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1. Master integrals for the mixed QCD-QED corrections to the Drell-Yan production of a massive lepton pair

   Hasan, S.M.; Schubert, U. (November 2020, The Journal of high energy physics)

   null (Ed.)

   We showcase the calculation of the master integrals needed for the two loop mixed QCD-QED virtual corrections to the neutral current Drell-Yan process (𝑞𝑞 → l+l−). After establishing a basis of 51 master integrals, we cast the latter into canonical form by using the Magnus algorithm. The dependence on the lepton mass is then expanded such that potentially large logarithmic contributions are kept. After determining all boundary constants, we give the coefficients of the Taylor series around four space-time dimensions in terms of generalized polylogarithms up to weight four. 

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2. Three-loop helicity amplitudes for four-quark scattering in massless QCD

   https://doi.org/10.1007/JHEP10(2021)206  

   Caola, Fabrizio; Chakraborty, Amlan; Gambuti, Giulio; von Manteuffel, Andreas; Tancredi, Lorenzo (October 2021, Journal of High Energy Physics)

   A bstract We compute the three-loop corrections to the helicity amplitudes for q $$ \overline{q} $$ q ¯ → Q $$ \overline{Q} $$ Q ¯ scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours. 

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3. The four-loop $$ \mathcal{N} $$ = 4 SYM Sudakov form factor

   https://doi.org/10.1007/JHEP01(2022)091  

   Lee, Roman N.; von Manteuffel, Andreas; Schabinger, Robert M.; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias (January 2022, Journal of High Energy Physics)

   A bstract We present the Sudakov form factor in full color $$ \mathcal{N} $$ N = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight. 

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4. Master integrals for four-loop massless form factors

   https://doi.org/10.1140/epjc/s10052-023-12179-2  

   Lee, Roman N.; von Manteuffel, Andreas; Schabinger, Robert M.; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias (November 2023, The European Physical Journal C)

   Abstract We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details. 

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5. Near mass-shell double boxes

   https://doi.org/10.1007/JHEP05(2024)155  

   Belitsky, A V; Smirnov, V A (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle virtualities. The latter serve as regulators of infrared divergences, thus making these observables finite in four space-time dimensions. In this paper, we use the method of canonical differential equations for the calculation of (non)planar double box integrals in the near mass-shell kinematical regime, i.e., where virtualities of external particles are much smaller than the Mandelstam variables involved. We deduce a basis of master integrals with uniform transcendental weight based on the analysis of leading singularities employing the Baikov representation as well as an array of complementary techniques. We dub the former asymptotically canonical since it is valid in the near mass-shell limit of interest. We iteratively solve resulting differential equations up to weight four in terms of multiple polylogarithms. 

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