BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

The two-loop sunrise graph with arbitrary masses

“…We note that the algebraic prefactor can already be obtained from the homogeneous solution in Eq. (20). The point t = (m 1 + m 2 ) 2 is called the threshold, the point t = (m 1 − m 2 ) 2 is called the pseudo-threshold.…”

“…For practical purposes, numerical evaluations are available. [18][19][20] The two-loop sunrise integral with non-zero masses is relevant for precision calculations in electro-weak physics, 3 where non-zero masses naturally occur. In addition, the two-loop sunrise integral with non-zero masses appears as a sub-topology in many advanced higher-order calculations, like the two-loop corrections to top-pair production or in the computation of higher-point functions in massless theories.…”

The iterated structure of the all-order result for the two-loop sunrise integral

“…The simplest Feynman integral which cannot be expressed in terms of multiple polylogarithms is the two-loop sunrise integral with non-vanishing masses. This Feynman integral has already received considerable attention in the literature [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. In this paper we study the two-loop sunrise integral with equal non-zero masses in D = 2 − 2ε space-time dimensions.…”

Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions

“…NICODEMOS [44] is based on contour deformations. There are also complete programs dedicated specifically to the precise calculation of two-loop self-energy diagrams [45,46]. These are so far the only public numerical multiloop projects where calculation in Minkowskian regions is feasable, some other proposals have been anounced for instance in [47,48,49,50,51].…”