The Precision Monte Carlo Event Generator KK For Two-Fermion Final States In e+e- Collisions

TL;DR

KK v4.13 delivers a high-precision Monte Carlo framework for two-fermion final states in e+e- collisions, combining CEEX amplitude-level exponentiation with full spin correlations, ISR/FSR interferences, and exact two-photon emissions. It integrates electroweak corrections via DIZET, beamstrahlung via CIRCE, tau decays with TAUOLA, and hadronization with JETSET, offering a modular, upgradable approach suitable for LEP, SLC, and future linear colliders. The paper details the dual QED matrix-element schemes (CEEX and EEX), a sophisticated Monte Carlo algorithm (weights, phase-space mappings, and partition sums), and a comprehensive software structure with multiple interfacing libraries. The work demonstrates substantial improvements over KORALZ/KORALB/BHLUMI, particularly in ISR-FSR interference, higher-order QED corrections, and exact multi-photon processes, establishing KK as a robust SM prediction tool for precision electroweak studies and collider phenomenology.

Abstract

We present the Monte Carlo event generator KK version 4.13 for precision predictions of the Electroweak Standard Model for the process $e^+e^-\to f\bar{f} +nγ$, $f=μ,τ,d,u,s,c,b$ at centre of mass energies from $τ$ lepton threshold to 1TeV, that is for LEP, SLC, future Linear Colliders, $b,c,τ$-factories etc. Effects due to photon emission from initial beams and outgoing fermions are calculated in QED up to second order, including all interference effects, within Coherent Exclusive Exponentiation (CEEX), which is based on Yennie-Frautschi-Suura exponentiation. Electroweak corrections are included in first order, with higher order extensions, using the DIZET 6.x library. Final state quarks hadronize according to the parton shower model using JETSET. Beams can be polarized longitudinally and transversely. Decay of the tau leptons is simulated using the TAUOLA library, taking into account spin polarization effects as well. In particular the complete spin correlations density matrix of the initial state beams and final state tau's is incorporated in an exact manner. Effects due to beamstrahlung are simulated in a realistic way. The main improvements with respect to KORALZ are: (a) inclusion of the initial-final state QED interference, (b) inclusion of the exact matrix element for two photons, and (c) inclusion of the transverse spin correlations in $τ$ decays (as in KORALB).

Figures (2)

• Figure 1: Topography of the distribution directory
• Figure 2: Test of the normalization of the low-level part of the Monte Carlo, for simplified QED multiphoton distribution. The difference of the MC result and semianalytical result divided by semianalytical is plotted as a function of $v_{\max}=1-s'_{\min}/s$. Test is done for $\mu^+\mu^-$ final state at $\sqrt{s}=189$GeV. In case (a) $v_{\max}=1-4m_\mu^2/s$ is taken; the last bin represent the entire phase phase space. In case (b) $v_{\max}=0.999$.