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2011

Simplifying 5-point tensor reduction

Fleischer, J., Riemann, T.

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The 5-point tensors have the property that after insertion of the metric tensor $g^{\mu \nu}$ in terms of external momenta, all $g^{\mu \nu}$-contributions in the tensor decomposition cancel.

If furthermore the tensors are contracted with external momenta, the inverse 5-point Gram determinant $()_5$ cancels automatically.
If the remaining 4-point sub-Gram determinant ${s\choose s}_5$ is not small then this approach appears to be particularly efficient in numerical calculations.
We also indicate how to deal with small ${s\choose s}_5$.

Simplifying 5-point tensor reduction · Around

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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.
doi:10.1016/0370-2693(91)91715-8
A. I. Davydychev, A simple formula for reducing Feynman diagrams to scalar integrals, Phys. Lett. B263 (1991) 107–111 · 1991
Earlier work this paper cites.

Similar

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
Cited alongside, same era.
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
Cited alongside, same era.

Then

arXiv:1009.4436
Original
J. Fleischer, T. Riemann, Complete algebraic reduction of one-loop tensor Feynman integrals, Phys. Rev. D83 (2011) 073004 · 2011
Closest in time.
arXiv:1104.4067
Original
J. Fleischer, T. Riemann, Calculating contracted tensor Feynman integrals, Phys.Lett. B701 (2011) 646–653 · 2011
Closest in time.

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