Forward-backward charge asymmetry ine+e−annihilation into hadrons at high energies

Abstract

The forward-backward asymmetry in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into a quark-antiquark pair is considered in the double-logarithmic approximation at energies much higher than the masses of the weak bosons. It is shown that after accounting for the exchange of virtual photons and $W,Z$ bosons to all orders one is led to the following effect (asymmetry): quarks with positive electric charge (e.g., u, $\overline{d})$ tend to move in the ${e}^{+}$ direction whereas quarks with negative charges (e.g., d, $\ifmmode \bar{u}\else \={u}\fi{})$ tend to move in the ${e}^{\ensuremath{-}}$ direction. The value of the asymmetry grows with increasing energy when the produced quarks are within a cone with an opening angle, in the center of mass frame, ${\ensuremath{\theta}}_{0}\ensuremath{\sim}{2M}_{Z}/\sqrt{s}$ around the ${e}^{+}{e}^{\ensuremath{-}}$ beam. Outside this cone, at ${\ensuremath{\theta}}_{0}\ensuremath{\ll}\ensuremath{\theta}\ensuremath{\ll}1,$ the asymmetry is inversely proportional to $\ensuremath{\theta}.$