Built on

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.
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.
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses , JHEP 08
Original
1904
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. Henn, T. Peraro et al., 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.
M. Heller, A. von Manteuffel and R.M. Schabinger, Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals , Phys. Rev. D 102
Original
1907
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.
N. Byers and C.N. 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.
C. Poon, Kinematics of many-particle processes in invariant variables: Physical regions, phase space and all that , Nuclear Physics B 20
1970
Earlier work this paper cites.
E. Byckling and K. Kajantie, Particle Kinematics: (Chapters I-VI, X) , University of Jyvaskyla, Jyvaskyla, Finland (1971)
1971
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. Am. Math. Soc. 83
1977
Earlier work this paper cites.
F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions , Phys. Lett. B 100
1981
Earlier work this paper cites.
K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B 192
1981
Earlier work this paper cites.
R. Kleiss, W.J. Stirling and S.D. Ellis, A New Monte Carlo Treatment of Multiparticle Phase Space at High-energies , Comput. Phys. Commun. 40
1986
Earlier work this paper cites.
A.V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B 254
1991
Earlier work this paper cites.
H.R.P. Ferguson and D.H. Bailey, A Polynomial Time, Numerically Stable Integer Relation Algorithm , RNR Technical Report RNR-91-032 (1992)
1992
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.
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A 15
2000
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. A15
2000
Earlier work this paper cites.
D.H. Bailey and D.J. Broadhurst, Parallel integer relation detection: Techniques and applications , Math. Comput. 70
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.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
Earlier work this paper cites.

Similar

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 , JHEP 10
Original
2003
Cited alongside, same era.
D. Binosi and L. Theußl, Jaxodraw: A graphical user interface for drawing feynman diagrams , Computer Physics Communications 161
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 , JHEP 11
Original
2005
Cited alongside, same era.
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms , Comput. Phys. Commun. 167
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

Then

C.G. Papadopoulos, D. Tommasini and C. Wever, Two-loop Master Integrals with the Simplified Differential Equations approach , JHEP 01
Original
2015
Later among the works it cites.
T. Gehrmann, A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for q q ¯ ′ → V 1 V 2 → 4 q\overline{q}^{\prime}\to{V}_{1}{V}_{2}\to 4 leptons , JHEP 09
Original
2015
Later among the works it cites.
A. von Manteuffel and R.M. Schabinger, A novel approach to integration by parts reduction , Phys. Lett. B 744
Original
2015
Later among the works it cites.
J. Kuipers, T. Ueda and J. Vermaseren, Code Optimization in FORM , Comput. Phys. Commun. 189
Original
2015
Later among the works it cites.
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

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Reading the bibliography…

2021

Pentagon Functions for One-Mass Planar Scattering Amplitudes

Chicherin, Dmitry, Sotnikov, Vasily, Zoia, Simone

Understand

We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg.

We express the integrals in terms of a basis of algebraically-independent transcendental functions, which we call one-mass pentagon functions.
We construct them by using the properties of iterated integrals with logarithmic kernels.
The pentagon functions are manifestly free of unphysical branch cuts, do not require analytic continuation, and can be readily evaluated over the whole physical phase space of the massive particle production channel.

Built on

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.
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.
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses , JHEP 08
Original
1904
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. Henn, T. Peraro et al., 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.
M. Heller, A. von Manteuffel and R.M. Schabinger, Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals , Phys. Rev. D 102
Original
1907
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.
N. Byers and C.N. 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.
C. Poon, Kinematics of many-particle processes in invariant variables: Physical regions, phase space and all that , Nuclear Physics B 20
1970
Earlier work this paper cites.
E. Byckling and K. Kajantie, Particle Kinematics: (Chapters I-VI, X) , University of Jyvaskyla, Jyvaskyla, Finland (1971)
1971
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. Am. Math. Soc. 83
1977
Earlier work this paper cites.
F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions , Phys. Lett. B 100
1981
Earlier work this paper cites.
K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B 192
1981
Earlier work this paper cites.
R. Kleiss, W.J. Stirling and S.D. Ellis, A New Monte Carlo Treatment of Multiparticle Phase Space at High-energies , Comput. Phys. Commun. 40
1986
Earlier work this paper cites.
A.V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B 254
1991
Earlier work this paper cites.
H.R.P. Ferguson and D.H. Bailey, A Polynomial Time, Numerically Stable Integer Relation Algorithm , RNR Technical Report RNR-91-032 (1992)
1992
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.
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A 15
2000
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. A15
2000
Earlier work this paper cites.
D.H. Bailey and D.J. Broadhurst, Parallel integer relation detection: Techniques and applications , Math. Comput. 70
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.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
Earlier work this paper cites.

Similar

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 , JHEP 10
Original
2003
Cited alongside, same era.
D. Binosi and L. Theußl, Jaxodraw: A graphical user interface for drawing feynman diagrams , Computer Physics Communications 161
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 , JHEP 11
Original
2005
Cited alongside, same era.
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms , Comput. Phys. Commun. 167
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

Then

C.G. Papadopoulos, D. Tommasini and C. Wever, Two-loop Master Integrals with the Simplified Differential Equations approach , JHEP 01
Original
2015
Later among the works it cites.
T. Gehrmann, A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for q q ¯ ′ → V 1 V 2 → 4 q\overline{q}^{\prime}\to{V}_{1}{V}_{2}\to 4 leptons , JHEP 09
Original
2015
Later among the works it cites.
A. von Manteuffel and R.M. Schabinger, A novel approach to integration by parts reduction , Phys. Lett. B 744
Original
2015
Later among the works it cites.
J. Kuipers, T. Ueda and J. Vermaseren, Code Optimization in FORM , Comput. Phys. Commun. 189
Original
2015
Later among the works it cites.
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

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2005

Cited alongside, same era.

M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions , Comput. Phys. Commun. 269

Original

2006

Cited alongside, same era.

F. Brown and C. Duhr, A double integral of dlog forms which is not polylogarithmic , 6, 2020 [ 2006.09413 ]

Original

2006

Cited alongside, same era.

M. Bonetti, E. Panzer, V.A. Smirnov and L. Tancredi, Two-loop mixed QCD-EW corrections to g g → H g gg\to Hg , JHEP 11

Original

2007

Cited alongside, same era.

D. Chicherin and V. Sotnikov, Pentagon Functions for Scattering of Five Massless Particles , JHEP 12

Original

2009

Cited alongside, same era.

D.D. Canko, C.G. Papadopoulos and N. Syrrakos, Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg , JHEP 01

Original

2009

Cited alongside, same era.

S. Abreu, B. Page, E. Pascual and V. Sotnikov, Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders , JHEP 01

Original

2010

Cited alongside, same era.

G. De Laurentis and D. Maître, Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism , JHEP 02

Original

2010

Cited alongside, same era.

Original

2016