The dimensional recurrence and analyticity method for multicomponent master integrals: Using unitarity cuts to construct homogeneous solutions

Journal of High Energy Physics

Volumn 2012, Issue 12, 2012, Pages

  Lee, R N ^a,b,c   Smirnov, V A ^d  

^a BUDKER INSTITUTE OF NUCLEAR PHYSICS   (Russian Federation)

^b NOVOSIBIRSK STATE UNIVERSITY   (Russian Federation)

^c KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^d MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

NLO Computations; QCD Phenomenology

Indexed keywords

EID: 84875881509     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP12(2012)104     Document Type: Article

References (33)

1. O. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev. D 54 (1996) 6479 [ hep-th/9606018 ].
2. R.N. Lee, Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D, Nucl. Phys. B 830 (2010) 474 [ arXiv:0911.0252 ].
3. R.N. Lee, A.V. Smirnov and V.A. Smirnov, Analytic results for massless three-loop form factors, JHEP 04 (2010) 020 [ arXiv:1001.2887 ].
4. R.N. Lee, Calculating multiloop integrals using dimensional recurrence relation and D-analyticity, Nucl. Phys. Proc. Suppl. 205-206 (2010) 135 [ arXiv:1007.2256 ].
5. R.N. Lee, A.V. Smirnov and V.A. Smirnov, Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in Ïμ, Nucl. Phys. Proc. Suppl. 205-206 (2010) 308 [ arXiv:1005.0362 ].
6. R.N. Lee and I.S. Terekhov, Application of the DRA method to the calculation of the four-loop QED-type tadpoles, JHEP 01 (2011) 068 [ arXiv:1010.6117 ].
7. R.N. Lee and V.A. Smirnov, Analytic Ïμ-expansions of master integrals corresponding to massless three-loop form factors and three-loop g - 2 up to four-loop transcendentality weight, JHEP 02 (2011) 102 [ arXiv:1010.1334 ].
8. R.N. Lee, A.V. Smirnov and V.A. Smirnov, On Ïμ-expansions of four-loop non-planar massless propagator diagrams, Eur. Phys. J. C 71 (2011) 1708 [ arXiv:1103.3409 ].
9. R.N. Lee, A.V. Smirnov and V.A. Smirnov, Master integrals for four-loop massless propagators up to transcendentality weight twelve, Nucl. Phys. B 856 (2012) 95 [ arXiv:1108.0732 ].
10. A. Smirnov, Algorithm FIRE - Feynman Integral REduction, JHEP 10 (2008) 107 [ arXiv:0807.3243 ].
11. A.V. Smirnov, V.A. Smirnov and M. Tentyukov, FIESTA 2: parallelizeable multiloop numerical calculations, Comput. Phys. Commun. 182 (2011) 790 [ arXiv:0912.0158 ].
12. V.A. Smirnov, Analytical result for dimensionally regularized massless on shell double box, Phys. Lett. B 460 (1999) 397 [ hep-ph/9905323 ].
13. J.B. Tausk, Nonplanar massless two loop Feynman diagrams with four on-shell legs, Phys. Lett. B 469 (1999) 225 [ hep-ph/9909506 ].
14. M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [ hep-ph/0511200 ]. (Pubitemid 44415767)
15. V.A. Smirnov, Feynman integral calculus, Springer, Berlin Germany (2006).
16. V.A. Smirnov, Evaluating feynman integrals, Springer Tracts in Modern Physics volume 211, Springer, U.S.A. (2004).
17. A. Smirnov and V. Smirnov, On the resolution of singularities of multiple Mellin-Barnes integrals, Eur. Phys. J. C 62 (2009) 445 [ arXiv:0901.0386 ].
18. H.R.P. Ferguson and D.H. Bailey, A polynomial time, numerically stable integer relation algorithm, technocal report (1991).
19. P. Baikov and K. Chetyrkin, Four loop massless propagators: an algebraic evaluation of all master integrals, Nucl. Phys. B 837 (2010) 186 [ arXiv:1004.1153 ].
20. M. Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symb. Comput. 14 (1992) 243.
21. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Full result for the three-loop static quark potential, PoS(RADCOR2009)075 [ arXiv:1001.2668 ].
22. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Fermionic contributions to the three-loop static potential, Phys. Lett. B 668 (2008) 293 [ arXiv:0809.1927 ].
23. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Three-loop static potential, Phys. Rev. Lett. 104 (2010) 112002 [ arXiv:0911.4742 ].
24. C. Anzai, Y. Kiyo and Y. Sumino, Static QCD potential at three-loop order, Phys. Rev. Lett. 104 (2010) 112003 [ arXiv:0911.4335 ].
25. R.N. Lee, DRA method: powerful tool for the calculation of the loop integrals, J. Phys. Conf. Ser. 368 (2012) 012050.
26. 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 ].
27. 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 ].
28. P.A. Baikov, Explicit solutions of the multiloop integral recurrence relations and its application, Nucl. Instrum. Meth. A 389 (1997) 347 [ hep-ph/9611449 ].
29. P.A. Baikov, Explicit solutions of the three loop vacuum integral recurrence relations, Phys. Lett. B 385 (1996) 404 [ hep-ph/9603267 ].
30. D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990) 207.
31. D. Zeilberger, The method of creative telescoping, J. Symb. Comput. 11 (1991) 195.
32. R.N. Lee, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Analytic result for the three-loop static quark potential, to appear.
33. L.J. Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge U.K. (1966).