Abstract.
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D = 6, a triangle integral in D = 4, and a general two-point integral in D space-time dimensions. All the divergences present in the original integral are contained in the general two-point integral and associated coefficients. The problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner. Being derived with no restrictions regarding the external momenta, the method is completely general and applicable for arbitrary kinematics. In particular, it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta, which are unavoidable when calculating one-loop contributions to the hard-scattering amplitude for exclusive hadronic processes at large-momentum transfer in PQCD. The iterative structure makes it easy to implement the formalism in an algebraic computer program.
Similar content being viewed by others
References
G. Passarino, M. Veltman, Nucl. Phys. B 160, 151 (1979); G.J. van Oldenborgh, J.A.M. Vermaseren, Z. Phys. C 46, 425 (1990); W.L. van Neerven, J.A.M. Vermaseren, Phys. Lett. B 137, 241 (1984)
A.I. Davydychev, Phys. Lett. B 263, 107 (1991)
Z. Bern, L.J. Dixon, D.A. Kosower, Phys. Lett. B 302, 299 (1993) [Erratum B 318, 649 (1993)] [hep-ph/9212308]
Z. Bern, L.J. Dixon, D.A. Kosower, Nucl. Phys. B 412, 751 (1994) [hep-ph/9306240]
O.V. Tarasov, Phys. Rev. D 54, 6479 (1996) [hep-th/9606018]
J. Fleischer, F. Jegerlehner, O.V. Tarasov, Nucl. Phys. B 566, 423 (2000) [hep-ph/9907327]
T. Binoth, J.P. Guillet, G. Heinrich, Nucl. Phys. B 572, 361 (2000) [hep-ph/9911342]; G. Heinrich, T. Binoth, Nucl. Phys. Proc. Suppl. 89, 246 (2000) [hep-ph/0005324]
T. Binoth, J.P. Guillet, G. Heinrich, C. Schubert, Nucl. Phys. B 615, 385 (2001) [hep-ph/0106243]
J.M. Campbell, E.W. Glover, D.J. Miller, Nucl. Phys. B 498, 397 (1997) [hep-ph/9612413]
A. Denner, S. Dittmaier, Nucl. Phys. B 658, 175 (2003) [hep-ph/0212259]
G. Duplanči\’ c, B. Niži\’ c, Eur. Phys. J. C 20, 357 (2001) [hep-ph/0006249]
G. Duplanči\’ c, B. Niži\’ c, Eur. Phys. J. C 24, 385 (2002) [hep-ph/0201306]
A.I. Davydychev, J. Phys. A 25, 5587 (1992)
K.G. Chetyrkin, F.V. Tkachov, Nucl. Phys. B 192, 159 (1981); F.V. Tkachov, Phys. Lett. B 100, 65 (1981)
F. Jegerlehner, O. Tarasov, Nucl. Phys. Proc. Suppl. 116, 83 (2003) [hep-ph/0212004]
A.T. Suzuki, E.S. Santos, A.G. Schmidt, Eur. Phys. J. C 26, 125 (2002) [hep-th/0205158]
C. Anastasiou, E.W. Glover, C. Oleari, Nucl. Phys. B 565, 445 (2000) [hep-ph/9907523]; A.T. Suzuki, E.S. Santos, A.G. Schmidt, hep-ph/0210083
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 18 August 2003, Revised: 6 February 2004, Published online: 23 April 2004
Rights and permissions
About this article
Cite this article
Duplančić, G., Nižić, B. Reduction method for dimensionally regulatedone-loop N-point Feynman integrals. Eur. Phys. J. C 35, 105–118 (2004). https://doi.org/10.1140/epjc/s2004-01723-7
Issue Date:
DOI: https://doi.org/10.1140/epjc/s2004-01723-7