Low-energy $e^+\,e^-\toγ\,γ$ at NNLO in QED

TL;DR

This work delivers a fully differential NNLO QED calculation of $e^+\,e^- \to \gamma\gamma$ at low energies, implemented in the McMule framework to provide precise predictions for luminosity-sensitive observables in $e^+e^-$ colliders up to a few GeV. The calculation separates photonic and fermion-loop contributions, employing massification for double virtual terms, OpenLoops for real-virtual corrections, and a dispersive approach for vacuum polarisation, while neglecting subdominant heavy-lepton and hadronic LbL effects. The results show NNLO photonic corrections at the permille level with non-photonic effects generally smaller, validating comparison with NLO+PS predictions and supporting a total theoretical accuracy around $0.1\%$ for typical low-energy scenarios. The study includes differential distributions for KLOE- and Belle-like setups, illustrating the impact of NNLO corrections on angular observables and reinforcing the utility of McMule for precision luminosity determinations at low-energy colliders.

Abstract

We present a fully differential computation of $e^+\,e^-\toγ\,γ$ at next-to-next-to-leading order in QED. The process has been implemented into McMule, completing its set of next-to-next-to-leading-order calculations for the most important $2 \to 2$ processes. The results allow for generic applications to electron-positron colliders with centre-of-mass energies up to a few GeV, particularly for luminosity measurements.

Figures (4)

• Figure 1: Representative diagrams of the squared matrix element for the double-virtual (left), real-virtual (middle), and double-real (right) contributions to the photonic corrections $\sigma^{(2,\gamma)}$.
• Figure 2: Representative diagrams of the squared matrix element contributing to $\sigma^{(2,\text{VP})}$ (left), $\sigma^{(2,\text{LbL})}$ (middle), and $\sigma^{(2,\text{rLBL})}$ (right).
• Figure 3: Differential distribution with respect to $\theta_{\rm av}$ for the KLOE-like scenario. The blue, orange, and green curves in the upper panel correspond to LO-, NLO-, and NNLO-precise distributions, respectively. The size of NNLO photonic and non-photonic corrections are presented in the lower panel with respect to the NLO distribution, with varying enhancing factors for the latter.
• Figure 4: Differential distribution with respect to $\theta_{\rm av}$ for the Belle-like scenario. The blue, orange, and green curves in the upper panel correspond to LO-, NLO-, and NNLO-precise distributions, respectively. The size of NNLO photonic and non-photonic corrections are presented in the lower panel with respect to the NLO distribution, with varying enhancing factors for the latter.