DecayΣ+→pℓ+ℓ−within the standard model

Abstract

The HyperCP collaboration has recently reported the observation of three events for the decay ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. They have suggested that new physics may be required to understand the implied decay rate and the observed ${M}_{\ensuremath{\mu}\ensuremath{\mu}}$ distribution. Motivated by this result, we reexamine this mode within the standard model, considering both the short-distance and long-distance contributions. The long-distance part depends on four complex form factors. We determine their imaginary parts from unitarity, fix two of the real parts from the ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p\ensuremath{\gamma}$ measurements, and estimate the other two with vector-meson-dominance models. Taking into account constraints from ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p{e}^{+}{e}^{\ensuremath{-}}$, we find that ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ is long-distance dominated and its rate falls within the range suggested by the HyperCP measurement.