (2018) · Zbl 1384.81131
[13] Neerven, WL, Infrared Behavior of On-shell Form-factors in a N = 4 Supersymmetric Yang-Mills Field Theory, Z. Phys., C 30, 595, (1986)
[14] Konishi, K., Anomalous Supersymmetry Transformation of Some Composite Operators in SQCD, Phys. Lett., 135B, 439, (1984)
[15] Eden, B.; Schubert, C.; Sokatchev, E., Three loop four point correlator in N = 4 SYM, Phys. Lett., B 482, 309, (2000) · Zbl 0990.81121
[16] Anselmi, D.; Grisaru, MT; Johansen, A., A critical behavior of anomalous currents, electric-magnetic universality and CFT in four-dimensions, Nucl. Phys., B 491, 221, (1997) · Zbl 0925.81384
[17] Bianchi, M.; Kovacs, S.; Rossi, G.; Stanev, YS, Anomalous dimensions in N = 4 SYM theory at order g4, Nucl. Phys., B 584, 216, (2000) · Zbl 0984.81155
[18] 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].
[19] Eden, B.; Jarczak, C.; Sokatchev, E., A three-loop test of the dilatation operator in N = 4 SYM, Nucl. Phys., B 712, 157, (2005) · Zbl 1109.81354
[20] Bajnok, Z.; Janik, RA, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys., B 807, 625, (2009) · Zbl 1192.81255
[21] Bajnok, Z.; Hegedus, A.; Janik, RA; Lukowski, T., Five loop Konishi from AdS/CFT, Nucl. Phys., B 827, 426, (2010) · Zbl 1203.81132
[22] Fiamberti, F.; Santambrogio, A.; Sieg, C.; Zanon, D., Wrapping at four loops in N = 4 SYM, Phys. Lett., B 666, 100, (2008) · Zbl 1328.81202
[23] Fiamberti, F.; Santambrogio, A.; Sieg, C.; Zanon, D., Anomalous dimension with wrapping at four loops in N = 4 SYM, Nucl. Phys., B 805, 231, (2008) · Zbl 1190.81092
[24] Velizhanin, VN, The four-loop anomalous dimension of the Konishi operator in N = 4 supersymmetric Yang-Mills theory, JETP Lett., 89, 6, (2009)
[25] Eden, B.; Heslop, P.; Korchemsky, GP; Smirnov, VA; Sokatchev, E., Five-loop Konishi in N = 4 SYM, Nucl. Phys., B 862, 123, (2012) · Zbl 1246.81452
[26] Nandan, D.; Sieg, C.; Wilhelm, M.; Yang, G., Cutting through form factors and cross sections of non-protected operators in \( \mathcal{N} \) = 4 SYM, JHEP, 06, 156, (2015) · Zbl 1388.81393
[27] Banerjee, P.; Dhani, PK; Mahakhud, M.; Ravindran, V.; Seth, S., Finite remainders of the Konishi at two loops in \( \mathcal{N} \) = 4 SYM, JHEP, 05, 085, (2017) · Zbl 1380.81202
[28] Gehrmann, T.; Manteuffel, A.; Tancredi, L., The two-loop helicity amplitudes for \( q\overline{q}^{\prime } \) → V_{1}V_{2} → 4 leptons, JHEP, 09, 128, (2015)
[29] Manteuffel, A.; Tancredi, L., The two-loop helicity amplitudes for gg → V_{1}V_{2} → 4 leptons, JHEP, 06, 197, (2015)
[30] T. Ahmed, P. Banerjee, A. Chakraborty, P.K. Dhani and V. Ravindran, in preparation.
[31] Banerjee, P.; Borowka, S.; Dhani, PK; Gehrmann, T.; Ravindran, V., Two-loop massless QCD corrections to the g + g → H + H four-point amplitude, JHEP, 11, 130, (2018)
[32] A.A. H et al., Two-loop QCD corrections to b + \( \overline{b} \) → \(H\) + H amplitude, arXiv:1811.01853 [INSPIRE].
[33] Bern, Z.; Kosower, DA, The computation of loop amplitudes in gauge theories, Nucl. Phys., B 379, 451, (1992)
[34] 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].
[35] Siegel, W., Supersymmetric Dimensional Regularization via Dimensional Reduction, Phys. Lett., 84B, 193, (1979)
[36] 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].
[37] G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys.B 44 (1972) 189 [INSPIRE].
[38] Bern, Z.; Czakon, M.; Dixon, LJ; Kosower, DA; Smirnov, VA, The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev., D 75, (2007)
[39] Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., On planar gluon amplitudes/Wilson loops duality, Nucl. Phys., B 795, 52, (2008) · Zbl 1219.81191
[40] Naculich, SG; Nastase, H.; Schnitzer, HJ, Subleading-color contributions to gluon-gluon scattering in N = 4 SYM theory and relations to N = 8 supergravity, JHEP, 11, 018, (2008)
[41] B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
[42] Drummond, J.; Duhr, C.; Eden, B.; Heslop, P.; Pennington, J.; Smirnov, VA, Leading singularities and off-shell conformal integrals, JHEP, 08, 133, (2013) · Zbl 1342.81574
[43] Basso, B.; Gonçalves, V.; Komatsu, S.; Vieira, P., Gluing Hexagons at Three Loops, Nucl. Phys., B 907, 695, (2016) · Zbl 1336.81052
[44] Gonçalves, V., Extracting OPE coefficient of Konishi at four loops, JHEP, 03, 079, (2017) · Zbl 1377.81171
[45] Arkani-Hamed, N.; Bourjaily, JL; Cachazo, F.; Trnka, J., Local Integrals for Planar Scattering Amplitudes, JHEP, 06, 125, (2012) · Zbl 1397.81428
[46] Drummond, JM; Henn, JM, Simple loop integrals and amplitudes in N = 4 SYM, JHEP, 05, 105, (2011) · Zbl 1296.81058
[47] Drummond, JM; Henn, JM; Trnka, J., New differential equations for on-shell loop integrals, JHEP, 04, 083, (2011) · Zbl 1250.81064
[48] J.B. Tausk, Nonplanar massless two loop Feynman diagrams with four on-shell legs, Phys. Lett.B 469 (1999) 225 [hep-ph/9909506] [INSPIRE].
[49] Naculich, SG; Nastase, H.; Schnitzer, HJ, Two-loop graviton scattering relation and IR behavior in N = 8 supergravity, Nucl. Phys., B 805, 40, (2008) · Zbl 1190.83096
[50] A. Brandhuber, P. Heslop, A. Nasti, B. Spence and G. Travaglini, Four-point Amplitudes in N = 8 Supergravity and Wilson Loops, Nucl. Phys.B 807 (2009) 290 [arXiv:0805.2763] [INSPIRE]. · Zbl 1192.83064
[51] L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories, Nucl. Phys.B 121 (1977) 77 [INSPIRE].
[52] Gliozzi, F.; Scherk, J.; Olive, DI, Supersymmetry, Supergravity Theories and the Dual Spinor Model, Nucl. Phys., B 122, 253, (1977)
[53] Jones, DRT, Charge Renormalization in a Supersymmetric Yang-Mills Theory, Phys. Lett., 72B, 199, (1977)
[54] Poggio, EC; Pendleton, HN, Vanishing of Charge Renormalization and Anomalies in a Supersymmetric Gauge Theory, Phys. Lett., 72B, 200, (1977)
[55] E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys.B 182 (1981) 173 [INSPIRE].
[56] S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
[57] G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett.B 552 (2003) 48 [hep-ph/0210130] [INSPIRE].
[58] T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett.102 (2009) 162001 [Erratum ibid.111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].
[59] Gardi, E.; Magnea, L., Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP, 03, 079, (2009)
[60] Nogueira, P., Automatic Feynman graph generation, J. Comput. Phys., 105, 279, (1993) · Zbl 0782.68091
[61] J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
[62] A. von Manteuffel and C. Studerus, Reduze 2Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
[63] C. Studerus, Reduze-Feynman Integral Reduction in C++, Comput. Phys. Commun.181 (2010) 1293 [arXiv:0912.2546] [INSPIRE]. · Zbl 1219.81133
[64] Tkachov, FV, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett., 100B, 65, (1981)
[65] Chetyrkin, KG; Tkachov, FV, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys., B 192, 159, (1981)
[66] T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys.B 580 (2000) 485 [hep-ph/9912329] [INSPIRE]. · Zbl 1071.81089
[67] Lee, RN, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, JHEP, 07, 031, (2008)
[68] R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
[69] R.N. Lee and A.A. Pomeransky, Critical points and number of master integrals, JHEP11 (2013) 165 [arXiv:1308.6676] [INSPIRE].
[70] Maierhöfer, P.; Usovitsch, J.; Uwer, P., Kira — A Feynman integral reduction program, Comput. Phys. Commun., 230, 99, (2018)
[71] P. Maierhöfer and J. Usovitsch, Kira 1.2 Release Notes, arXiv:1812.01491 [INSPIRE].
[72] Smirnov, AV, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun., 189, 182, (2015) · Zbl 1344.81030
[73] Henn, JM; Melnikov, K.; Smirnov, VA, Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions, JHEP, 05, 090, (2014)
[74] Caola, F.; Henn, JM; Melnikov, K.; Smirnov, VA, Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons, JHEP, 09, 043, (2014)
[75] Papadopoulos, CG; Tommasini, D.; Wever, C., Two-loop Master Integrals with the Simplified Differential Equations approach, JHEP, 01, 072, (2015)
[76] Chavez, F.; Duhr, C., Three-mass triangle integrals and single-valued polylogarithms, JHEP, 11, 114, (2012) · Zbl 1397.81071
[77] C. Anastasiou et al., NNLO QCD corrections to pp → \(γ\)*\(γ\)*in the large N_{\(F\)}limit, JHEP02 (2015) 182 [arXiv:1408.4546] [INSPIRE].
[78] https://vvamp.hepforge.org/.
[79] Bartels, J.; Lipatov, LN; Sabio Vera, A., BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev., D 80, (2009)
[80] Bern, Z.; etal., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev., D 78, (2008)
[81] 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].
[82] Banerjee, P.; Chakraborty, A.; Dhani, PK; Ravindran, V.; Seth, S., Second order splitting functions and infrared safe cross sections in \( \mathcal{N} \) = 4 SYM theory, JHEP, 04, 058, (2019) · Zbl 1415.81098
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.