Coherent Exclusive Exponentiation For Precision Monte Carlo Calculations

TL;DR

This work introduces Coherent Exclusive Exponentiation (CEEX) for precision Monte Carlo calculations of e^+e^- -> f fbar + n gamma, contrasting it with traditional Exclusive Exponentiation (EEX) and semi-analytical Inclusive Exponentiation (IEX). CEEX performs IR exponentiation directly at the spin-amplitude level, enabling full spin correlations, initial-final interference (IFI), and-resonance robust treatment, while EEX and IEX serve testing and cross-check roles. The paper develops comprehensive master formulas, IR structure, and partition-based formalisms, and demonstrates numerical precision at LEP2 and 500 GeV linear collider energies with explicit EW corrections via DIZET/ZFITTER. The results establish subpercent physical precision for total cross sections and charge asymmetries across realistic cuts, underscoring CEEX as a flexible, accurate framework for SM predictions relevant to current and future lepton colliders. It also outlines the path toward broader final states and higher-order corrections, positioning CEEX as a foundation for next-generation Bhabha-like and four-fermion MC generators.

Abstract

We present the new Coherent Exclusive Exponentiation (CEEX), the older Exclusive Exponentiation (EEX) and the semi-analytical Inclusive Exponentiation (IEX) for the process $e^+e^-\to f\bar{f} +nγ$, $f=μ,τ,d,u,s,c,b$ with validity for centre of mass energies from $τ$ lepton threshold to 1TeV, that is for LEP1, LEP2, SLC, future Linear Colliders, $b,c,τ$-factories etc. They are based on Yennie-Frautschi-Suura exponentiation. In CEEX effects due to photon emission from initial beams and outgoing fermions are calculated in QED up to second-order, including all interference effects. Electroweak corrections are included in first-order, at the amplitude level. Beams can be polarized longitudinally and transversely, and all spin correlations are incorporated in an exact manner. EEX is more primitive, lacks initial-final interferences, but it is valuable for testing the newer CEEX. IEX provides us set of a sophisticated semi-analytical formulas for the total cross section and selected inclusive distributions which are mainly used for cross-checks of the MC results. We analyse numerical results at the Z-peak 189 GeV and 500 GeV for simple kinematical cuts (comparisons with IEX) and for realistic experimental cuts. Physical precision and technical precision are determined for the total cross section and for the charge asymmetry.

Figures (28)

• Figure 1: QED perturbative leading and subleading corrections. Rows represent corrections in consecutive perturbative orders -- first row is Born contribution. First column represents leading logarithmic (LL) approximation and second column depicts next-to-leading (NLL) approximation. In the figure terms selected for (a) second and (b) third-order pragmatic expansion are limited with help of additional line.
• Figure 2: Kinematics of the process with multiple photon emission from the initial- and final-fermions in the annihilation process.
• Figure 3: First order diagrams.
• Figure 4: Second order vertex diagrams.
• Figure 5: Missing second order diagrams.