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 theZ0 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.