The Width of a Beta-decay-induced Antineutrino Wavepacket

TL;DR

This paper predicts the size of electron antineutrino wavepackets produced by beta decay using quantum system formalism, finding sizes that are too small to affect current neutrino oscillation experiments.

Contribution

It provides a systematic theoretical prediction for beta-decay-induced antineutrino wavepacket sizes based on nuclear localization scales, filling a gap in neutrino physics theory.

Findings

Wavepacket widths range from 10 to 400 pm for energies above 1.8 MeV.

Wavepacket sizes are too small to impact current neutrino oscillation measurements.

The size depends on nucleus size, neutrino energy, and recoil kinematics.

Abstract

The time evolution of a neutrino is dependent on its initial properties at creation including flavor, energy, and wavepacket size. There exists no solid theoretical prediction for the latter property in the context of nuclear beta decay, despite the importance of this process for the past, present, and future of neutrino experimentation. In this paper, we provide a quantitative prediction for the size of a beta-decay-induced electron antineutrino wavepacket by treating the parent nucleus decaying to an entangled antineutrino-recoil system using the formalism of open quantum systems. Of central importance is the delocalization scale of the parent particle. We construct a systematic description of the hierarchy of localizing entanglements that provides an unambiguous statement of the relevant localization scale, found to be closely related to the diameter of the parent nucleus (e.g. $\sim$5-6~fm for beta-decaying fission daughters) and as low as the typical nucleon-nucleon correlation distance ($\sim$1~fm). Inside a nuclear reactor, for example, this translates to initial electron antineutrino wavepacket widths in the $\sigma_{\nu,x}\sim10\mathrm{-}400$~pm range for $E_{\overline{\nu}_e}>1.8$~MeV, with dependencies on decaying nucleus size, the emitted antineutrino energy, and the kinematics of the recoiling system. Wavepacket sizes in this envelope do not produce an observable effect on oscillation probability in foreseeable reactor experiments in the standard three-neutrino model, including JUNO which is expected to be sensitive to $\sigma_{\nu,x}\lesssim3$~pm.