Radiation of Light Fermions in Heavy Fermion Production

Abstract

The rate for the production of a pair of massive fermions in $e^+ e^-$ annihilation plus real or virtual radiation of a pair of massless fermions is calculated analytically. The contributions for real and virtual radiation are displayed separately. The asymptotic behaviour close to threshold and for high energies is given in a compact form. These approximations provide arguments for the appropriate choice of the scale in the ${\cal O}(α)$ result, such that no large logarithms remain in the final answer.

Figures (3)

• Figure 1: Characteristic Feynman diagrams describing the production of a pair of massive and a (real or virtual) pair of massless fermions.
• Figure 2: Production rate $R_{f_1 \bar{f}_1 f_2 \bar{f}_2}$ based on the exact result (solid line) and approximations described in the text as functions of $m_1^2/s$ with $m_1 = m_{\tau}$ and $m_2 = m_e$.
• Figure 3: ${\cal O}(\alpha^2_s(s))$ correction to the inclusive production rate $R_{f_1 \bar{f}_1}$ based on the exact result (solid line) and approximations described in the text.