Hadron-jet production in high-energy electron-positron annihilation

A simple model is developed for the conversion of an initially produced quark-antiquark pair into hadron jets in electron-positron annihilation. The model assumes that only two quark flavors ($u$ and $d$) are produced, both quarks have the same mass, and all final-state hadrons are pions. In the model, hadrons are produced in two oppositely directed jets in the center-of-momentum (c.m.) frame of the annihilating electron and positron, and the average hadron momentum transverse to the jet direction is constant. The average multiplicity of charged hadrons and the average energy per charged hadron rise as $s^{\frac{1}{4}}$ at high energies, where $s$ is the square of the total c.m. energy. If the component of the final-state hadron momentum parallel to the jet direction is denoted by $p_{\parallel }$, and the average value of the momentum component perpendicular to the jet axis is calculated for hadrons with different values of $x_{\parallel }=\frac{2p_{\parallel }}{s^{\frac{1}{2}}}$, a seagull effect is observed. Particle-density distributions of the charged final-state hadrons can also be calculated as a function of $x_{\parallel }$. These distributions rise to a peak as $x_{\parallel }\to 0$ and are not strongly dependent on the c.m. energy.