Built on

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.
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses , JHEP 08
Original
1904
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.
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.
C.G. Papadopoulos and C. Wever, Internal Reduction method for computing Feynman Integrals , JHEP 02
Original
1910
Earlier work this paper cites.
K.-T. Chen, Iterated path integrals , Bull. Am. Math. Soc. 83
1977
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.V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B 254
1991
Earlier work this paper cites.
A.V. Kotikov, Differential equations method: The Calculation of vertex type Feynman diagrams , Phys. Lett. B 259
1991
Earlier work this paper cites.
A.V. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams , Phys. Lett. B 267
1991
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. 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
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.
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.
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.

Similar

T. Huber and D. Maitre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters , Comput. Phys. Commun. 175
2006
Cited alongside, same era.
M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals , Comput. Phys. Commun. 175
2006
Cited alongside, same era.
S. Moch and P. Uwer, XSummer: Transcendental functions and symbolic summation in form , Comput. Phys. Commun. 174
2006
Cited alongside, same era.
J. Vollinga, GiNaC: Symbolic computation with C++ , Nucl. Instrum. Meth. A 559
2006
Cited alongside, same era.
T. Huber and D. Maitre, HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters , Comput. Phys. Commun. 178
Original
2008
Cited alongside, same era.

Then

J.M. Henn, Multiloop integrals in dimensional regularization made simple , Phys. Rev. Lett. 110
Original
2013
Later among the works it cites.
C.G. Papadopoulos, Simplified differential equations approach for Master Integrals , JHEP 07
Original
2014
Later among the works it cites.
1410.7939
Original
S.C. Borowka, Evaluation of multi-loop multi-scale integrals and phenomenological two-loop applications , Ph.D. thesis, Munich, Tech. U., 2014 · 2014
Later among the works it cites.
S. Caron-Huot and J.M. Henn, Iterative structure of finite loop integrals , JHEP 06
Original
2014
Later among the works it cites.
J.M. Henn, Lectures on differential equations for Feynman integrals , J. Phys. A 48

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2022

Two-loop non-planar hexa-box integrals with one massive leg

Kardos, Adam, Papadopoulos, Costas G., Smirnov, Alexander V. et al.

Understand

Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals.

We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of Generalised Polylogarithms, when the alphabet contains non-factorisable square roots.
The results are relevant to the study of NNLO QCD corrections for $W,Z$ and Higgs-boson production in association with two hadronic jets.

Built on

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.
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses , JHEP 08
Original
1904
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.
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.
C.G. Papadopoulos and C. Wever, Internal Reduction method for computing Feynman Integrals , JHEP 02
Original
1910
Earlier work this paper cites.
K.-T. Chen, Iterated path integrals , Bull. Am. Math. Soc. 83
1977
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.V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation , Phys. Lett. B 254
1991
Earlier work this paper cites.
A.V. Kotikov, Differential equations method: The Calculation of vertex type Feynman diagrams , Phys. Lett. B 259
1991
Earlier work this paper cites.
A.V. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams , Phys. Lett. B 267
1991
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. 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
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.
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.
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.

Similar

T. Huber and D. Maitre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters , Comput. Phys. Commun. 175
2006
Cited alongside, same era.
M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals , Comput. Phys. Commun. 175
2006
Cited alongside, same era.
S. Moch and P. Uwer, XSummer: Transcendental functions and symbolic summation in form , Comput. Phys. Commun. 174
2006
Cited alongside, same era.
J. Vollinga, GiNaC: Symbolic computation with C++ , Nucl. Instrum. Meth. A 559
2006
Cited alongside, same era.
T. Huber and D. Maitre, HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters , Comput. Phys. Commun. 178
Original
2008
Cited alongside, same era.