Determine Arbitrary Feynman Integrals by Vacuum Integrals

H. Frellesvig, F. Gasparotto, S. Laporta, M. Mandal, P. Mastrolia, L. Mattiazzi, and S. Mizera, Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers

Original

1901

Earlier work this paper cites.

N. I. Usyukina, On a Representation for Three Point Function

1975

Earlier work this paper cites.

G. Passarino and M. J. G. Veltman, One Loop Corrections for e + ​ e − e^{+}e^{-} Annihilation Into μ + ​ μ − \mu^{+}\mu^{-} in the Weinberg Model

1979

Earlier work this paper cites.

G. ’t Hooft and M. J. G. Veltman, Scalar One Loop Integrals

1979

Earlier work this paper cites.

K. G. Chetyrkin and F. V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops

1981

Earlier work this paper cites.

G. J. van Oldenborgh and J. A. M. Vermaseren, New Algorithms for One Loop Integrals

1990

Earlier work this paper cites.

A. V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation

1991

Earlier work this paper cites.

A. I. Davydychev, A Simple formula for reducing Feynman diagrams to scalar integrals

1991

Earlier work this paper cites.

Z. Bern, L. J. Dixon, and D. A. Kosower, Dimensionally regulated one loop integrals

1993

Earlier work this paper cites.

A. I. Davydychev and J. B. Tausk, Two loop selfenergy diagrams with different masses and the momentum expansion

1993

Earlier work this paper cites.

V. A. Smirnov, Asymptotic expansions in momenta and masses and calculation of Feynman diagrams

1995

Earlier work this paper cites.

O. V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension

1996

Earlier work this paper cites.

E. Remiddi, Differential equations for Feynman graph amplitudes

1997

Earlier work this paper cites.

O. V. Tarasov, Generalized recurrence relations for two loop propagator integrals with arbitrary masses

1997

Earlier work this paper cites.

V. A. Smirnov, Analytical result for dimensionally regularized massless on shell double box

1999

Earlier work this paper cites.

J. B. Tausk, Nonplanar massless two loop Feynman diagrams with four on-shell legs

1999

Earlier work this paper cites.

D. J. Broadhurst, Massive three - loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity

1999

Earlier work this paper cites.

T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals

2000

Earlier work this paper cites.

T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions

2000

Earlier work this paper cites.

S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations

2000

Earlier work this paper cites.

V. A. Smirnov, Applied asymptotic expansions in momenta and masses

2002

Earlier work this paper cites.

G. Heinrich and V. A. Smirnov, Analytical evaluation of dimensionally regularized massive on-shell double boxes

2004

Earlier work this paper cites.

G. Duplancic and B. Nizic, Reduction method for dimensionally regulated one loop N point Feynman integrals

2004

Earlier work this paper cites.

R. Britto, F. Cachazo, and B. Feng, Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills

2005

Earlier work this paper cites.

M. Czakon, J. Gluza, and T. Riemann, Master integrals for massive two-loop bhabha scattering in QED

2005

Earlier work this paper cites.

Y. Schröder and A. Vuorinen, High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles

2005

Earlier work this paper cites.

A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals

2006

Earlier work this paper cites.

M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals

2006

Cited alongside, same era.

C. Anastasiou and A. Daleo, Numerical evaluation of loop integrals

2006

Cited alongside, same era.

G. Ossola, C. G. Papadopoulos, and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level

2007

Cited alongside, same era.

J. Gluza, K. Kajda, and T. Riemann, AMBRE: A Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

Original

2007

Cited alongside, same era.

W. T. Giele, Z. Kunszt, and K. Melnikov, Full one-loop amplitudes from tree amplitudes

Original

2008

Cited alongside, same era.

I. Dubovyk, A. Freitas, J. Gluza, T. Riemann, and J. Usovitsch, The two-loop electroweak bosonic corrections to sin 2 ⁡ θ e ​ f ​ f b \sin^{2}\theta^{b}_{eff}

Original

2016

Later among the works it cites.

K. J. Larsen and Y. Zhang, Integration-by-parts reductions from unitarity cuts and algebraic geometry

Original

2016

Later among the works it cites.

H. Ita, Two-loop Integrand Decomposition into Master Integrals and Surface Terms

Original

2016

Later among the works it cites.

S. Badger, G. Mogull, and T. Peraro, Local integrands for two-loop all-plus Yang-Mills amplitudes

Original

2016

Later among the works it cites.

P. Mastrolia, T. Peraro, and A. Primo, Adaptive Integrand Decomposition in parallel and orthogonal space