Built on

HL-LHC, HE-LHC Working Group
Original
1902
Earlier work this paper cites.
S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD , JHEP 05
Original
1904
Earlier work this paper cites.
H. B. Hartanto, S. Badger, C. Brønnum-Hansen and T. Peraro, A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons , JHEP 09
Original
1906
Earlier work this paper cites.
M. Delto, M. Jaquier, K. Melnikov and R. Röntsch, Mixed QCD ⊗ \otimes QED corrections to on-shell Z Z boson production at the LHC , 1909.08428
Original
1909
Earlier work this paper cites.
K. Chetyrkin and F. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl.Phys. B192
1981
Earlier work this paper cites.
F. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions , Phys.Lett. B100
1981
Earlier work this paper cites.
A. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys.Lett. B254
1991
Earlier work this paper cites.
A. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams , Phys.Lett. B267
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, Dimensionally regulated one loop integrals , Phys.Lett. B302
1993
Earlier work this paper cites.
E. Remiddi, Differential equations for Feynman graph amplitudes , Nuovo Cim. A110
1997
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int. J. Mod. Phys. A15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions , Nucl.Phys. B580
2000
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, Harmonic polylogarithms , Int.J.Mod.Phys. A15
2000
Earlier work this paper cites.
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms , Comput.Phys.Commun. 167
2005
Earlier work this paper cites.

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T. Gehrmann, J. M. Henn and N. A. Lo Presti, Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD , Phys. Rev. Lett. 116
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Later among the works it cites.
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Later among the works it cites.
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Later among the works it cites.
1710.04998

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2019

Internal Reduction method for computing Feynman Integrals

Papadopoulos, Costas G., Wever, Christopher

Understand

A new approach to compute Feynman Integrals is presented.

It relies on an integral representation of a given Feynman Integral in terms of simpler ones.
Using this approach, we present, for the first time, results for a certain family of non-planar five-point two-loop Master Integrals with one external off-shell particle, relevant for instance for $H+2$ jets production at the LHC, in both Euclidean and physical kinematical regions.

Built on

HL-LHC, HE-LHC Working Group
Original
1902
Earlier work this paper cites.
S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD , JHEP 05
Original
1904
Earlier work this paper cites.
H. B. Hartanto, S. Badger, C. Brønnum-Hansen and T. Peraro, A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons , JHEP 09
Original
1906
Earlier work this paper cites.
M. Delto, M. Jaquier, K. Melnikov and R. Röntsch, Mixed QCD ⊗ \otimes QED corrections to on-shell Z Z boson production at the LHC , 1909.08428
Original
1909
Earlier work this paper cites.
K. Chetyrkin and F. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl.Phys. B192
1981
Earlier work this paper cites.
F. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions , Phys.Lett. B100
1981
Earlier work this paper cites.
A. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys.Lett. B254
1991
Earlier work this paper cites.
A. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams , Phys.Lett. B267
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, Dimensionally regulated one loop integrals , Phys.Lett. B302
1993
Earlier work this paper cites.
E. Remiddi, Differential equations for Feynman graph amplitudes , Nuovo Cim. A110
1997
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int. J. Mod. Phys. A15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions , Nucl.Phys. B580
2000
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, Harmonic polylogarithms , Int.J.Mod.Phys. A15
2000
Earlier work this paper cites.
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms , Comput.Phys.Commun. 167
2005
Earlier work this paper cites.

Similar

G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl.Phys. B763
2007
Cited alongside, same era.
J. M. Henn, Multiloop integrals in dimensional regularization made simple , Phys.Rev.Lett. 110
Original
2013
Cited alongside, same era.
C. G. Papadopoulos, Simplified differential equations approach for Master Integrals , JHEP 1407
Original
2014
Cited alongside, same era.
J. M. Henn, K. Melnikov and V. A. Smirnov, Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions , JHEP 1405
Original
2014
Cited alongside, same era.
F. Caola, J. M. Henn, K. Melnikov and V. A. Smirnov, Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons , JHEP 09

Then

T. Gehrmann, J. M. Henn and N. A. Lo Presti, Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD , Phys. Rev. Lett. 116
Original
2016
Later among the works it cites.
C. G. Papadopoulos, D. Tommasini and C. Wever, The Pentabox Master Integrals with the Simplified Differential Equations approach , JHEP 04
Original
2016
Later among the works it cites.
E. Remiddi and L. Tancredi, Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral , Nucl. Phys. B907
Original
2016
Later among the works it cites.
M. Mangano, Physics at the FCC-hh, a 100 TeV pp collider , CERN Yellow Rep. Monogr. 3
Original
2017
Later among the works it cites.
1710.04998

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2014

Cited alongside, same era.

E. Panzer, Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals , Comput. Phys. Commun. 188

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Cited alongside, same era.

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C. G. Papadopoulos, D. Tommasini and C. Wever, Two-loop Master Integrals with the Simplified Differential Equations approach , JHEP 01

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Original

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Later among the works it cites.

S. Badger, C. Brønnum-Hansen, H. B. Hartanto and T. Peraro, First look at two-loop five-gluon scattering in QCD , Phys. Rev. Lett. 120

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Later among the works it cites.

S. Abreu, F. Febres Cordero, H. Ita, B. Page and M. Zeng, Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity , Phys. Rev. D97

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