A complete set of scalar master integrals for massive 2-loop Bhabha scattering: where we are

TL;DR

This work establishes a complete scalar master-integral basis for massive two-loop QED Bhabha scattering to enable NNLO corrections and precise luminosity predictions. It employs the Laporta-Remiddi framework with IBP/LI identities and a DiaGen/IdSolver pipeline to identify and reduce master integrals, delivering new analytic results for four 2-loop 3-point MIs and introducing a new 2-loop box MI solved via differential equations. The results are cross-checked with sector-decomposition-based numerical methods, reinforcing their reliability. Overall, the paper lays essential groundwork toward full massive 2-loop QED amplitudes and their integration into collider phenomenology.

Abstract

We define a complete set of scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering. Among others, there are thirty three 2-loop box type MIs. Five of them have been published in (semi-)analytical form, one is determined here, the rest remains to be calculated. Further, the last four so far unknown 2-loop 3-point MIs are identified and also computed here.

Figures (7)

• Figure 1: The 2-loop self energy diagrams.
• Figure 2: The 2-loop vertex diagrams.
• Figure 3: The 2-loop box diagrams.
• Figure 4: The six 2-loop 2-point MIs. The multiplication factor stands for the number of masters for the given diagram when different from 1.
• Figure 5: The nineteen 2-loop 3-point MIs (the multiplication factors as in Fig. \ref{['LL7']}.)