Built on

J. M. Henn, T. Peraro, M. Stahlhofen and P. Wasser, Matter dependence of the four-loop cusp anomalous dimension , Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
A. V. Smirnov and F. S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic , Comput. Phys. Commun. 247
Original
1901
Earlier work this paper cites.
H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi et al., Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers , JHEP 05
Original
1901
Earlier work this paper cites.
A. von Manteuffel and R. M. Schabinger, Planar master integrals for four-loop form factors , JHEP 05
Original
1903
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.
L. Chen, A prescription for projectors to compute helicity amplitudes in D dimensions , Eur. Phys. J. C 81
Original
1904
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.
G. Laurentis and D. Maître, Extracting analytical one-loop amplitudes from numerical evaluations , JHEP 07
Original
1904
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. M. 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.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover, A. Huss and J. Pires, Triple Differential Dijet Cross Section at the LHC , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
T. Peraro and L. Tancredi, Physical projectors for multi-leg helicity amplitudes , JHEP 07
Original
1906
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.
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.
F. Buccioni, J.-N. Lang, J. M. Lindert, P. Maierhöfer, S. Pozzorini, H. Zhang et al., OpenLoops 2 , Eur. Phys. J. C 79
Original
1907
Earlier work this paper cites.
M. Czakon, A. van Hameren, A. Mitov and R. Poncelet, Single-jet inclusive rates with exact color at 𝒪 \mathcal{O} ( α s 4 {\alpha}_{s}^{4} ) , JHEP 10
Original
1907
Earlier work this paper cites.
J. Blümlein, P. Marquard, N. Rana and C. Schneider, The Heavy Fermion Contributions to the Massive Three Loop Form Factors , Nucl. Phys. B 949
Original
1908
Earlier work this paper cites.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn et al., Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
Earlier work this paper cites.
J. Campbell and T. Neumann, Precision Phenomenology with MCFM , JHEP 12
Original
1909
Earlier work this paper cites.
L. Naterop, A. Signer and Y. Ulrich, handyG —Rapid numerical evaluation of generalised polylogarithms in Fortran , Comput. Phys. Commun. 253
Original
1909
Earlier work this paper cites.
G. Billis, M. A. Ebert, J. K. L. Michel and F. J. Tackmann, A toolbox for q T q_{T} and 0-jettiness subtractions at N 3 LO \hbox{N}^{3}\hbox{LO} , Eur. Phys. J. Plus 136
Original
1909
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.
K. Asteriadis, F. Caola, K. Melnikov and R. Röntsch, Analytic results for deep-inelastic scattering at NNLO QCD with the nested soft-collinear subtraction scheme , Eur. Phys. J. C 80
Original
1910
Earlier work this paper cites.
J. M. Henn, G. P. Korchemsky and B. Mistlberger, The full four-loop cusp anomalous dimension in 𝒩 = 4 \mathcal{N}=4 super Yang-Mills and QCD , JHEP 04
Original
1911
Earlier work this paper cites.
L. Chen, G. Heinrich, S. Jahn, S. P. Jones, M. Kerner, J. Schlenk et al., Photon pair production in gluon fusion: Top quark effects at NLO with threshold matching , JHEP 04
Original
1911
Earlier work this paper cites.
H. Frellesvig, M. Hidding, L. Maestri, F. Moriello and G. Salvatori, The complete set of two-loop master integrals for Higgs + jet production in QCD , JHEP 06
Original
1911
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.
C. Duhr and L. Tancredi, Algorithms and tools for iterated Eisenstein integrals , JHEP 02
Original
1912
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.
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.
E. Remiddi and J. A. M. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals , Nucl. Phys. B 585
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.
S. Pozzorini, H. Zhang and M. F. Zoller, Rational Terms of UV Origin at Two Loops , JHEP 05
Original
2001
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. von Manteuffel, E. Panzer and R. M. Schabinger, Cusp and collinear anomalous dimensions in four-loop QCD from form factors , Phys. Rev. Lett. 124
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.
J. Usovitsch, Factorization of denominators in integration-by-parts reductions , 2002.08173
Original
2002
Earlier work this paper cites.
L. Budge, J. M. Campbell, G. De Laurentis, R. K. Ellis and S. Seth, The one-loop amplitudes for Higgs + 4 partons with full mass effects , JHEP 05
Original
2002
Earlier work this paper cites.
F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals , JHEP 07
2004
Earlier work this paper cites.
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order , Nucl. Phys. B 724
2005
Earlier work this paper cites.
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
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.
A. Gehrmann-De Ridder, T. Gehrmann and E. W. N. Glover, Antenna subtraction at NNLO , JHEP 09
2005
Earlier work this paper cites.
G. Somogyi, Z. Trocsanyi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements , JHEP 06
2005
Earlier work this paper cites.
K. Melnikov and F. Petriello, The W W boson production cross section at the LHC through O ⁡ ( α s 2 ) O(\alpha^{2}_{s}) , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
S. Pozzorini and E. Remiddi, Precise numerical evaluation of the two loop sunrise graph master integrals in the equal mass case , Comput. Phys. Commun. 175
2006
Earlier work this paper cites.
M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions , Comput. Phys. Commun. 269
Original
2006
Earlier work this paper cites.
M. A. Ebert, B. Mistlberger and G. Vita, Transverse momentum dependent PDFs at N 3 LO , JHEP 09
Original
2006
Earlier work this paper cites.
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
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl. Phys. B 763
2007
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Numerical evaluation of six-photon amplitudes , JHEP 07
Original
2007
Earlier work this paper cites.
J.-N. Lang, S. Pozzorini, H. Zhang and M. F. Zoller, Two-Loop Rational Terms in Yang-Mills Theories , JHEP 10
Original
2007
Earlier work this paper cites.
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC , Phys. Rev. Lett. 98
2007
Earlier work this paper cites.
U. Aglietti, R. Bonciani, L. Grassi and E. Remiddi, The Two loop crossed ladder vertex diagram with two massive exchanges , Nucl. Phys. B 789
Original
2008
Earlier work this paper cites.
R. K. Ellis, W. T. Giele and Z. Kunszt, A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes , JHEP 03
Original
2008
Earlier work this paper cites.
W. T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes , JHEP 04
Original
2008
Earlier work this paper cites.
C. F. Berger, Z. Bern, L. J. Dixon, F. Febres Cordero, D. Forde, H. Ita et al., An Automated Implementation of On-Shell Methods for One-Loop Amplitudes , Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods , Comput. Phys. Commun. 266
Original
2008
Earlier work this paper cites.
M. Czakon, A. Mitov and R. Poncelet, NNLO QCD corrections to leptonic observables in top-quark pair production and decay , JHEP 05
Original
2008
Earlier work this paper cites.
A. Denner, J.-N. Lang and M. Pellen, Full NLO QCD corrections to off-shell tt¯bb¯ production , Phys. Rev. D 104
Original
2008
Earlier work this paper cites.
C. Brønnum-Hansen and C.-Y. Wang, Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion , JHEP 01
Original
2009
Earlier work this paper cites.
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
Earlier work this paper cites.
D. Chicherin and V. Sotnikov, Pentagon Functions for Scattering of Five Massless Particles , JHEP 20
Original
2009
Earlier work this paper cites.

Similar

F. Brown, The Massless higher-loop two-point function , Commun. Math. Phys. 287
Original
2009
Cited alongside, same era.
X. Liu, Y.-Q. Ma, W. Tao and P. Zhang, Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow , Chin. Phys. C 45
Original
2009
Cited alongside, same era.
S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, M. Kraus, B. Page et al., Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity , Comput. Phys. Commun. 267
Original
2009
Cited alongside, same era.
G. Heinrich, Collider Physics at the Precision Frontier , Phys. Rept. 922
Original
2009
Cited alongside, same era.
A. Behring, F. Buccioni, F. Caola, M. Delto, M. Jaquier, K. Melnikov et al., Mixed QCD-electroweak corrections to W W -boson production in hadron collisions , Phys. Rev. D 103

Then

A. A. Vladimirov, Correspondence between Soft and Rapidity Anomalous Dimensions , Phys. Rev. Lett. 118
Original
2017
Later among the works it cites.
I. Moult, L. Rothen, I. W. Stewart, F. J. Tackmann and H. X. Zhu, Subleading Power Corrections for N-Jettiness Subtractions , Phys. Rev. D 95
Original
2017
Later among the works it cites.
J. Currie, A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover, A. Huss and J. Pires, Precise predictions for dijet production at the LHC , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
F. Caola, K. Melnikov and R. Röntsch, Nested soft-collinear subtractions in NNLO QCD computations , Eur. Phys. J. C 77
Original
2017
Later among the works it cites.
T. Gehrmann, J. M. Henn and N. A. Lo Presti, Pentagon functions for massless planar scattering amplitudes , JHEP 10

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2022

Computational challenges for multi-loop collider phenomenology

Cordero, Fernando Febres, von Manteuffel, Andreas, Neumann, Tobias

Understand

Precision measurements at the LHC and future colliders require theory predictions with uncertainties at the percent level for many observables.

Theory uncertainties due to the perturbative truncation are particularly relevant and must be reduced to fully exploit the physics potential of collider experiments.
In recent years the theoretical high energy physics community has made tremendous analytical and numerical advances to address this challenge.
In this white paper, we survey state-of-the-art calculations in perturbative quantum field theory for collider phenomenology with a particular focus on the computational requirements at high perturbative orders.

Built on

J. M. Henn, T. Peraro, M. Stahlhofen and P. Wasser, Matter dependence of the four-loop cusp anomalous dimension , Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
A. V. Smirnov and F. S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic , Comput. Phys. Commun. 247
Original
1901
Earlier work this paper cites.
H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi et al., Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers , JHEP 05
Original
1901
Earlier work this paper cites.
A. von Manteuffel and R. M. Schabinger, Planar master integrals for four-loop form factors , JHEP 05
Original
1903
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.
L. Chen, A prescription for projectors to compute helicity amplitudes in D dimensions , Eur. Phys. J. C 81
Original
1904
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.
G. Laurentis and D. Maître, Extracting analytical one-loop amplitudes from numerical evaluations , JHEP 07
Original
1904
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. M. 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.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover, A. Huss and J. Pires, Triple Differential Dijet Cross Section at the LHC , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
T. Peraro and L. Tancredi, Physical projectors for multi-leg helicity amplitudes , JHEP 07
Original
1906
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.
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.
F. Buccioni, J.-N. Lang, J. M. Lindert, P. Maierhöfer, S. Pozzorini, H. Zhang et al., OpenLoops 2 , Eur. Phys. J. C 79
Original
1907
Earlier work this paper cites.
M. Czakon, A. van Hameren, A. Mitov and R. Poncelet, Single-jet inclusive rates with exact color at 𝒪 \mathcal{O} ( α s 4 {\alpha}_{s}^{4} ) , JHEP 10
Original
1907
Earlier work this paper cites.
J. Blümlein, P. Marquard, N. Rana and C. Schneider, The Heavy Fermion Contributions to the Massive Three Loop Form Factors , Nucl. Phys. B 949
Original
1908
Earlier work this paper cites.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn et al., Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
Earlier work this paper cites.
J. Campbell and T. Neumann, Precision Phenomenology with MCFM , JHEP 12
Original
1909
Earlier work this paper cites.
L. Naterop, A. Signer and Y. Ulrich, handyG —Rapid numerical evaluation of generalised polylogarithms in Fortran , Comput. Phys. Commun. 253
Original
1909
Earlier work this paper cites.
G. Billis, M. A. Ebert, J. K. L. Michel and F. J. Tackmann, A toolbox for q T q_{T} and 0-jettiness subtractions at N 3 LO \hbox{N}^{3}\hbox{LO} , Eur. Phys. J. Plus 136
Original
1909
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.
K. Asteriadis, F. Caola, K. Melnikov and R. Röntsch, Analytic results for deep-inelastic scattering at NNLO QCD with the nested soft-collinear subtraction scheme , Eur. Phys. J. C 80
Original
1910
Earlier work this paper cites.
J. M. Henn, G. P. Korchemsky and B. Mistlberger, The full four-loop cusp anomalous dimension in 𝒩 = 4 \mathcal{N}=4 super Yang-Mills and QCD , JHEP 04
Original
1911
Earlier work this paper cites.
L. Chen, G. Heinrich, S. Jahn, S. P. Jones, M. Kerner, J. Schlenk et al., Photon pair production in gluon fusion: Top quark effects at NLO with threshold matching , JHEP 04
Original
1911
Earlier work this paper cites.
H. Frellesvig, M. Hidding, L. Maestri, F. Moriello and G. Salvatori, The complete set of two-loop master integrals for Higgs + jet production in QCD , JHEP 06
Original
1911
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.
C. Duhr and L. Tancredi, Algorithms and tools for iterated Eisenstein integrals , JHEP 02
Original
1912
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.
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.
E. Remiddi and J. A. M. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals , Nucl. Phys. B 585
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.
S. Pozzorini, H. Zhang and M. F. Zoller, Rational Terms of UV Origin at Two Loops , JHEP 05
Original
2001
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. von Manteuffel, E. Panzer and R. M. Schabinger, Cusp and collinear anomalous dimensions in four-loop QCD from form factors , Phys. Rev. Lett. 124
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.
J. Usovitsch, Factorization of denominators in integration-by-parts reductions , 2002.08173
Original
2002
Earlier work this paper cites.
L. Budge, J. M. Campbell, G. De Laurentis, R. K. Ellis and S. Seth, The one-loop amplitudes for Higgs + 4 partons with full mass effects , JHEP 05
Original
2002
Earlier work this paper cites.
F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals , JHEP 07
2004
Earlier work this paper cites.
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order , Nucl. Phys. B 724
2005
Earlier work this paper cites.
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
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.
A. Gehrmann-De Ridder, T. Gehrmann and E. W. N. Glover, Antenna subtraction at NNLO , JHEP 09
2005
Earlier work this paper cites.
G. Somogyi, Z. Trocsanyi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements , JHEP 06
2005
Earlier work this paper cites.
K. Melnikov and F. Petriello, The W W boson production cross section at the LHC through O ⁡ ( α s 2 ) O(\alpha^{2}_{s}) , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
S. Pozzorini and E. Remiddi, Precise numerical evaluation of the two loop sunrise graph master integrals in the equal mass case , Comput. Phys. Commun. 175
2006
Earlier work this paper cites.
M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions , Comput. Phys. Commun. 269
Original
2006
Earlier work this paper cites.
M. A. Ebert, B. Mistlberger and G. Vita, Transverse momentum dependent PDFs at N 3 LO , JHEP 09
Original
2006
Earlier work this paper cites.
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
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl. Phys. B 763
2007
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Numerical evaluation of six-photon amplitudes , JHEP 07
Original
2007
Earlier work this paper cites.
J.-N. Lang, S. Pozzorini, H. Zhang and M. F. Zoller, Two-Loop Rational Terms in Yang-Mills Theories , JHEP 10
Original
2007
Earlier work this paper cites.
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC , Phys. Rev. Lett. 98
2007
Earlier work this paper cites.
U. Aglietti, R. Bonciani, L. Grassi and E. Remiddi, The Two loop crossed ladder vertex diagram with two massive exchanges , Nucl. Phys. B 789
Original
2008
Earlier work this paper cites.
R. K. Ellis, W. T. Giele and Z. Kunszt, A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes , JHEP 03
Original
2008
Earlier work this paper cites.
W. T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes , JHEP 04
Original
2008
Earlier work this paper cites.
C. F. Berger, Z. Bern, L. J. Dixon, F. Febres Cordero, D. Forde, H. Ita et al., An Automated Implementation of On-Shell Methods for One-Loop Amplitudes , Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods , Comput. Phys. Commun. 266
Original
2008
Earlier work this paper cites.
M. Czakon, A. Mitov and R. Poncelet, NNLO QCD corrections to leptonic observables in top-quark pair production and decay , JHEP 05
Original
2008
Earlier work this paper cites.
A. Denner, J.-N. Lang and M. Pellen, Full NLO QCD corrections to off-shell tt¯bb¯ production , Phys. Rev. D 104
Original
2008
Earlier work this paper cites.
C. Brønnum-Hansen and C.-Y. Wang, Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion , JHEP 01
Original
2009
Earlier work this paper cites.
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
Earlier work this paper cites.
D. Chicherin and V. Sotnikov, Pentagon Functions for Scattering of Five Massless Particles , JHEP 20
Original
2009
Earlier work this paper cites.

Similar

F. Brown, The Massless higher-loop two-point function , Commun. Math. Phys. 287
Original
2009
Cited alongside, same era.
X. Liu, Y.-Q. Ma, W. Tao and P. Zhang, Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow , Chin. Phys. C 45
Original
2009
Cited alongside, same era.
S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, M. Kraus, B. Page et al., Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity , Comput. Phys. Commun. 267
Original
2009
Cited alongside, same era.
G. Heinrich, Collider Physics at the Precision Frontier , Phys. Rept. 922
Original
2009
Cited alongside, same era.
A. Behring, F. Buccioni, F. Caola, M. Delto, M. Jaquier, K. Melnikov et al., Mixed QCD-electroweak corrections to W W -boson production in hadron collisions , Phys. Rev. D 103

Then

A. A. Vladimirov, Correspondence between Soft and Rapidity Anomalous Dimensions , Phys. Rev. Lett. 118
Original
2017
Later among the works it cites.
I. Moult, L. Rothen, I. W. Stewart, F. J. Tackmann and H. X. Zhu, Subleading Power Corrections for N-Jettiness Subtractions , Phys. Rev. D 95
Original
2017
Later among the works it cites.
J. Currie, A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover, A. Huss and J. Pires, Precise predictions for dijet production at the LHC , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
F. Caola, K. Melnikov and R. Röntsch, Nested soft-collinear subtractions in NNLO QCD computations , Eur. Phys. J. C 77
Original
2017
Later among the works it cites.
T. Gehrmann, J. M. Henn and N. A. Lo Presti, Pentagon functions for massless planar scattering amplitudes , JHEP 10

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Original

2009

Cited alongside, same era.

M. Walden and S. Weinzierl, Numerical evaluation of iterated integrals related to elliptic Feynman integrals , Comput. Phys. Commun. 265

Original

2010

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.

I. W. Stewart, F. J. Tackmann and W. J. Waalewijn, N-Jettiness: An Inclusive Event Shape to Veto Jets , Phys. Rev. Lett. 105

Original

2010

Cited alongside, same era.

M. Czakon, A novel subtraction scheme for double-real radiation at NNLO , Phys. Lett. B 693

Original

2010

Cited alongside, same era.

S. Kallweit, V. Sotnikov and M. Wiesemann, Triphoton production at hadron colliders in NNLO QCD , Phys. Lett. B 812

Original

2010

Cited alongside, same era.

D. Lombardi, M. Wiesemann and G. Zanderighi, Advancing MıNNLO PS

Original

2010

Cited alongside, same era.

B. Agarwal, S. P. Jones and A. von Manteuffel, Two-loop helicity amplitudes for g g → Z Z gg\to ZZ with full top-quark mass effects , JHEP 05

Original

2011

Cited alongside, same era.

Original

2018