Charged Lepton Spectrum Approximation in a Three Body Nucleon Decay

Abstract

Only phase space is typically used to obtain final state particle spectra in rare decay searches, which is a crude approximation in the case of three body processes. We will demonstrate how both dynamics and phase space can be approximately accounted for, in processes such as nucleon decays $p\to e^{+}\bar{\hat{I}}½\hat{I}½$ or $p\to \hat{I}{¼}^{+}\bar{\hat{I}}½\hat{I}½$ originating from Grand Unification models, using general effective Fermi theory formalism of electroweak muon decay $\hat{I}¼\to e^{+}\bar{\hat{I}}½\hat{I}½$. This approach allows for a more precise and only weakly model dependent approximation of final particle spectra for these and similar decays, which may improve rare process searches in current and near-future experiments.

4 pages, 2 figures