Monodromy-like relations for finite loop amplitudes. (English) Zbl 1296.81124
Summary: We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number of external legs.
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T18 | Feynman diagrams |
References:
| [1] | F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys.B 306 (1988) 759 [SPIRES]. · doi:10.1016/0550-3213(88)90442-7 |
| [2] | R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys.B 715 (2005) 499 [hep-th/0412308] [SPIRES]. · Zbl 1207.81088 · doi:10.1016/j.nuclphysb.2005.02.030 |
| [3] | 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] [SPIRES]. · doi:10.1103/PhysRevLett.94.181602 |
| [4] | J.M. Drummond and J.M. Henn, All tree-level amplitudes in N = 4 SYM, JHEP04 (2009) 018 [arXiv:0808.2475] [SPIRES]. · doi:10.1088/1126-6708/2009/04/018 |
| [5] | R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys.B 725 (2005) 275 [hep-th/0412103] [SPIRES]. · Zbl 1178.81202 · doi:10.1016/j.nuclphysb.2005.07.014 |
| [6] | D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev.D 75 (2007) 125019 [arXiv:0704.1835] [SPIRES]. |
| [7] | C.F. Berger et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev.D 78 (2008) 036003 [arXiv:0803.4180] [SPIRES]. |
| [8] | S. Badger, B. Biedermann and P. Uwer, NGluon: a package to calculate one-loop multi-gluon amplitudes, arXiv:1011.2900 [SPIRES]. · Zbl 1262.81102 |
| [9] | J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP01 (2007) 064 [hep-th/0607160] [SPIRES]. · doi:10.1088/1126-6708/2007/01/064 |
| [10] | J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys.B 828 (2010) 317 [arXiv:0807.1095] [SPIRES]. · Zbl 1203.81112 · doi:10.1016/j.nuclphysb.2009.11.022 |
| [11] | A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix, Phys. Rev.D 78 (2008) 125005 [arXiv:0807.4097] [SPIRES]. |
| [12] | Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev.D 78 (2008) 085011 [arXiv:0805.3993] [SPIRES]. |
| [13] | 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] [SPIRES]. · doi:10.1103/PhysRevLett.105.061602 |
| [14] | Z. Bern and T. Dennen, A color dual form for gauge-theory amplitudes, arXiv:1103.0312 [SPIRES]. |
| [15] | 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] [SPIRES]. |
| [16] | 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] [SPIRES]. · doi:10.1103/PhysRevLett.72.2134 |
| [17] | G. Mahlon, Multi-gluon helicity amplitudes involving a quark loop, Phys. Rev.D 49 (1994) 4438 [hep-ph/9312276] [SPIRES]. |
| [18] | 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] [SPIRES]. · doi:10.1103/PhysRevLett.103.161602 |
| [19] | R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys.B 312 (1989) 616 [SPIRES]. · doi:10.1016/0550-3213(89)90574-9 |
| [20] | 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] [SPIRES]. · doi:10.1016/S0550-3213(99)00809-3 |
| [21] | S. Stieberger and T.R. Taylor, Multi-gluon scattering in open superstring theory, Phys. Rev.D 74 (2006) 126007 [hep-th/0609175] [SPIRES]. |
| [22] | R.M. Schabinger, One-loop N = 4 super Yang-Mills scattering amplitudes to all orders in the dimensional regularization parameter, arXiv:1103.2769 [SPIRES]. · Zbl 1270.81141 |
| [23] | S. Stieberger, Open & closed vs. pure open string disk amplitudes, arXiv:0907.2211 [SPIRES]. · Zbl 1284.81245 |
| [24] | C. Cheung, D. O’Connell and B. Wecht, BCFW recursion relations and string theory, JHEP09 (2010) 052 [arXiv:1002.4674] [SPIRES]. · Zbl 1291.81301 · doi:10.1007/JHEP09(2010)052 |
| [25] | R.H. Boels, D. Marmiroli and N.A. Obers, On-shell recursion in string theory, JHEP10 (2010) 034 [arXiv:1002.5029] [SPIRES]. · Zbl 1291.81297 · doi:10.1007/JHEP10(2010)034 |
| [26] | C.R. Mafra, O. Schlotterer, S. Stieberger and D. Tsimpis, A recursive formula for N-point SYM tree amplitudes, arXiv:1012.3981 [SPIRES]. |
| [27] | C.R. Mafra, Simplifying the tree-level superstring massless five-point amplitude, JHEP01 (2010) 007 [arXiv:0909.5206] [SPIRES]. · Zbl 1269.81165 · doi:10.1007/JHEP01(2010)007 |
| [28] | S.H. Henry Tye and Y. Zhang, Dual identities inside the gluon and the graviton scattering amplitudes, JHEP06 (2010) 071 [arXiv:1003.1732] [SPIRES]. · Zbl 1288.81150 · doi:10.1007/JHEP06(2010)071 |
| [29] | N.E.J. 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] [SPIRES]. · Zbl 1290.83015 · doi:10.1007/JHEP06(2010)003 |
| [30] | B. Feng, R. Huang and Y. Jia, Gauge amplitude identities by on-shell recursion relation in S-matrix program, Phys. Lett.B 695 (2011) 350 [arXiv:1004.3417] [SPIRES]. |
| [31] | Y.-X. Chen, Y.-J. Du and B. Feng, A proof of the explicit minimal-basis expansion of tree amplitudes in gauge field theory, JHEP02 (2011) 112 [arXiv:1101.0009] [SPIRES]. · Zbl 1294.81273 · doi:10.1007/JHEP02(2011)112 |
| [32] | T. Sondergaard, New relations for gauge-theory amplitudes with matter, Nucl. Phys.B 821 (2009) 417 [arXiv:0903.5453] [SPIRES]. · Zbl 1196.81243 · doi:10.1016/j.nuclphysb.2009.07.002 |
| [33] | Y. Jia, R. Huang and C.-Y. Liu, U(1)-decoupling, KK and BCJ relations in \(\mathcal{N} = 4\) SYM, Phys. Rev.D 82 (2010) 065001 [arXiv:1005.1821] [SPIRES]. |
| [34] | 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] [SPIRES]. · doi:10.1016/S0550-3213(99)00809-3 |
| [35] | Z. Bern and D.A. Kosower, Color decomposition of one loop amplitudes in gauge theories, Nucl. Phys.B 362 (1991) 389 [SPIRES]. · doi:10.1016/0550-3213(91)90567-H |
| [36] | L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [SPIRES]. |
| [37] | Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop self-dual and N = 4 super Yang-Mills, Phys. Lett.B 394 (1997) 105 [hep-th/9611127] [SPIRES]. |
| [38] | 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] [SPIRES]. · Zbl 1049.81644 · doi:10.1016/0550-3213(94)90179-1 |
| [39] | M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S matrix, Phys. Rev.D 15 (1977) 996 [SPIRES]. |
| [40] | Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys.B 379 (1992) 451 [SPIRES]. · doi:10.1016/0550-3213(92)90134-W |
| [41] | Z. Bern, L.J. Dixon and D.A. Kosower, New QCD results from string theory, hep-th/9311026 [SPIRES]. · Zbl 0844.58111 |
| [42] | Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes, Phys. Rev. Lett.70 (1993) 2677 [hep-ph/9302280] [SPIRES]. · doi:10.1103/PhysRevLett.70.2677 |
| [43] | Z. Bern, L.J. Dixon and D.A. Kosower, The last of the finite loop amplitudes in QCD, Phys. Rev.D 72 (2005) 125003 [hep-ph/0505055] [SPIRES]. |
| [44] | Z. Bern, L.J. Dixon and D.A. Kosower, On-shell recurrence relations for one-loop QCD amplitudes, Phys. Rev.D 71 (2005) 105013 [hep-th/0501240] [SPIRES]. |
| [45] | C.F. Berger, Z. Bern, L.J. Dixon, D. Forde and D.A. Kosower, Bootstrapping one-loop QCD amplitudes with general helicities, Phys. Rev.D 74 (2006) 036009 [hep-ph/0604195] [SPIRES]. |
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