Coherence of$u\bar u$ and$d\bar d$ final states: Possible influence onZ ⁰ decay width ande ⁺ e ⁻ annihilation cross section

Abstract

The decay width of theZ ⁰ associated with its coupling tou andd quarks is usually expressed as the incoherent sum of the widths into$u\bar u$ and$d\bar d$ final states,$\Gamma (u\bar u) + \Gamma (d\bar d)$. We examine a specific correction to this estimate arising from the coherence of the$u\bar u$ and$d\bar d$ systems, dictated by isospin symmetry. The decay width is written in the alternative form Γ(G=+1)+Γ(G=−1), which recognises that final hadronic states can be classified according to even and odd G-parity. Assuming that states withG=+1(−1) evolve from configurations containing even (odd) numbers ofG=−1 systems, and considering various multiplicity distributions for such systems, small corrections are obtained relative to the conventional estimate. A similar analysis applied to the cross section for$e^ + e^ - \to u\bar u, d\bar d$ yields small energy-dependent corrections to the parameter R.