Abstract
We characterise possible identities among the two-loop partial amplitudes of gluon scattering in Yang-Mills theory. We use known amplitudes in an exhaustive search to identify potential new relations. We find two candidate relations which may extend to all-n amplitudes.
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S. Amoroso et al., Les Houches 2019: physics at TeV colliders. Standard Model working group report, in the proceedings of the 11th Les Houches workshop on physics at TeV colliders: PhysTeV Les Houches, (2020) [arXiv:2003.01700] [INSPIRE].
R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [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].
S.G. Naculich, All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes, Phys. Lett. B 707 (2012) 191 [arXiv:1110.1859] [INSPIRE].
A.C. Edison and S.G. Naculich, SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders, Nucl. Phys. B 858 (2012) 488 [arXiv:1111.3821] [INSPIRE].
A.C. Edison and S.G. Naculich, Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes, JHEP 09 (2012) 069 [arXiv:1207.5511] [INSPIRE].
E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two loop QCD corrections to gluon-gluon scattering, Nucl. Phys. B 605 (2001) 467 [hep-ph/0102201] [INSPIRE].
Z. Bern, A. De Freitas and L.J. Dixon, Two loop helicity amplitudes for gluon-gluon scattering in QCD and supersymmetric Yang-Mills theory, JHEP 03 (2002) 018 [hep-ph/0201161] [INSPIRE].
T. Gehrmann, J.M. Henn and N.A. Lo Presti, Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD, Phys. Rev. Lett. 116 (2016) 062001 [Erratum ibid. 116 (2016) 189903] [arXiv:1511.05409] [INSPIRE].
D.C. Dunbar and W.B. Perkins, Two-loop five-point all plus helicity Yang-Mills amplitude, Phys. Rev. D 93 (2016) 085029 [arXiv:1603.07514] [INSPIRE].
Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower, One loop N gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett. 72 (1994) 2134 [hep-ph/9312333] [INSPIRE].
S. Badger, C. Brønnum-Hansen, H.B. Hartanto and T. Peraro, Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case, JHEP 01 (2019) 186 [arXiv:1811.11699] [INSPIRE].
S. Abreu et al., Analytic form of the planar two-loop five-parton scattering amplitudes in QCD, JHEP 05 (2019) 084 [arXiv:1904.00945] [INSPIRE].
S. Badger et al., Analytic form of the full two-loop five-gluon all-plus helicity amplitude, Phys. Rev. Lett. 123 (2019) 071601 [arXiv:1905.03733] [INSPIRE].
D.C. Dunbar, J.H. Godwin, W.B. Perkins and J.M.W. Strong, Color dressed unitarity and recursion for Yang-Mills two-loop all-plus amplitudes, Phys. Rev. D 101 (2020) 016009 [arXiv:1911.06547] [INSPIRE].
A.R. Dalgleish, D.C. Dunbar, W.B. Perkins and J.M.W. Strong, Full color two-loop six-gluon all-plus helicity amplitude, Phys. Rev. D 101 (2020) 076024 [arXiv:2003.00897] [INSPIRE].
D.C. Dunbar, W.B. Perkins and J.M.W. Strong, n-point QCD two-loop amplitude, Phys. Rev. D 101 (2020) 076001 [arXiv:2001.11347] [INSPIRE].
P. Cvitanovic, P.G. Lauwers and P.N. Scharbach, Gauge invariance structure of quantum chromodynamics, Nucl. Phys. B 186 (1981) 165 [INSPIRE].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [INSPIRE].
M.L. Mangano, The color structure of gluon emission, Nucl. Phys. B 309 (1988) 461 [INSPIRE].
D. Kosower, B.-H. Lee and V.P. Nair, Multi gluon scattering: a string based calculation, Phys. Lett. B 201 (1988) 85 [INSPIRE].
D.A. Kosower, Color factorization for fermionic amplitudes, Nucl. Phys. B 315 (1989) 391 [INSPIRE].
V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal basis for gauge theory amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
Z. Bern and D.A. Kosower, Color decomposition of one loop amplitudes in gauge theories, Nucl. Phys. B 362 (1991) 389 [INSPIRE].
B. Feng, Y. Jia and R. Huang, Relations of loop partial amplitudes in gauge theory by unitarity cut method, Nucl. Phys. B 854 (2012) 243 [arXiv:1105.0334] [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].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop selfdual and N = 4 superYang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [INSPIRE].
R. Britto, G.R. Jehu and A. Orta, The dimension-shift conjecture for one-loop amplitudes, JHEP 04 (2021) 276 [arXiv:2011.13821] [INSPIRE].
A.R. Dalgleish, W.B. Perkins and J.M.W. Strong, The seven-point two-loop full-colour all-plus helicity Yang-Mills amplitude, to appear.
D.A. Kosower and S. Pögel, A unitarity approach to two-loop all-plus rational terms, arXiv:2206.14445 [INSPIRE].
S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
Z. Kunszt, A. Signer and Z. Trocsanyi, Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross-sections of multiparton processes, Nucl. Phys. B 420 (1994) 550 [hep-ph/9401294] [INSPIRE].
D.C. Dunbar, G.R. Jehu and W.B. Perkins, Two-loop six gluon all plus helicity amplitude, Phys. Rev. Lett. 117 (2016) 061602 [arXiv:1605.06351] [INSPIRE].
S. Badger, G. Mogull and T. Peraro, Local integrands for two-loop all-plus Yang-Mills amplitudes, JHEP 08 (2016) 063 [arXiv:1606.02244] [INSPIRE].
D.C. Dunbar, J.H. Godwin, G.R. Jehu and W.B. Perkins, Analytic all-plus-helicity gluon amplitudes in QCD, Phys. Rev. D 96 (2017) 116013 [arXiv:1710.10071] [INSPIRE].
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Dunbar, D.C. Identities amongst the two loop partial amplitudes of Yang-Mills theory. J. High Energ. Phys. 2023, 58 (2023). https://doi.org/10.1007/JHEP10(2023)058
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DOI: https://doi.org/10.1007/JHEP10(2023)058