Built on

Y. Wang, Z. Li and N. Ul Basat, Direct reduction of multiloop multiscale scattering amplitudes , Phys. Rev. D 101
Original
1901
Earlier work this paper cites.
D. Chicherin, T. Gehrmann, J. M. Henn, P. Wasser, Y. Zhang and S. Zoia, The two-loop five-particle amplitude in 𝒩 \mathcal{N} = 8 supergravity , JHEP 03
Original
1901
Earlier work this paper cites.
S. Abreu, L. J. Dixon, E. Herrmann, B. Page and M. Zeng, The two-loop five-point amplitude in 𝒩 \mathcal{N} = 8 supergravity , JHEP 03
Original
1901
Earlier work this paper cites.
J. M. Henn and B. Mistlberger, Four-graviton scattering to three loops in 𝒩 = 8 \mathcal{N}=8 supergravity , JHEP 05
Original
1902
Earlier work this paper cites.
J. Klappert and F. Lange, Reconstructing rational functions with FireFly , Comput. Phys. Commun. 247
Original
1904
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.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. Henn, T. Peraro, P. Wasser, Y. Zhang and S. Zoia, Analytic form of the full two-loop five-gluon all-plus helicity amplitude , Phys. Rev. Lett. 123
Original
1905
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.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops , JHEP 01
Original
1907
Earlier work this paper cites.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn, P. Wasser and Y. Zhang, Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
Earlier work this paper cites.
C. G. Papadopoulos and C. Wever, Internal Reduction method for computing Feynman Integrals , JHEP 02
Original
1910
Earlier work this paper cites.
H. A. Chawdhry, M. L. Czakon, A. Mitov and R. Poncelet, NNLO QCD corrections to three-photon production at the LHC , JHEP 02
Original
1911
Earlier work this paper cites.
X. Guan, X. Liu and Y.-Q. Ma, Complete reduction of two-loop five-light-parton scattering amplitudes , Chin. Phys. C 44
Original
1912
Earlier work this paper cites.
N. Byers and C. Yang, Physical Regions in Invariant Variables for n Particles and the Phase-Space Volume Element , Rev. Mod. Phys. 36
1964
Earlier work this paper cites.
H. Takahasi and M. Mori, Double exponential formulas for numerical integration , Publ. Res. Inst. Math. Sci. 9
1973
Earlier work this paper cites.
K.-T. Chen, Iterated path integrals , Bull. Amer. Math. Soc. 83
1977
Earlier work this paper cites.
K. Chetyrkin and F. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B 192
1981
Earlier work this paper cites.
A. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams , Phys. Lett. B 267
1991
Earlier work this paper cites.
A. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B 254
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, Dimensionally regulated pentagon integrals , Nucl. Phys. B 412
1994
Earlier work this paper cites.
E. Remiddi, Differential equations for Feynman graph amplitudes , Nuovo Cim. A 110
1997
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions , Nucl. Phys. B 580
2000
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Two loop master integrals for gamma* —> 3 jets: The Planar topologies , Nucl. Phys. B 601
2001
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Two loop master integrals for gamma* –> 3 jets: The Nonplanar topologies , Nucl. Phys. B 601
2001
Earlier work this paper cites.
Y. Hida, S. Li and D. Bailey, “Quad-double arithmetic: Algorithms, implementation, and application.” http://crd-legacy.lbl.gov/~dhbailey/mpdist/ , 07, 2001
2001
Earlier work this paper cites.
C. Dlapa, J. Henn and K. Yan, Deriving canonical differential equations for Feynman integrals from a single uniform weight integral , JHEP 05
Original
2002
Earlier work this paper cites.
J. Henn, B. Mistlberger, V. A. Smirnov and P. Wasser, Constructing d-log integrands and computing master integrals for three-loop four-particle scattering , JHEP 04
Original
2002
Earlier work this paper cites.
A. Smirnov and V. Smirnov, How to choose master integrals , 2002.08042
Original
2002
Earlier work this paper cites.

Similar

J. Usovitsch, Factorization of denominators in integration-by-parts reductions , 2002.08173
Original
2002
Cited alongside, same era.
C. W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language , J. Symb. Comput. 33
2002
Cited alongside, same era.
S. Amoroso et al., Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report , in 11th Les Houches Workshop on Physics at TeV Colliders: PhysTeV Les Houches , 3, 2020, 2003.01700
Original
2003
Cited alongside, same era.
A. R. Dalgleish, D. C. Dunbar, W. B. Perkins and J. M. Strong, Full color two-loop six-gluon all-plus helicity amplitude , Phys. Rev. D 101
Original
2003
Cited alongside, same era.
S. Caron-Huot, D. Chicherin, J. Henn, Y. Zhang and S. Zoia, Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in 𝒩 = 4 \mathcal{N}=4 Super Yang-Mills and 𝒩 = 8 \mathcal{N}=8 Supergravity , 2003.03120

Then

T. Gehrmann, J. Henn and N. 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.
S. Caron-Huot, L. J. Dixon, A. McLeod and M. von Hippel, Bootstrapping a Five-Loop Amplitude Using Steinmann Relations , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
A. Denner, S. Dittmaier and L. Hofer, Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations , Comput. Phys. Commun. 212
Original
2017
Later among the works it cites.
L. J. Dixon, J. Drummond, T. Harrington, A. J. McLeod, G. Papathanasiou and M. Spradlin, Heptagons from the Steinmann Cluster Bootstrap , JHEP 02

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2020

Pentagon Functions for Scattering of Five Massless Particles

Chicherin, Dmitry, Sotnikov, Vasily

Understand

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes.

We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space.
We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts.
We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

Built on

Y. Wang, Z. Li and N. Ul Basat, Direct reduction of multiloop multiscale scattering amplitudes , Phys. Rev. D 101
Original
1901
Earlier work this paper cites.
D. Chicherin, T. Gehrmann, J. M. Henn, P. Wasser, Y. Zhang and S. Zoia, The two-loop five-particle amplitude in 𝒩 \mathcal{N} = 8 supergravity , JHEP 03
Original
1901
Earlier work this paper cites.
S. Abreu, L. J. Dixon, E. Herrmann, B. Page and M. Zeng, The two-loop five-point amplitude in 𝒩 \mathcal{N} = 8 supergravity , JHEP 03
Original
1901
Earlier work this paper cites.
J. M. Henn and B. Mistlberger, Four-graviton scattering to three loops in 𝒩 = 8 \mathcal{N}=8 supergravity , JHEP 05
Original
1902
Earlier work this paper cites.
J. Klappert and F. Lange, Reconstructing rational functions with FireFly , Comput. Phys. Commun. 247
Original
1904
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.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. Henn, T. Peraro, P. Wasser, Y. Zhang and S. Zoia, Analytic form of the full two-loop five-gluon all-plus helicity amplitude , Phys. Rev. Lett. 123
Original
1905
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.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops , JHEP 01
Original
1907
Earlier work this paper cites.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn, P. Wasser and Y. Zhang, Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
Earlier work this paper cites.
C. G. Papadopoulos and C. Wever, Internal Reduction method for computing Feynman Integrals , JHEP 02
Original
1910
Earlier work this paper cites.
H. A. Chawdhry, M. L. Czakon, A. Mitov and R. Poncelet, NNLO QCD corrections to three-photon production at the LHC , JHEP 02
Original
1911
Earlier work this paper cites.
X. Guan, X. Liu and Y.-Q. Ma, Complete reduction of two-loop five-light-parton scattering amplitudes , Chin. Phys. C 44
Original
1912
Earlier work this paper cites.
N. Byers and C. Yang, Physical Regions in Invariant Variables for n Particles and the Phase-Space Volume Element , Rev. Mod. Phys. 36
1964
Earlier work this paper cites.
H. Takahasi and M. Mori, Double exponential formulas for numerical integration , Publ. Res. Inst. Math. Sci. 9
1973
Earlier work this paper cites.
K.-T. Chen, Iterated path integrals , Bull. Amer. Math. Soc. 83
1977
Earlier work this paper cites.
K. Chetyrkin and F. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B 192
1981
Earlier work this paper cites.
A. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams , Phys. Lett. B 267
1991
Earlier work this paper cites.
A. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B 254
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, Dimensionally regulated pentagon integrals , Nucl. Phys. B 412
1994
Earlier work this paper cites.
E. Remiddi, Differential equations for Feynman graph amplitudes , Nuovo Cim. A 110
1997
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions , Nucl. Phys. B 580
2000
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Two loop master integrals for gamma* —> 3 jets: The Planar topologies , Nucl. Phys. B 601
2001
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Two loop master integrals for gamma* –> 3 jets: The Nonplanar topologies , Nucl. Phys. B 601
2001
Earlier work this paper cites.
Y. Hida, S. Li and D. Bailey, “Quad-double arithmetic: Algorithms, implementation, and application.” http://crd-legacy.lbl.gov/~dhbailey/mpdist/ , 07, 2001
2001
Earlier work this paper cites.
C. Dlapa, J. Henn and K. Yan, Deriving canonical differential equations for Feynman integrals from a single uniform weight integral , JHEP 05
Original
2002
Earlier work this paper cites.
J. Henn, B. Mistlberger, V. A. Smirnov and P. Wasser, Constructing d-log integrands and computing master integrals for three-loop four-particle scattering , JHEP 04
Original
2002
Earlier work this paper cites.
A. Smirnov and V. Smirnov, How to choose master integrals , 2002.08042
Original
2002
Earlier work this paper cites.

Similar

J. Usovitsch, Factorization of denominators in integration-by-parts reductions , 2002.08173
Original
2002
Cited alongside, same era.
C. W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language , J. Symb. Comput. 33
2002
Cited alongside, same era.
S. Amoroso et al., Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report , in 11th Les Houches Workshop on Physics at TeV Colliders: PhysTeV Les Houches , 3, 2020, 2003.01700
Original
2003
Cited alongside, same era.
A. R. Dalgleish, D. C. Dunbar, W. B. Perkins and J. M. Strong, Full color two-loop six-gluon all-plus helicity amplitude , Phys. Rev. D 101
Original
2003
Cited alongside, same era.
S. Caron-Huot, D. Chicherin, J. Henn, Y. Zhang and S. Zoia, Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in 𝒩 = 4 \mathcal{N}=4 Super Yang-Mills and 𝒩 = 8 \mathcal{N}=8 Supergravity , 2003.03120

Then

T. Gehrmann, J. Henn and N. 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.
S. Caron-Huot, L. J. Dixon, A. McLeod and M. von Hippel, Bootstrapping a Five-Loop Amplitude Using Steinmann Relations , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
A. Denner, S. Dittmaier and L. Hofer, Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations , Comput. Phys. Commun. 212
Original
2017
Later among the works it cites.
L. J. Dixon, J. Drummond, T. Harrington, A. J. McLeod, G. Papathanasiou and M. Spradlin, Heptagons from the Steinmann Cluster Bootstrap , JHEP 02

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

2003

Cited alongside, same era.

J. Klappert, S. Y. Klein and F. Lange, Interpolation of Dense and Sparse Rational Functions and other Improvements in FireFly

Original

2004

Cited alongside, same era.

S. Abreu, H. Ita, F. Moriello, B. Page, W. Tschernow and M. Zeng, Two-Loop Integrals for Planar Five-Point One-Mass Processes , 2005.04195

Original

2005

Cited alongside, same era.

A. van Hameren, J. Vollinga and S. Weinzierl, Automated computation of one-loop integrals in massless theories , Eur. Phys. J. C 41

2005

Cited alongside, same era.

D. H. Bailey, K. Jeyabalan and X. S. Li, A comparison of three high-precision quadrature schemes , Experimental Mathematics 14

2005

Cited alongside, same era.

M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions , 2006.05510

Original

2006

Cited alongside, same era.

L. J. Dixon and Y.-T. Liu, Lifting Heptagon Symbols to Functions , 2007.12966

Original

2007

Cited alongside, same era.

J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral Reduction with Kira 2.0 and Finite Field Methods , 2008.06494

Original

2008

Cited alongside, same era.

Original

2017

Later among the works it cites.

N. Thompson and J. Maddock, “Double-exponential quadrature.” https://www.boost.org/doc/libs/1_73_0/libs/math/doc/html/math_toolkit/double_exponential.html , 2017

2017

Later among the works it cites.

J. Böhm, A. Georgoudis, K. J. Larsen, H. Schönemann and Y. Zhang, Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections , JHEP 09

Original

2018

Later among the works it cites.

S. Badger, C. Brønnum-Hansen, T. Gehrmann, H. B. Hartanto, J. Henn, N. A. Lo Presti and T. Peraro, Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD , PoS LL2018

Original

2018

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

Original