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Two-Loop Photonic Corrections to Massive Bhabha Scattering

A. A. Penin

TL;DR

This work addresses the need for high-precision predictions of Bhabha scattering by computing the two-loop photonic corrections with a finite electron mass. It develops an infrared-matching framework that relates the massive amplitude to the massless result through the vector form factor and Catani-style factorization, enabling a finite, regulator-independent cross-section correction. The authors derive and validate the nonlogarithmic part of the two-loop photonic contribution, including consistency checks in the small-angle limit, and emphasize the necessity of incorporating these results into Monte Carlo event generators for current and future colliders. The findings have direct implications for luminosity determinations at LEP-era, ILC-era, and low-energy experiments, and they complement existing fermionic and electroweak corrections to achieve permill- or sub-permill precision.

Abstract

We describe the details of the evaluation of the two-loop radiative photonic corrections to Bhabha scattering. The role of the corrections in the high-precision luminosity determination at present and future electron-positron colliders is discussed.

Two-Loop Photonic Corrections to Massive Bhabha Scattering

TL;DR

This work addresses the need for high-precision predictions of Bhabha scattering by computing the two-loop photonic corrections with a finite electron mass. It develops an infrared-matching framework that relates the massive amplitude to the massless result through the vector form factor and Catani-style factorization, enabling a finite, regulator-independent cross-section correction. The authors derive and validate the nonlogarithmic part of the two-loop photonic contribution, including consistency checks in the small-angle limit, and emphasize the necessity of incorporating these results into Monte Carlo event generators for current and future colliders. The findings have direct implications for luminosity determinations at LEP-era, ILC-era, and low-energy experiments, and they complement existing fermionic and electroweak corrections to achieve permill- or sub-permill precision.

Abstract

We describe the details of the evaluation of the two-loop radiative photonic corrections to Bhabha scattering. The role of the corrections in the high-precision luminosity determination at present and future electron-positron colliders is discussed.

Paper Structure

This paper contains 9 sections, 40 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Perturbative expansion of the cross section
  3. Structure of infrared logarithms
  4. Vector form factor
  5. Scattering amplitude
  6. Two-loop corrections to the massive Bhabha cross section
  7. Two-loop infrared matching
  8. The result
  9. Numerical estimates and summary

Figures (2)

  • Figure 1: $(a)$ Logarithmically enhanced (dashed line) and nonlogarithmic (solid line) second order corrections to the differential cross section of the small angle Bhabha scattering as functions of the scattering angle for $\sqrt{s}=100$ GeV and $\ln(\varepsilon_{cut}/\varepsilon)=0$, in permill. $(b)$ The same as (a) but for the large angle Bhabha scattering and $\sqrt{s}=1$ GeV.
  • Figure 2: $(a)$ Photonic (solid line) and fermionic (dashed line) second order corrections to the differential cross section of the small angle Bhabha scattering as functions of the scattering angle for $\sqrt{s}=100$ GeV and $\ln(\varepsilon_{cut}/\varepsilon)=\ln(\varepsilon^{e^+e^-}_{cut}/\varepsilon)=0$, in permill. $(b)$ The same as $(a)$ but for the large angle Bhabha scattering and $\sqrt{s}=1$ GeV.