×

zbMATH — the first resource for mathematics

Reducing full one-loop amplitudes to scalar integrals at the integrand level. (English) Zbl 1116.81067
Summary: We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation.

MSC:
81U05 \(2\)-body potential quantum scattering theory
Software:
HELAC; CutTools
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Berends, F.A.; Giele, W.T.; Berends, F.A.; Giele, W.T.; Kuijf, H.; Berends, F.A.; Kuijf, H.; Tausk, B.; Giele, W.T.; Caravaglios, F.; Moretti, M.; Draggiotis, P.; Kleiss, R.H.; Papadopoulos, C.G.; Kanaki, A.; Papadopoulos, C.G.; Draggiotis, P.D.; Kleiss, R.H.; Papadopoulos, C.G.; Mangano, M.L.; Moretti, M.; Piccinini, F.; Pittau, R.; Polosa, A.D.; Papadopoulos, C.G.; Worek, M.; Duhr, C.; Hoche, S.; Maltoni, F., Nucl. phys. B, Phys. lett. B, Nucl. phys. B, Phys. lett. B, Phys. lett. B, Comput. phys. commun., Eur. phys. J. C, Jhep, 0307, 001, (2003)
[2] ’t Hooft, G.; Veltman, M.J.G., Nucl. phys. B, 153, 365, (1979)
[3] Passarino, G.; Veltman, M.J.G., Nucl. phys. B, 160, 151, (1979)
[4] Denner, A.; Dittmaier, S.; Roth, M.; Wieders, L.H.; Denner, A.; Dittmaier, S.; Roth, M.; Wieders, L.H.; Belanger, G.; Boudjema, F.; Fujimoto, J.; Ishikawa, T.; Kaneko, T.; Kato, K.; Shimizu, Y.; Montagna, G.; Piccinini, F.; Nicrosini, O.; Passarino, G.; Pittau, R., Phys. lett. B, Nucl. phys. B, Phys. rep., Nucl. phys. B, 401, 3, (1993)
[5] Denner, A.; Dittmaier, S., Nucl. phys. B, 734, 62, (2006)
[6] Ferroglia, A.; Passera, M.; Passarino, G.; Uccirati, S.; Giele, W.T.; Glover, E.W.N.; Binoth, T.; Guillet, J.P.; Heinrich, G.; Duplancic, G.; Nizic, B.; Binoth, T.; Heinrich, G.; Kauer, N.; Soper, D.E.; Soper, D.E.; Nagy, Z.; Soper, D.E.; van Hameren, A.; Vollinga, J.; Weinzierl, S., Nucl. phys. B, Nucl. phys. B, Nucl. phys. B, Phys. rev. D, Phys. rev. D, Jhep, Eur. phys. J. C, 41, 361, (2005)
[7] del Aguila, F.; Pittau, R.; Pittau, R., Jhep, 0407, 017, (2004)
[8] Bern, Z.; Dixon, L.J.; Dunbar, D.C.; Kosower, D.A., Nucl. phys. B, 435, 59, (1995)
[9] Britto, R.; Cachazo, F.; Feng, B., Nucl. phys. B, 725, 275, (2005)
[10] Berger, C.F.; Bern, Z.; Dixon, L.J.; Forde, D.; Kosower, D.A.; Berger, C.F.; Bern, Z.; Dixon, L.J.; Forde, D.; Kosower, D.A.; Bern, Z.; Dixon, L.J.; Kosower, D.A., Phys. rev. D, 73, 065013, (2006)
[11] Källén, G.; Toll, J., J. math. phys., 6, 299, (1965)
[12] van Neerven, W.L.; Vermaseren, J.A.M., Phys. lett. B, 137, 241, (1984)
[13] Xiao, Z.G.; Yang, G.; Zhu, C.J.; Su, X.; Xiao, Z.G.; Yang, G.; Zhu, C.J.
[14] Melrose, D.B., Nuovo cimento, 40, 181, (1965)
[15] Denner, A., Fortschr. phys., 41, 307, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.