Prompt neutrino production in beam-dump experiments

Purely leptonic decays of the charm $D$ and $F$ mesons are investigated quantitatively as a source of asymmetry between prompt (${\nu }_e+{\overline{\nu }}_e$) and (${\nu }_{\mu }+{\overline{\nu }}_{\mu }$) neutrino rates from hadronic beam dumps. We define and compute the values of two different ratios $R$ of the numbers of events produced in a neutrino detector exposed to prompt ${\nu }_e\text{'}\mathrm{s}$ and ${\nu }_{\mu }\text{'}\mathrm{s}$, applying selections identical to those used in analyses of data. The decay mode $F\to \mu {\nu }_{\mu }$ is shown to depress the ratio $R_1$ to values perhaps as low as 0.9; $R_1$ is determined from data in which electrons and muons are identified on an event-by-event basis. A ratio $R_2$ may be determined if electrons are not identified. Owing to $F\to \tau {\nu }_{\tau }$, $R_2$ is increased above $R_1$, and values of $R_2$ may exceed unity. Interpreted in this context, values of $R$ substantially below unity, as observed in some experiments, would require very large values for the weak-decay constant $f_F$ and for the inclusive $F$-production cross section.