Loops and trees

Journal of High Energy Physics

Volumn 2011, Issue 5, 2011, Pages

  Caron Huot, S ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

NLO computations; QCD; Supersymmetric gauge theory

Indexed keywords

EID: 80053116221     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP05(2011)080     Document Type: Article

References (41)

1. R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix, Cambridge University Press, Cambridge U.K. (1966).
2. 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].
3. 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] [SPIRES].
4. 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].
5. C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes, JHEP 03 (2007) 111 [hep-ph/0612277] [SPIRES].
6. D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [SPIRES].
7. Z. Bern, L.J. Dixon and D.A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [SPIRES].
8. C.F. Berger and D. Forde, Multi-Parton Scattering Amplitudes via On-Shell Methods, arXiv:0912.3534 [SPIRES].
9. S.D. Badger, Direct Extraction Of One Loop Rational Terms, JHEP 01 (2009) 049 [arXiv:0806.4600] [SPIRES].
10. R.P. Feynman, Quantum theory of gravitation, Acta Phys. Polon. 24 (1963) 697 [SPIRES].
11. K.-c. Chou, Z.-b. Su, B.-l. Hao and L. Yu, Equilibrium and Nonequilibrium Formalisms Made Unified, Phys. Rept. 118 (1985) 1 [SPIRES].
12. S. Catani, T. Gleisberg, F. Krauss, G. Rodrigo and J.-C. Winter, From loops to trees by-passing Feynman's theorem, JHEP 09 (2008) 065 [arXiv:0804.3170] [SPIRES].
13. A. Brandhuber, B. Spence and G. Travaglini, From trees to loops and back, JHEP 01 (2006) 142 [hep-th/0510253] [SPIRES].
14. D. Vaman and Y.-P. Yao, QCD recursion relations from the largest time equation, JHEP 04 (2006) 030 [hep-th/0512031] [SPIRES].
15. D. Vaman and Y.-P. Yao, The Space-Cone Gauge, Lorentz Invariance and On-Shell Recursion for One-Loop Yang-Mills amplitudes, arXiv:0805.2645 [SPIRES].
16. B. Holdom, Approaching quantum behavior with classical fields, J. Phys. A 39 (2006) 7485 [hep-th/0602236] [SPIRES].
17. G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [SPIRES].
18. F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals, JHEP 07 (2004) 017 [hep-ph/0404120] [SPIRES].
19. M.A. van Eijck, R. Kobes and C.G. van Weert, Transformations of real time finite temperature Feynman rules, Phys. Rev. D 50 (1994) 4097 [hep-ph/9406214] [SPIRES].
20. A.H. Mueller and D.T. Son, On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers, Phys. Lett. B 582 (2004) 279 [hep-ph/0212198] [SPIRES].
21. T.S. Evans, N point finite temperature expectation values at real times, Nucl. Phys. B 374 (1992) 340 [SPIRES].
22. P.C. Martin, E.D. Siggia and H.A. Rose, Statistical Dynamics of Classical Systems, Phys. Rev. A 8 (1973) 423 [SPIRES].
23. A.O.G. Kallen and A. Sabry, Fourth order vacuum polarization, Kong. Dan. Vid. Sel. Mat. Fys. Med. 29 (1955) 1 [SPIRES].
24. F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett. B 100 (1981) 65 [SPIRES].
25. 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 [SPIRES].
26. E.W. Nigel Glover and C. Williams, One-Loop Gluonic Amplitudes from Single Unitarity Cuts, JHEP 12 (2008) 067 [arXiv:0810.2964] [SPIRES].
27. P. Elmfors, T.H. Hansson and I. Zahed, A simple derivation of the hard thermal loop effective action, Phys. Rev. D 59 (1999) 045018 [hep-th/9809013] [SPIRES].
28. S. Caron-Huot, On supersymmetry at finite temperature, Phys. Rev. D 79 (2009) 125002 [arXiv:0808.0155] [SPIRES].
29. 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].
30. 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].
31. 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 [SPIRES].
32. F. Gelis and R. Venugopalan, Particle production in field theories coupled to strong external sources, Nucl. Phys. A 776 (2006) 135 [hep-ph/0601209] [SPIRES].
33. F. Gelis and R. Venugopalan, Particle production in field theories coupled to strong external sources. II: Generating functions, Nucl. Phys. A 779 (2006) 177 [hep-ph/0605246] [SPIRES].
34. Z. Bern, J.J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The Ultraviolet Behavior of N = 8 Supergravity at Four Loops, Phys. Rev. Lett. 103 (2009) 081301 [arXiv:0905.2326] [SPIRES].
35. R. Dashen, S.-K. Ma and H.J. Bernstein, S Matrix formulation of statistical mechanics, Phys. Rev. 187 (1969) 345 [SPIRES].
36. S. Jeon and P.J. Ellis, Multiple scattering expansion of the self-energy at finite temperature, Phys. Rev. D 58 (1998) 045013 [hep-ph/9802246] [SPIRES].
37. J.-P. Blaizot and U. Reinosa, Isolating vacuum amplitudes in quantum field calculations at finite temperature, Nucl. Phys. A 764 (2006) 393 [hep-ph/0406109] [SPIRES].
38. I. Bierenbaum, Towards a Loop-Tree Duality at Two Loops and Beyond, Nucl. Phys. Proc. Suppl. 205-206 (2010) 164 [arXiv:1007.0213] [SPIRES].
39. I. Bierenbaum, S. Catani, P. Draggiotis and G. Rodrigo, A Tree-Loop Duality Relation at Two Loops and Beyond, JHEP 10 (2010) 073 [arXiv:1007.0194] [SPIRES].
40. Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [SPIRES].
41. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].