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Calculating contracted tensor Feynman integrals · Around

2011

Calculating contracted tensor Feynman integrals

Fleischer, J., Riemann, T.

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A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically.

In this letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta.
This is based on sums over signed minors weighted with scalar products of the external momenta.
With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.

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doi:10.1007/BF028329
D. B. Melrose, Reduction of Feynman diagrams, Nuovo Cim. 40 (1965) 181–213 · 1965
Earlier work this paper cites.
arXiv:hep-ph/9907327
J. Fleischer, F. Jegerlehner, O. Tarasov, Algebraic reduction of one-loop Feynman graph amplitudes, Nucl. Phys. B566 (2000) 423–440 · 2000
Earlier work this paper cites.
arXiv:hep-ph/0404120
F. del Aguila, R. Pittau, Recursive numerical calculus of one-loop tensor integrals, JHEP 0407 (2004) 017, erratum added online, feb/4/2005 · 2004
Earlier work this paper cites.

Similar

arXiv:hep-ph/0609007
G. Ossola, C. Papadopoulos, R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B763 (2007) 147–169 · 2006
Cited alongside, same era.
arXiv:0812.2134
Original
T. Diakonidis, J. Fleischer, J. Gluza, K. Kajda, T. Riemann, J. Tausk, A complete reduction of one-loop tensor 5- and 6-point integrals, Phys. Rev. D80 (2009) 036003 · 2009
Cited alongside, same era.

Then

arXiv:0907.2115
Original
T. Diakonidis, J. Fleischer, T. Riemann, J. B. Tausk, A recursive reduction of tensor Feynman integrals, Phys. Lett. B683 (2010) 69–74 · 2009
Later among the works it cites.
arXiv:1009.4436
Original
J. Fleischer, T. Riemann, Complete algebraic reduction of one-loop tensor Feynman integrals, Phys. Rev. D83 (2011) 073004 · 2011
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