Dispersion approach in two-loop calculations

A Aleksejevs

doi:10.1103/physrevd.98.036021

A Aleksejevs

Open Access

https://doi.org/10.1103/physrevd.98.036021

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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 M{\o}ller 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.

Highlights

The electroweak precision searches for the physics beyond the standard model (BSM) frequently demand a subpercent level of accuracy from both experiment and theory
This can be achieved by extending the perturbation expansion of the scattering matrix element to the two-loop level
We extend this for self-energy, vertex and box subloop insertions of the general tensor structure

Summary

Aleksejevs*

Grenfell Campus of Memorial University, 20 University Dr, Corner Brook, Newfoundland and Labrador A2H 5G4, Canada (Received 11 June 2018; published 27 August 2018). The higher-order corrections become increasingly important with experiments reaching the subpercent 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 subloop insertion approach and develop two-loop integrals using two-point functions basis. We introduce a partial tensor reduction for many-point Passarino-Veltman functions, which later could be used in computer algebra packages. We have considered self-energy, triangle and box subloop insertions into self-energy, vertex and box topology

INTRODUCTION

ALEKSEJEVS

Self-energy subloop

Box subloop

NUMERICAL EXAMPLE

CONCLUSION