Dispersion Approach in Two-Loop Calculations

Abstract

The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak corrections to Møller or electron-proton scattering. It is a demanding task which requires an application of various approaches where two-loop calculations can be automatized. We choose to employ dispersive sub-loop insertion approach and develop two-loop integrals using two-point functions basis. In that basis, we introduce a partial tensor reduction for many-point Passarino-Veltman functions, which later could be used in computer algebra packages. In this paper, we have considered self-energy, triangle and box sub-loop insertions into self-energy, vertex and box topology.

fixed typos in Eq.(35) and Eq.(41)

References in corpus (3)

• Electroweak two-loop corrections to the effective weak mixing angle
• Numerical multi-loop integrals and applications
• SecDec: A tool for numerical multi-loop calculations

Cited by in corpus (4)

• On the evaluation of two-loop electroweak box diagrams for $e^{+}{e}^{-}\to HZ$ production
• Parity-Violating Møller Scattering at NNLO: Closed Fermion Loops
• Possible bound states in the triple-${\eta }_c$ and triple-$J/\psi$ systems
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations