Bhabha scattering at high energy

QED vertex form factors at two loops

“…(12)(13)(14), expanded up to the first order in (D − 4). The Feynman diagrams involved are those in Fig.…”

Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry

“…The solution of the system proceeds orderby-order in (D − 4), as explained in [7]; one obtains a set of chained systems, one for each power of (D − 4), all with the same homogeneous parts. Following again [15,7], the two-by-two first-order systems are transformed in the equivalent single equations of the second order, and all the resulting first and second-order single equations are solved by using Euler's method of the variation of the constants. The method requires the explicit knowledge of the solutions of the associated homogeneous equations; as in previous work, the solutions of all the homogeneous equations were simple algebraic functions, found immediately by inspecting the equations, so that we will not report them here too.…”

“…17 of them were already calculated in [7]. We present here the analytical evaluation of the remaining 18, obtained by means of the differential equations method [13,14,15] or, when all the propagators are massless, via direct integration with the Feynman parameters. The Master Integrals are Laurent-expanded around D = 4 and the coefficients of the Laurent-expansion are then expressed in terms of 1-dimensional harmonic polylogarithms (HPLs) [16,17].…”

Differential equations for Feynman integrals beyond multiple polylogarithms

“…The simplest example is given by the two-loop sunrise integral [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] with equal masses. A slightly more complicated integral is the two-loop kite integral [45][46][47][48][49], which contains the sunrise integral as a sub-topology.…”