Abstract
We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.
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References
D.A. Kosower and K.J. Larsen, Maximal Unitarity at Two Loops, Phys. Rev. D 85 (2012) 045017 [arXiv:1108.1180] [INSPIRE].
P. Mastrolia and G. Ossola, On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes, JHEP 11 (2011) 014 [arXiv:1107.6041] [INSPIRE].
S. Badger, H. Frellesvig and Y. Zhang, Hepta-Cuts of Two-Loop Scattering Amplitudes, JHEP 04 (2012) 055 [arXiv:1202.2019] [INSPIRE].
Y. Zhang, Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods, JHEP 09 (2012) 042 [arXiv:1205.5707] [INSPIRE].
P. Mastrolia, E. Mirabella, G. Ossola and T. Peraro, Scattering Amplitudes from Multivariate Polynomial Division, Phys. Lett. B 718 (2012) 173 [arXiv:1205.7087] [INSPIRE].
P. Mastrolia, E. Mirabella, G. Ossola and T. Peraro, Integrand-Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division, Phys. Rev. D 87 (2013) 085026 [arXiv:1209.4319] [INSPIRE].
H. Ita, Two-loop Integrand Decomposition into Master Integrals and Surface Terms, Phys. Rev. D 94 (2016) 116015 [arXiv:1510.05626] [INSPIRE].
S. Badger, H. Frellesvig and Y. Zhang, A Two-Loop Five-Gluon Helicity Amplitude in QCD, JHEP 12 (2013) 045 [arXiv:1310.1051] [INSPIRE].
S. Badger, G. Mogull, A. Ochirov and D. O’Connell, A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory, JHEP 10 (2015) 064 [arXiv:1507.08797] [INSPIRE].
S. Abreu, F. Febres Cordero, H. Ita, M. Jaquier, B. Page and M. Zeng, Two-Loop Four-Gluon Amplitudes from Numerical Unitarity, Phys. Rev. Lett. 119 (2017) 142001 [arXiv:1703.05273] [INSPIRE].
S. Abreu et al., Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity, Comput. Phys. Commun. 267 (2021) 108069 [arXiv:2009.11957] [INSPIRE].
J.R. Andersen et al., Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report, in proceedings of the 9th Les Houches Workshop on Physics at TeV Colliders, Les Houches, France, 1–19 June 2015, arXiv:1605.04692 [INSPIRE].
J.R. Andersen et al., Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report, arXiv:1803.07977 [INSPIRE].
S. Amoroso et al., Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report, in proceedings of the 11th Les Houches Workshop on Physics at TeV Colliders: PhysTeV Les Houches, Les Houches, France, 10–28 June 2019, arXiv:2003.01700 [INSPIRE].
H.A. Chawdhry, M. Czakon, A. Mitov and R. Poncelet, NNLO QCD corrections to diphoton production with an additional jet at the LHC, arXiv:2105.06940 [INSPIRE].
D. Chicherin, J.M. Henn and V. Mitev, Bootstrapping pentagon functions, JHEP 05 (2018) 164 [arXiv:1712.09610] [INSPIRE].
C.G. Papadopoulos, D. Tommasini and C. Wever, The Pentabox Master Integrals with the Simplified Differential Equations approach, JHEP 04 (2016) 078 [arXiv:1511.09404] [INSPIRE].
T. Gehrmann, J.M. Henn and N.A. Lo Presti, Pentagon functions for massless planar scattering amplitudes, JHEP 10 (2018) 103 [arXiv:1807.09812] [INSPIRE].
D. Chicherin, T. Gehrmann, J.M. Henn, N.A. Lo Presti, V. Mitev and P. Wasser, Analytic result for the nonplanar hexa-box integrals, JHEP 03 (2019) 042 [arXiv:1809.06240] [INSPIRE].
D. Chicherin, T. Gehrmann, J.M. Henn, P. Wasser, Y. Zhang and S. Zoia, All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order, Phys. Rev. Lett. 123 (2019) 041603 [arXiv:1812.11160] [INSPIRE].
D. Chicherin and V. Sotnikov, Pentagon Functions for Scattering of Five Massless Particles, JHEP 12 (2020) 167 [arXiv:2009.07803] [INSPIRE].
F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett. B 100 (1981) 65 [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [hep-ph/0404258] [INSPIRE].
C. Studerus, Reduze-Feynman Integral Reduction in C++, Comput. Phys. Commun. 181 (2010) 1293 [arXiv:0912.2546] [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
A.V. Smirnov and F.S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic, Comput. Phys. Commun. 247 (2020) 106877 [arXiv:1901.07808] [INSPIRE].
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods, Comput. Phys. Commun. 266 (2021) 108024 [arXiv:2008.06494] [INSPIRE].
J. Gluza, K. Kajda and D.A. Kosower, Towards a Basis for Planar Two-Loop Integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472] [INSPIRE].
R.M. Schabinger, A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations, JHEP 01 (2012) 077 [arXiv:1111.4220] [INSPIRE].
K.J. Larsen and Y. Zhang, Integration-by-parts reductions from unitarity cuts and algebraic geometry, Phys. Rev. D 93 (2016) 041701 [arXiv:1511.01071] [INSPIRE].
J. Böhm, A. Georgoudis, K.J. Larsen, M. Schulze and Y. Zhang, Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals, Phys. Rev. D 98 (2018) 025023 [arXiv:1712.09737] [INSPIRE].
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 (2018) 024 [arXiv:1805.01873] [INSPIRE].
J. Boehm, M. Wittmann, Z. Wu, Y. Xu and Y. Zhang, IBP reduction coefficients made simple, JHEP 12 (2020) 054 [arXiv:2008.13194] [INSPIRE].
P. Mastrolia and S. Mizera, Feynman Integrals and Intersection Theory, JHEP 02 (2019) 139 [arXiv:1810.03818] [INSPIRE].
H. Frellesvig, F. Gasparotto, M.K. Mandal, P. Mastrolia, L. Mattiazzi and S. Mizera, Vector Space of Feynman Integrals and Multivariate Intersection Numbers, Phys. Rev. Lett. 123 (2019) 201602 [arXiv:1907.02000] [INSPIRE].
H. Frellesvig et al., Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers, JHEP 05 (2019) 153 [arXiv:1901.11510] [INSPIRE].
H. Frellesvig et al., Decomposition of Feynman Integrals by Multivariate Intersection Numbers, JHEP 03 (2021) 027 [arXiv:2008.04823] [INSPIRE].
X. Liu, Y.-Q. Ma and C.-Y. Wang, A Systematic and Efficient Method to Compute Multi-loop Master Integrals, Phys. Lett. B 779 (2018) 353 [arXiv:1711.09572] [INSPIRE].
X. Liu and Y.-Q. Ma, Determining arbitrary Feynman integrals by vacuum integrals, Phys. Rev. D 99 (2019) 071501 [arXiv:1801.10523] [INSPIRE].
X. Guan, X. Liu and Y.-Q. Ma, Complete reduction of integrals in two-loop five-light-parton scattering amplitudes, Chin. Phys. C 44 (2020) 093106 [arXiv:1912.09294] [INSPIRE].
P. Zhang, C.-Y. Wang, X. Liu, Y.-Q. Ma, C. Meng and K.-T. Chao, Semi-analytical calculation of gluon fragmentation into 1\( {S}_0^{\left[1,8\right]} \) quarkonia at next-to-leading order, JHEP 04 (2019) 116 [arXiv:1810.07656] [INSPIRE].
Y. Wang, Z. Li and N. Ul Basat, Direct reduction of multiloop multiscale scattering amplitudes, Phys. Rev. D 101 (2020) 076023 [arXiv:1901.09390] [INSPIRE].
D.A. Kosower, Direct Solution of Integration-by-Parts Systems, Phys. Rev. D 98 (2018) 025008 [arXiv:1804.00131] [INSPIRE].
A. von Manteuffel and R.M. Schabinger, A novel approach to integration by parts reduction, Phys. Lett. B 744 (2015) 101 [arXiv:1406.4513] [INSPIRE].
T. Peraro, Scattering amplitudes over finite fields and multivariate functional reconstruction, JHEP 12 (2016) 030 [arXiv:1608.01902] [INSPIRE].
J. Klappert and F. Lange, Reconstructing rational functions with FireFly, Comput. Phys. Commun. 247 (2020) 106951 [arXiv:1904.00009] [INSPIRE].
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs, JHEP 07 (2019) 031 [arXiv:1905.08019] [INSPIRE].
J. Klappert, S.Y. Klein and F. Lange, Interpolation of dense and sparse rational functions and other improvements in FireFly, Comput. Phys. Commun. 264 (2021) 107968 [arXiv:2004.01463] [INSPIRE].
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 (2018) 092001 [arXiv:1712.02229] [INSPIRE].
S. Abreu, F. Febres Cordero, H. Ita, B. Page and M. Zeng, Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity, Phys. Rev. D 97 (2018) 116014 [arXiv:1712.03946] [INSPIRE].
S. Badger et al., Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD, PoS LL2018 (2018) 006 [arXiv:1807.09709] [INSPIRE].
S. Abreu, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity, JHEP 11 (2018) 116 [arXiv:1809.09067] [INSPIRE].
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 (2016) 062001 [Erratum ibid. 116 (2016) 189903] [arXiv:1511.05409] [INSPIRE].
S. Badger, C. Brønnum-Hansen, H.B. Hartanto and T. Peraro, Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case, JHEP 01 (2019) 186 [arXiv:1811.11699] [INSPIRE].
S. Abreu, J. Dormans, F. Febres Cordero, H. Ita and B. Page, Analytic Form of Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD, Phys. Rev. Lett. 122 (2019) 082002 [arXiv:1812.04586] [INSPIRE].
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 (2019) 084 [arXiv:1904.00945] [INSPIRE].
S. Abreu, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Leading-color two-loop QCD corrections for three-jet production at hadron colliders, JHEP 07 (2021) 095 [arXiv:2102.13609] [INSPIRE].
S. Abreu, B. Page, E. Pascual and V. Sotnikov, Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders, JHEP 01 (2021) 078 [arXiv:2010.15834] [INSPIRE].
H.A. Chawdhry, M. Czakon, A. Mitov and R. Poncelet, Two-loop leading-color helicity amplitudes for three-photon production at the LHC, JHEP 06 (2021) 150 [arXiv:2012.13553] [INSPIRE].
H.A. Chawdhry, M.L. Czakon, A. Mitov and R. Poncelet, NNLO QCD corrections to three-photon production at the LHC, JHEP 02 (2020) 057 [arXiv:1911.00479] [INSPIRE].
S. Kallweit, V. Sotnikov and M. Wiesemann, Triphoton production at hadron colliders in NNLO QCD, Phys. Lett. B 812 (2021) 136013 [arXiv:2010.04681] [INSPIRE].
M. Czakon, A. Mitov and R. Poncelet, Next-to-Next-to-Leading Order Study of Three-Jet Production at the LHC, Phys. Rev. Lett. 127 (2021) 152001 [arXiv:2106.05331] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett. 108 (2012) 072001 [Erratum ibid. 117 (2016) 089901] [arXiv:1110.2375] [INSPIRE].
J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP 07 (2016) 148 [arXiv:1603.02663] [INSPIRE].
C. Anastasiou, E.W.N. Glover and M.E. Tejeda-Yeomans, Two loop QED and QCD corrections to massless fermion boson scattering, Nucl. Phys. B 629 (2002) 255 [hep-ph/0201274] [INSPIRE].
Z. Bern, A. De Freitas and L.J. Dixon, Two loop amplitudes for gluon fusion into two photons, JHEP 09 (2001) 037 [hep-ph/0109078] [INSPIRE].
B. Agarwal, F. Buccioni, A. von Manteuffel and L. Tancredi, Two-loop leading colour QCD corrections to q\( \overline{q} \) → γγg and qg → γγq, JHEP 04 (2021) 201 [arXiv:2102.01820] [INSPIRE].
H.A. Chawdhry, M. Czakon, A. Mitov and R. Poncelet, Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC, JHEP 07 (2021) 164 [arXiv:2103.04319] [INSPIRE].
B. Agarwal, F. Buccioni, A. von Manteuffel and L. Tancredi, Two-loop helicity amplitudes for diphoton plus jet production in full color, arXiv:2105.04585 [INSPIRE].
S. Badger, B. Biedermann, P. Uwer and V. Yundin, Numerical evaluation of virtual corrections to multi-jet production in massless QCD, Comput. Phys. Commun. 184 (2013) 1981 [arXiv:1209.0100] [INSPIRE].
D.A. Dicus and S.S.D. Willenbrock, Photon Pair Production and the Intermediate Mass Higgs Boson, Phys. Rev. D 37 (1988) 1801 [INSPIRE].
D. de Florian and Z. Kunszt, Two photons plus jet at LHC: The NNLO contribution from the gg initiated process, Phys. Lett. B 460 (1999) 184 [hep-ph/9905283] [INSPIRE].
S. Catani, The Singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
T. Becher and M. Neubert, On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP 06 (2009) 081 [Erratum JHEP 11 (2013) 024] [arXiv:0903.1126] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [Erratum ibid. 111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].
E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [INSPIRE].
E. Gardi and L. Magnea, Infrared singularities in QCD amplitudes, Nuovo Cim. C 32N5-6 (2009) 137 [Frascati Phys. Ser. 50 (2010) 137] [arXiv:0908.3273] [INSPIRE].
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 (2019) 119 [arXiv:1906.11862] [INSPIRE].
S. Badger, E. Chaubey, H.B. Hartanto and R. Marzucca, Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel, JHEP 06 (2021) 163 [arXiv:2102.13450] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
J. Kuipers, T. Ueda, J.A.M. Vermaseren and J. Vollinga, FORM version 4.0, Comput. Phys. Commun. 184 (2013) 1453 [arXiv:1203.6543] [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
G. Cullen, M. Koch-Janusz and T. Reiter, Spinney: A Form Library for Helicity Spinors, Comput. Phys. Commun. 182 (2011) 2368 [arXiv:1008.0803] [INSPIRE].
A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135 [arXiv:0905.1473] [INSPIRE].
R. Eden, P. Landshoff, D. Olive and J. Polkinghorne, The Analytic S-Matrix, Cambridge University Press, Cambridge U.K. (2002).
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [INSPIRE].
F. Cachazo, Sharpening The Leading Singularity, arXiv:0803.1988 [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo and J. Trnka, Local Integrals for Planar Scattering Amplitudes, JHEP 06 (2012) 125 [arXiv:1012.6032] [INSPIRE].
D.C. Dunbar and W.B. Perkins, Two-loop five-point all plus helicity Yang-Mills amplitude, Phys. Rev. D 93 (2016) 085029 [arXiv:1603.07514] [INSPIRE].
S. Badger et al., Analytic form of the full two-loop five-gluon all-plus helicity amplitude, Phys. Rev. Lett. 123 (2019) 071601 [arXiv:1905.03733] [INSPIRE].
D.C. Dunbar, J.H. Godwin, W.B. Perkins and J.M.W. Strong, Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes, Phys. Rev. D 101 (2020) 016009 [arXiv:1911.06547] [INSPIRE].
G. De Laurentis and D. Maître, Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism, JHEP 02 (2021) 016 [arXiv:2010.14525] [INSPIRE].
M. Heller and A. von Manteuffel, MultivariateApart: Generalized partial fractions, Comput. Phys. Commun. 271 (2022) 108174 [arXiv:2101.08283] [INSPIRE].
E.K. Leinartas, Factorization of rational functions of several variables into partial fractions, Izv. Vyssh. Uchebn. Zaved. Mat. 47 (1978) 47.
A. Raichev, Leinartas’s partial fraction decomposition, arXiv:1206.4740.
Z. Bern, L.J. Dixon and D.A. Kosower, New QCD results from string theory, in proceedings of the International Conference on Strings 93, Berkeley, CA, U.S.A., 24–29 May 1993, hep-th/9311026 [INSPIRE].
G. Mahlon, Multi-gluon helicity amplitudes involving a quark loop, Phys. Rev. D 49 (1994) 4438 [hep-ph/9312276] [INSPIRE].
Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower, One loop N gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett. 72 (1994) 2134 [hep-ph/9312333] [INSPIRE].
J.M. Henn, B. Power and S. Zoia, Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes, JHEP 02 (2020) 019 [arXiv:1911.12142] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
D.C. Dunbar, G.R. Jehu and W.B. Perkins, The two-loop n-point all-plus helicity amplitude, Phys. Rev. D 93 (2016) 125006 [arXiv:1604.06631] [INSPIRE].
D.C. Dunbar, G.R. Jehu and W.B. Perkins, Two-loop six gluon all plus helicity amplitude, Phys. Rev. Lett. 117 (2016) 061602 [arXiv:1605.06351] [INSPIRE].
S. Badger, G. Mogull and T. Peraro, Local integrands for two-loop all-plus Yang-Mills amplitudes, JHEP 08 (2016) 063 [arXiv:1606.02244] [INSPIRE].
D.C. Dunbar, J.H. Godwin, G.R. Jehu and W.B. Perkins, Analytic all-plus-helicity gluon amplitudes in QCD, Phys. Rev. D 96 (2017) 116013 [arXiv:1710.10071] [INSPIRE].
D.C. Dunbar, W.B. Perkins and J.M.W. Strong, n-point QCD two-loop amplitude, Phys. Rev. D 101 (2020) 076001 [arXiv:2001.11347] [INSPIRE].
A.R. Dalgleish, D.C. Dunbar, W.B. Perkins and J.M.W. Strong, Full color two-loop six-gluon all-plus helicity amplitude, Phys. Rev. D 101 (2020) 076024 [arXiv:2003.00897] [INSPIRE].
G. Guennebaud et al., Eigen v3, (2010) http://eigen.tuxfamily.org.
Y. Hida, X.S. Li and D.H. Bailey, libqd: quad-double/double-double computation package, (2010) https://www.davidhbailey.com/dhbsoftware/.
C.G. Papadopoulos and C. Wever, Internal Reduction method for computing Feynman Integrals, JHEP 02 (2020) 112 [arXiv:1910.06275] [INSPIRE].
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 (2020) 117 [arXiv:2005.04195] [INSPIRE].
D.D. Canko, C.G. Papadopoulos and N. Syrrakos, Analytic representation of all planar two-loop five-point Master Integrals with one off-shellleg, JHEP 01 (2021) 199 [arXiv:2009.13917] [INSPIRE].
N. Syrrakos, Pentagon integrals to arbitrary order in the dimensional regulator, JHEP 06 (2021) 037 [arXiv:2012.10635] [INSPIRE].
S. Badger, H.B. Hartanto and S. Zoia, Two-Loop QCD Corrections to Wbb- Production at Hadron Colliders, Phys. Rev. Lett. 127 (2021) 012001 [arXiv:2102.02516] [INSPIRE].
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Badger, S., Brønnum-Hansen, C., Chicherin, D. et al. Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders. J. High Energ. Phys. 2021, 83 (2021). https://doi.org/10.1007/JHEP11(2021)083
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DOI: https://doi.org/10.1007/JHEP11(2021)083