BCJ duality and the double copy in the soft limit. (English) Zbl 1342.81719
Summary: We examine the structure of infrared singularities in QCD and quantum General Relativity, from the point of view of the recently conjectured double copy property which relates scattering amplitudes in non-Abelian gauge theories with gravitational counterparts. We show that IR divergences in both theories are consistent with the double copy procedure, to all orders in perturbation theory, thus providing all loop-level evidence for the conjecture. We further comment on the relevance, or otherwise, to the so-called dipole formula, a conjecture for the complete structure of IR singularities in QCD.
MSC:
| 81V17 | Gravitational interaction in quantum theory |
References:
| [1] | Z. Bern, L.J. Dixon and R. Roiban, Is N = 8 supergravity ultraviolet finite?, Phys. Lett.B 644 (2007) 265 [hep-th/0611086] [INSPIRE]. · Zbl 1248.83136 |
| [2] | Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett.105 (2010) 061602 [arXiv:1004.0476] [INSPIRE]. · doi:10.1103/PhysRevLett.105.061602 |
| [3] | Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev.D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE]. |
| [4] | Z. Bern, J. Carrasco, L. Dixon, H. Johansson and R. Roiban, Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev.D 85 (2012) 105014 [arXiv:1201.5366] [INSPIRE]. |
| [5] | Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev.D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE]. |
| [6] | S.H. Henry Tye and Y. Zhang, Dual Identities inside the Gluon and the Graviton Scattering Amplitudes, JHEP06 (2010) 071 [Erratum ibid.1104 (2011) 114] [arXiv:1003.1732] [INSPIRE]. · Zbl 1288.81150 · doi:10.1007/JHEP06(2010)071 |
| [7] | N. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes, JHEP06 (2010) 003 [arXiv:1003.2403] [INSPIRE]. · Zbl 1290.83015 · doi:10.1007/JHEP06(2010)003 |
| [8] | J. Broedel and J.J.M. Carrasco, Virtuous Trees at Five and Six Points for Yang-Mills and Gravity, Phys. Rev.D 84 (2011) 085009 [arXiv:1107.4802] [INSPIRE]. |
| [9] | R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP07 (2011) 007 [arXiv:1105.2565] [INSPIRE]. · Zbl 1298.81401 · doi:10.1007/JHEP07(2011)007 |
| [10] | H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys.B 269 (1986) 1 [INSPIRE]. · doi:10.1016/0550-3213(86)90362-7 |
| [11] | Z. Bern, L.J. Dixon, D. Dunbar, M. Perelstein and J. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys.B 530 (1998) 401 [hep-th/9802162] [INSPIRE]. · doi:10.1016/S0550-3213(98)00420-9 |
| [12] | M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 Supergravity as Limits of String Theories, Nucl. Phys.B 198 (1982) 474 [INSPIRE]. · doi:10.1016/0550-3213(82)90336-4 |
| [13] | Z. Bern, J. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 super Yang-Mills, Phys. Lett.B 401 (1997) 273 [hep-ph/9702424] [INSPIRE]. |
| [14] | Z. Bern et al., Three-Loop Superfiniteness of N = 8 Supergravity, Phys. Rev. Lett.98 (2007) 161303 [hep-th/0702112] [INSPIRE]. · doi:10.1103/PhysRevLett.98.161303 |
| [15] | Z. Bern, J. Carrasco and H. Johansson, Progress on Ultraviolet Finiteness of Supergravity, arXiv:0902.3765 [INSPIRE]. |
| [16] | C. Boucher-Veronneau and L. Dixon, N ≥ 4 Supergravity Amplitudes from Gauge Theory at Two Loops, JHEP12 (2011) 046 [arXiv:1110.1132] [INSPIRE]. · Zbl 1306.81078 · doi:10.1007/JHEP12(2011)046 |
| [17] | S.G. Naculich, H. Nastase and H.J. Schnitzer, Linear relations between N ≥ 4 supergravity and subleading-color SYM amplitudes, JHEP01 (2012) 041 [arXiv:1111.1675] [INSPIRE]. · Zbl 1306.81125 · doi:10.1007/JHEP01(2012)041 |
| [18] | 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, JHEP11 (2008) 018 [arXiv:0809.0376] [INSPIRE]. · doi:10.1088/1126-6708/2008/11/018 |
| [19] | J. Broedel and L.J. Dixon, Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators, JHEP10 (2012) 091 [arXiv:1208.0876] [INSPIRE]. · doi:10.1007/JHEP10(2012)091 |
| [20] | J. Grammer, G. and D. Yennie, Improved treatment for the infrared divergence problem in quantum electrodynamics, Phys. Rev.D 8 (1973) 4332 [INSPIRE]. |
| [21] | A.H. Mueller, On the asymptotic behavior of the Sudakov form-factor, Phys. Rev.D 20 (1979) 2037 [INSPIRE]. |
| [22] | J.C. Collins, Algorithm to compute corrections to the Sudakov form-factor, Phys. Rev.D 22 (1980) 1478 [INSPIRE]. |
| [23] | A. Sen, Asymptotic Behavior of the Sudakov Form-Factor in QCD, Phys. Rev.D 24 (1981) 3281 [INSPIRE]. |
| [24] | A. Sen, Asymptotic Behavior of the Wide Angle On-Shell Quark Scattering Amplitudes in Nonabelian Gauge Theories, Phys. Rev.D 28 (1983) 860 [INSPIRE]. |
| [25] | J. Gatheral, Exponentiation of eikonal cross-sections in nonabelian gauge theories, Phys. Lett.B 133 (1983) 90 [INSPIRE]. |
| [26] | J. Frenkel and J. Taylor, Nonabelian eikonal exponentiation, Nucl. Phys.B 246 (1984) 231 [INSPIRE]. · doi:10.1016/0550-3213(84)90294-3 |
| [27] | L. Magnea and G.F. Sterman, Analytic continuation of the Sudakov form-factor in QCD, Phys. Rev.D 42 (1990) 4222 [INSPIRE]. |
| [28] | A. Mitov, G. Sterman and I. Sung, Diagrammatic Exponentiation for Products of Wilson Lines, Phys. Rev.D 82 (2010) 096010 [arXiv:1008.0099] [INSPIRE]. |
| [29] | E. Gardi, E. Laenen, G. Stavenga and C.D. White, Webs in multiparton scattering using the replica trick, JHEP11 (2010) 155 [arXiv:1008.0098] [INSPIRE]. · Zbl 1294.81278 · doi:10.1007/JHEP11(2010)155 |
| [30] | L.J. Dixon, L. Magnea and G.F. Sterman, Universal structure of subleading infrared poles in gauge theory amplitudes, JHEP08 (2008) 022 [arXiv:0805.3515] [INSPIRE]. · doi:10.1088/1126-6708/2008/08/022 |
| [31] | T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett.102 (2009) 162001 [arXiv:0901.0722] [INSPIRE]. · doi:10.1103/PhysRevLett.102.162001 |
| [32] | T. Becher and M. Neubert, On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP06 (2009) 081 [arXiv:0903.1126] [INSPIRE]. · doi:10.1088/1126-6708/2009/06/081 |
| [33] | E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP03 (2009) 079 [arXiv:0901.1091] [INSPIRE]. · doi:10.1088/1126-6708/2009/03/079 |
| [34] | E. Gardi and L. Magnea, Infrared singularities in QCD amplitudes, Nuovo Cim.C32N5-6 (2009) 137 [arXiv:0908.3273] [INSPIRE]. |
| [35] | L.J. Dixon, E. Gardi and L. Magnea, On soft singularities at three loops and beyond, JHEP02 (2010) 081 [arXiv:0910.3653] [INSPIRE]. · Zbl 1270.81217 · doi:10.1007/JHEP02(2010)081 |
| [36] | V. Del Duca, C. Duhr, E. Gardi, L. Magnea and C.D. White, An infrared approach to Reggeization, Phys. Rev.D 85 (2012) 071104 [arXiv:1108.5947] [INSPIRE]. |
| [37] | V. Del Duca, C. Duhr, E. Gardi, L. Magnea and C.D. White, The Infrared structure of gauge theory amplitudes in the high-energy limit, JHEP12 (2011) 021 [arXiv:1109.3581] [INSPIRE]. · Zbl 1306.81333 · doi:10.1007/JHEP12(2011)021 |
| [38] | L. Vernazza, Analysis of the Anomalous-Dimension Matrix of n-jet Operators at 4 Loops, PoS(EPS-HEP2011)284 [arXiv:1112.3375] [INSPIRE]. |
| [39] | V. Ahrens, M. Neubert and L. Vernazza, Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops, JHEP09 (2012) 138 [arXiv:1208.4847] [INSPIRE]. · doi:10.1007/JHEP09(2012)138 |
| [40] | N. Kidonakis, Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production, Phys. Rev. Lett.102 (2009) 232003 [arXiv:0903.2561] [INSPIRE]. · doi:10.1103/PhysRevLett.102.232003 |
| [41] | A. Mitov, G.F. Sterman and I. Sung, The Massive Soft Anomalous Dimension Matrix at Two Loops, Phys. Rev.D 79 (2009) 094015 [arXiv:0903.3241] [INSPIRE]. |
| [42] | T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev.D 79 (2009) 125004 [Erratum ibid.D 80 (2009) 109901] [arXiv:0904.1021] [INSPIRE]. |
| [43] | M. Beneke, P. Falgari and C. Schwinn, Soft radiation in heavy-particle pair production: All-order colour structure and two-loop anomalous dimension, Nucl. Phys.B 828 (2010) 69 [arXiv:0907.1443] [INSPIRE]. · Zbl 1203.81165 · doi:10.1016/j.nuclphysb.2009.11.004 |
| [44] | M. Czakon, A. Mitov and G.F. Sterman, Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log, Phys. Rev.D 80 (2009) 074017 [arXiv:0907.1790] [INSPIRE]. |
| [45] | A. Ferroglia, M. Neubert, B.D. Pecjak and L.L. Yang, Two-loop divergences of scattering amplitudes with massive partons, Phys. Rev. Lett.103 (2009) 201601 [arXiv:0907.4791] [INSPIRE]. · doi:10.1103/PhysRevLett.103.201601 |
| [46] | A. Ferroglia, M. Neubert, B.D. Pecjak and L.L. Yang, Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories, JHEP11 (2009) 062 [arXiv:0908.3676] [INSPIRE]. · doi:10.1088/1126-6708/2009/11/062 |
| [47] | J.-y. Chiu, A. Fuhrer, R. Kelley and A.V. Manohar, Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC, Phys. Rev.D 80 (2009) 094013 [arXiv:0909.0012] [INSPIRE]. |
| [48] | A. Mitov, G.F. Sterman and I. Sung, Computation of the Soft Anomalous Dimension Matrix in Coordinate Space, Phys. Rev.D 82 (2010) 034020 [arXiv:1005.4646] [INSPIRE]. |
| [49] | S. Weinberg, Infrared photons and gravitons, Phys. Rev.140 (1965) B516. · doi:10.1103/PhysRev.140.B516 |
| [50] | S.G. Naculich and H.J. Schnitzer, Eikonal methods applied to gravitational scattering amplitudes, JHEP05 (2011) 087 [arXiv:1101.1524] [INSPIRE]. · Zbl 1296.83028 · doi:10.1007/JHEP05(2011)087 |
| [51] | C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP05 (2011) 060 [arXiv:1103.2981] [INSPIRE]. · Zbl 1296.83030 · doi:10.1007/JHEP05(2011)060 |
| [52] | R. Akhoury, R. Saotome and G. Sterman, Collinear and Soft Divergences in Perturbative Quantum Gravity, Phys. Rev.D 84 (2011) 104040 [arXiv:1109.0270] [INSPIRE]. |
| [53] | Z. Bern and Y.-t. Huang, Basics of Generalized Unitarity, J. Phys.A 44 (2011) 454003 [arXiv:1103.1869] [INSPIRE]. · Zbl 1270.81209 |
| [54] | S. Catani and M. Seymour, The Dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett.B 378 (1996) 287 [hep-ph/9602277] [INSPIRE]. |
| [55] | S. Catani and M. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys.B 485 (1997) 291 [Erratum ibid.B 510 (1998) 503-504] [hep-ph/9605323] [INSPIRE]. · doi:10.1016/S0550-3213(96)00589-5 |
| [56] | S.M. Aybat, L.J. Dixon and G.F. Sterman, The Two-loop anomalous dimension matrix for soft gluon exchange, Phys. Rev. Lett.97 (2006) 072001 [hep-ph/0606254] [INSPIRE]. · Zbl 1228.81258 · doi:10.1103/PhysRevLett.97.072001 |
| [57] | S.M. Aybat, L.J. Dixon and G.F. Sterman, The Two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole, Phys. Rev.D 74 (2006) 074004 [hep-ph/0607309] [INSPIRE]. |
| [58] | E. Gardi and C.D. White, General properties of multiparton webs: Proofs from combinatorics, JHEP03 (2011) 079 [arXiv:1102.0756] [INSPIRE]. · Zbl 1301.81297 · doi:10.1007/JHEP03(2011)079 |
| [59] | E. Gardi, J.M. Smillie and C.D. White, On the renormalization of multiparton webs, JHEP09 (2011) 114 [arXiv:1108.1357] [INSPIRE]. · Zbl 1301.81296 · doi:10.1007/JHEP09(2011)114 |
| [60] | Y.-T. Chien, M.D. Schwartz, D. Simmons-Duffin and I.W. Stewart, Jet Physics from Static Charges in AdS, Phys. Rev.D 85 (2012) 045010 [arXiv:1109.6010] [INSPIRE]. |
| [61] | M. Beneke and G. Kirilin, Soft-collinear gravity, JHEP09 (2012) 066 [arXiv:1207.4926] [INSPIRE]. · Zbl 1398.83031 · doi:10.1007/JHEP09(2012)066 |
| [62] | E. Laenen, G. Stavenga and C.D. White, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP03 (2009) 054 [arXiv:0811.2067] [INSPIRE]. · doi:10.1088/1126-6708/2009/03/054 |
| [63] | E. Laenen, L. Magnea, G. Stavenga and C.D. White, Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach, JHEP01 (2011) 141 [arXiv:1010.1860] [INSPIRE]. · Zbl 1214.81303 · doi:10.1007/JHEP01(2011)141 |
| [64] | D. Miller and C. White, The Gravitational cusp anomalous dimension from AdS space, Phys. Rev.D 85 (2012) 104034 [arXiv:1201.2358] [INSPIRE]. |
| [65] | H.W. Hamber, Discrete and continuum quantum gravity, arXiv:0704.2895 [INSPIRE]. · Zbl 0957.83513 |
| [66] | J.J.M. Carrasco, M. Chiodaroli, M. Günaydin and R. Roiban, One-loop four-point amplitudes in pure and matter-coupled N ≥ 4 supergravity, arXiv:1212.1146 [INSPIRE]. · Zbl 1342.83455 |
| [67] | C. Boucher-Veronneau and A.J. Larkoski, Constructing Amplitudes from Their Soft Limits, JHEP09 (2011) 130 [arXiv:1108.5385] [INSPIRE]. · Zbl 1301.81107 · doi:10.1007/JHEP09(2011)130 |
| [68] | D.C. Dunbar, J.H. Ettle and W.B. Perkins, Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation, Phys. Rev.D 86 (2012) 026009 [arXiv:1203.0198] [INSPIRE]. |
| [69] | B.S. DeWitt, Quantum Theory of Gravity. 3. Applications of the Covariant Theory, Phys. Rev.162 (1967) 1239 [INSPIRE]. · Zbl 0161.46501 · doi:10.1103/PhysRev.162.1239 |
| [70] | R. Saotome and R. Akhoury, Relationship Between Gravity and Gauge Scattering in the High Energy Limit, JHEP01 (2013) 123 [arXiv:1210.8111] [INSPIRE]. · doi:10.1007/JHEP01(2013)123 |
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