ee$\in$MC: Higher Orders of Radiative Emissions for $e^{+}e^{-} \to \mu^{+}\mu^{-} (n\gamma)$ and $e^{+}e^{-} \to \tau^{+}\tau^{-} (n\gamma)$ Events

TL;DR

This paper extends the ee$ ext{ extbackslash in}$MC generator to include higher-order radiative emissions in electron-positron collision processes, providing more precise theoretical predictions and estimating uncertainties related to perturbative series truncation.

Contribution

It introduces higher-order radiative diagrams up to NNNLO in the generator for $e^{+}e^{-} o ext{lepton pairs}$, improving the accuracy of cross-section calculations.

Findings

Inclusion of NNNLO diagrams significantly affects the total cross-section.

Estimated theoretical uncertainties depend on the soft-photon cut-off.

The approach can be generalized to other physical observables.

Abstract

The radiative emissions in the ee$\in$MC generator are extended to include the Initial/Final-State radiative diagrams, with Initial-State/Final-State interference, for the NLO and NNLO calculations and the Initial-State radiative diagrams associated with the NNNLO calculation for $e^{+}e^{-} \to \mu^{+}\mu^{-} (n\gamma)$ and $e^{+}e^{-} \to \tau^{+}\tau^{-} (n\gamma)$ Events. The NNNLO Initial-State radiative diagrams represent the largest contribution to the perturbative Feynman series in the emission of 4 hard-photons. From the convergence of the total cross-section for $e^{+}e^{-} \to \mu^{+}\mu^{-} (n\gamma)$ and $e^{+}e^{-} \to \tau^{+}\tau^{-} (n\gamma)$, we estimate an uncertainty on the theoretical error corresponding to the truncation of the perturbative Feynman series as a function of the soft-photon cut-off applied in the exponentiation using the technique described in [1]. We discuss how this estimation procedure of the theoretical error associated with the truncation of the perturbative Feynman series can be extended to most experimentally measurable physical observables and the potential pitfalls of this strategy.