ZFITTER -- An Analytical Program for Fermion Pair Production in e+e- Annihilation

TL;DR

ZFITTER introduces a semi-analytical framework for fermion-pair production in $e^+e^-$ annihilation that integrates complete $O(\alpha)$ QED corrections and higher orders. It implements three calculational chains with different photon-phase-space restrictions and multiple branches, including a Standard Model branch with full electroweak corrections, plus model-independent and S-matrix inspired alternatives, complemented by a Bhabha-specific option. The package combines DIZET-based weak corrections, radiator-function convolutions for QED effects, and a set of interfaces (ZUTHSM, ZUTPSM, ZUXSA, ZUXSEC, ZUSMAT) to support cross sections, asymmetries, and tau polarization, enabling flexible fits to LEP I data and beyond. Across validations with ZSHAPE, ALIBABA, and others, ZFITTER achieves sub-percent agreement for most observables, confirming its utility for precision electroweak analyses and New Physics explorations.

Abstract

We describe how to use ZFITTER, a program based on a semi-analytical approach to fermion pair production in e+e- annihilation and Bhabha scattering. A flexible treatment of complete ${\cal O}(α)$ QED corrections, also including higher orders, allows for three calculational {\bf chains} with different realistic sets of restrictions in the photon phase space. {\tt ZFITTER} consists of several {\bf branches} with varying assumptions on the underlying hard scattering process. One includes complete ${\cal O}(α)$ weak loop corrections with a resummation of leading higher-order terms. Alternatively, an ansatz inspired from S-matrix theory, or several model-independent effective Born cross sections may be convoluted. The program calculates cross sections, forward-backward asymmetries, and for $τ$~pair production also the final-state polarization. Various {\bf interfaces} allow fits to be performed with different sets of free parameters.

Figures (7)

• Figure 1: Scattering angle $\vartheta$ in $e^+e^-$ annihilation.
• Figure 2: The structure of $_{Z\! F}\!I\!^{ T}\!\!T\!\!_ {{ E}\!R}$. ICUT=-1 gives observables without any cuts, ICUT=0,1 with cuts.
• Figure 3: Ratio of cross section predictions from $_{Z\! F}\!I\!^{ T}\!\!T\!\!_ {{ E}\!R}$ and ZSHAPE for muon and hadron production, as a function of the centre-of-mass energy, for three different values of $\Delta = 1 - s'_{\min}/s$; both programs with their 'recommended' choice of flags.
• Figure 4: Ratio of cross-section predictions from $_{Z\! F}\!I\!^{ T}\!\!T\!\!_ {{ E}\!R}$ and ZSHAPE for muon and quark production, as a function of the centre-of-mass energy, as in fig. \ref{['??1']}, but here flags are chosen such that the theoretical assumptions of both programs are as similar as possible.
• Figure 5: Ratio of cross sections, $\sigma^{\mu}$, and difference of forward--backward asymmetries, $A_{FB}^{\mu}$, as predicted by $_{Z\! F}\!I\!^{ T}\!\!T\!\!_ {{ E}\!R}$ and ALIBABA, as a function of the centre-of-mass energy. An acceptance cut of 44$^{\circ} \leq$$\vartheta$$\leq$ 136$^{\circ}$, an acollinearity cut of $\xi \leq 25^{\circ}$ and a muon energy cut of $E_f^{\min} = \newline 5$ GeV have been employed. The comparison is made for both the 'recommended' $_{Z\! F}\!I\!^{ T}\!\!T\!\!_ {{ E}\!R}$ flag values and those listed in table \ref{['tbest']}.