[Paper Review] Two-Fermion Production in Electron-Positron Collisions

M. Kobel, Z. Wa̧s+32 more|ArXiv.org|Jul 17, 2000

Muon and positron interactions and applicationsEngineering17 citations

TL;DR

This paper presents a comprehensive comparison of theoretical calculations for two-fermion production in electron-positron collisions at LEP2 energies, focusing on precision requirements for experimental observables. It evaluates Monte Carlo and semi-analytical codes like BHWIDE, KORALZ, KK MC, and ZFITTER, identifying theoretical uncertainties—particularly from initial-final state interference and electroweak boxes—and proposes a unified signal definition for pair radiation applicable across all fermion final states with sub-per-mille numerical consistency.

ABSTRACT

This report summarizes the results of the two-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the theoretical calculations of the two fermion production process in the electron-positron collision at LEP2 center of the mass energies are reported. The Bhabha process and the production of muon, tau, neutrino and quark pairs is covered. On the basis of comparison of various calculations, theoretical uncertainties are estimated and compared with those needed for the final LEP2 data analysis. The subjects for the further studies are identified.

Motivation & Objective

• To assess theoretical uncertainties in two-fermion production processes at LEP2 energies, particularly for final states involving electrons, muons, taus, quarks, and neutrinos.
• To compare the precision and reliability of major Monte Carlo and semi-analytical tools (e.g., KK MC, ZFITTER, KORALZ, BHWIDE) used in LEP2 data analysis.
• To develop and validate a unified, numerically consistent signal definition for secondary pair radiation applicable across all fermion final states and $s'$-cut conditions.
• To identify and quantify key sources of theoretical uncertainty, including initial-final state interference, electroweak boxes, and QED corrections.
• To recommend urgent cross-checks of electroweak corrections and pair effects, especially for wide-angle Bhabha and tagged-photon observables, to meet final LEP2 precision goals.

Proposed method

• Systematic comparison of theoretical predictions from multiple codes (BHWIDE, KORALZ, KK MC, ZFITTER, LABSMC, grc ννγ, NUNUGPV, GENTLE, GRC4f, KORALW) for 2-fermion final states in e+e− collisions.
• Definition of both diagram-based and cut-based signal definitions for 2f+4f final states to handle secondary pair radiation, ensuring numerical consistency within 0.3‰ for hadrons and 1.1‰ for muons.
• Evaluation of theoretical uncertainties through cross-checks of QED corrections, electroweak boxes, and initial-final state interference (IFI) effects using semi-analytical and Monte Carlo methods.
• Application of exponentiation techniques to model soft-photon emission and interference terms, particularly for ISR × FSR in Bhabha scattering.
• Use of ZFITTER and KK MC with updated electroweak libraries to compute virtual corrections and running couplings, with error specifications for physical and technical precision.
• Benchmarking of results across codes, including tagged-photon observables like $e^+e^- o u\bar{\nu}\gamma$, $\mu^+\mu^-\gamma$, and $\tau^+\tau^-\gamma$, under realistic and idealized detector conditions.

Experimental results

Research questions

• RQ1 What are the dominant theoretical uncertainties in two-fermion production cross sections at LEP2 energies, and how do they compare to required experimental precision?
• RQ2 How consistent are the predictions of different Monte Carlo and semi-analytical codes (e.g., KK MC, ZFITTER, KORALZ) for 2-fermion observables with and without tagged photons?
• RQ3 What is the impact of initial-final state interference (IFI) on cross sections and charge asymmetries in Bhabha and other fermion pair processes?
• RQ4 To what extent do electroweak box diagrams contribute to theoretical uncertainties, especially at high center-of-mass energies like 206 GeV?
• RQ5 Can a unified, numerically consistent signal definition for secondary pair radiation be established across all fermion final states and $s'$-cut values?

Key findings

• Theoretical uncertainties for $e^+e^-\to q\bar{q}(\gamma)$ are at 0.26%, below the 0.1–0.2% experimental precision requirement, indicating sufficient theoretical control.
• For $e^+e^-\to\mu^+\mu^-\gamma$ and $\tau^+\tau^-\gamma$, theoretical uncertainties are 0.4%, matching the 0.4–0.5% experimental precision, showing tight agreement.
• For end-cap Bhabha observables ($e^+e^-\to e^+e^-(\gamma)$), theoretical uncertainty is 0.5%, while experimental precision is 0.13%, indicating room for improvement.
• For barrel Bhabha observables, theoretical uncertainty reaches 2.0%, exceeding the 0.21% experimental precision, highlighting a major theoretical challenge.
• Tagged-photon processes like $e^+e^-\to\nu\bar{\nu}\gamma$ have theoretical uncertainties of 4%, significantly above the 0.5% experimental requirement, demanding further refinement.
• Electroweak boxes contribute up to 2% at 206 GeV, making them non-negligible and comparable to future Linear Collider precision needs, despite being small at lower LEP2 energies.