Feynman integral tables

This page collects values of dimensionally-regularized Feynman integrals in $d = 4 - 2 ε$ space-time dimensions, all in machine-readable (Mathematica) format.

[this page is under construction]

Integral definition

We define Feynman integrals as

I = \int (i = 1 \prod L \frac{d ^{d} l _{i}}{( 2 π ) ^{d}}) (i = 1 \prod N D_{i}^{- ν_{i}}),

where $l_{i}$ are the loop momenta, $D_{i}$ are the denominators, and $ν_{i}$ are denominator powers (indices).

Cut (phase-space) Feynman integrals are similar: TODO.

Four-loop propagator (2-point) master integrals

From [1]. TODO.

Cuts of four-loop propagators

From [2,3]. TODO.

Semi-inclusive cuts of four-loop propagators

TODO.

One-loop 1→3 integrals

TODO.

Two-loop 1→3 integrals

TODO.

References

P. A. Baikov and K. G. Chetyrkin. “Four Loop Massless Propagators: An Algebraic Evaluation of All Master Integrals”. In: Nucl. Phys. B837 (2010), pp. 186–220. DOI: 10.1016/j.nuclphysb.2010.05.004. arXiv: 1004.1153.
O. Gituliar, V. Magerya, and A. Pikelner. “Five-Particle Phase-Space Integrals in QCD”. In: JHEP 06 (2018), p. 099. DOI: 10.1007/JHEP06(2018)099. arXiv: 1803.09084.
V. Magerya and A. Pikelner. “Cutting massless four-loop propagators”. In: JHEP 12 (2019), p. 026. DOI: 10.1007/JHEP12(2019)026. arXiv: 1910.07522.