Brief ReviewNo Access

ALGEBRAIC-NUMERICAL METHODS FOR EVALUATING MULTI-LEG AND MULTI-LOOP FEYNMAN DIAGRAMS

SANDRO UCCIRATI

Dipartimento di Fisica Teorica, Università di Torino, Italy

INFN, Sezione di Torino, Italy

https://doi.org/10.1142/S0217732303012490Cited by:4 (Source: Crossref)

Abstract

We present some methods which aim to express multi-leg and multi-loop Feynman diagrams in a form suited for a fast and reliable numerical evaluation, without any restriction on masses and phase-space region of the process.

Keywords:

References

G. 't Hooft and M. Veltman, Nucl. Phys. B 153, 365 (1979), DOI: 10.1016/0550-3213(79)90605-9. Crossref, Web of Science, Google Scholar
W. L. van Neerven and J. A. Vermaseren, Phys. Lett. B137, 241 (1984); Z. Bern, L. J. Dixon and D. A. Kosower, Nucl. Phys. B412, 751 (1994); A. I. Davydychev, J. Math. Phys. 33, 358 (1992) . Google Scholar
A. Vicini, talk given at Loopfest, Brookhaven National Laboratory, Upton, NY, May 9-10, 2002 (http://www.pas.rochester.edu/dow/loopfest/parallel.html) . Google Scholar
G. Passarino and M. Veltman, Nucl. Phys. B 160, 151 (1979), DOI: 10.1016/0550-3213(79)90234-7. Crossref, Web of Science, ADS, Google Scholar
F. V. Tkachov, Nucl. Instrum. Methods A389, 309 (1997); L. N. Bertstein, Funct. Anal. Appl. 6, 66 (1972) . Google Scholar
J. Fleischer, F. Jegerlehner and O. V. Tarasov, Nucl. Phys. B 566, 423 (2000), DOI: 10.1016/S0550-3213(99)00678-1. Crossref, Web of Science, ADS, Google Scholar
O. V. Tarasov, Acta Phys. Pol. B 29, 2655 (1998). Web of Science, ADS, Google Scholar
Z. Bern, L. Dixon and D. A. Kosower, Nucl. Phys. B 412, 751 (1994), DOI: 10.1016/0550-3213(94)90398-0. Crossref, Web of Science, ADS, Google Scholar
O. V. Tarasov, Phys. Rev. D 54, 6479 (1996), DOI: 10.1103/PhysRevD.54.6479. Crossref, Web of Science, ADS, Google Scholar
G. Devaraj and R. G. Stuart, Nucl. Phys. B 519, 483 (1998), DOI: 10.1016/S0550-3213(98)00035-2. Crossref, Web of Science, ADS, Google Scholar
R. J. Eden et al. , The Analytic S Matrix ( Cambridge Univ. Press , 1966 ) . Google Scholar
L. D. Landau, Nucl. Phys. 13, 181 (1959). Crossref, Web of Science, Google Scholar
R. Erdelyi et al., Higher Transcendental Functions, Vol. 2, Bateman Manuscript Project (McGraw-Hill, 1953); L. J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, 1966) . Google Scholar
T. Binoth and G. Heinrich, Nucl. Phys. B 585, 741 (2000), DOI: 10.1016/S0550-3213(00)00429-6. Crossref, Web of Science, ADS, Google Scholar
G. Passarino, Nucl. Phys. B 619, 257 (2001), DOI: 10.1016/S0550-3213(01)00528-4. Crossref, Web of Science, ADS, Google Scholar
G. Passarino and S. Uccirati, Nucl. Phys. B 629, 97 (2002), DOI: 10.1016/S0550-3213(02)00138-4. Crossref, Web of Science, ADS, Google Scholar
A. Ferrogliaet al., Nucl. Phys. B 650, 162 (2003), DOI: 10.1016/S0550-3213(02)01070-2. Crossref, Web of Science, ADS, Google Scholar
A. Ferroglia, G. Passarino, M. Passera and S. Uccirati, "Two-loop vertices in quantum field theory: Non-infrared divergent scalar configurations", work in preparation . Google Scholar
A. Ferroglia, G. Passarino, M. Passera and S. Uccirati, "Two-loop vertices in quantum field theory: Infrared divergent configurations", work in preparation . Google Scholar