Title: The Width of an Electron-Capture Neutrino Wave Packet

Abstract: We expand on the methodology outlined in previous work that predicted the width of an antineutrino wave packet emerging from a beta-decaying nucleus, to the case of a neutrino from electron capture decay. Based on this result, we also respond to a recent Beryllium Electron capture in Superconducting Tunnel junctions Experiment (BeEST) paper which utilizes this previous work in forming their measurement of the neutrino wave packet width. According to our interpretation, the direct limit on the neutrino wave packet width from electron capture decay ($e^- + \mathrm{^{7}Be}\rightarrow\mathrm{^{7}Li+\nu_e}$) using the BeEST analysis should map to $\sigma_{\nu,x}>6.2\,\mathrm{pm}$ while our theoretical prediction is $\sigma_{\nu,x}\sim2.7\,\mathrm{nm}$.