# Coherence length of neutrino oscillations in quantum field-theoretical approach

## TL;DR

This paper introduces a quantum field-theoretical approach to neutrino oscillations that accounts for finite space-time intervals, revealing a shorter coherence length than traditional quantum-mechanical models due to production and detection process effects.

## Contribution

It presents a novel Feynman diagram technique in coordinate space for neutrino oscillations, avoiding wave packets and incorporating process-specific coherence length calculations.

## Key findings

- Neutrino coherence length is shorter than in standard quantum mechanics.
- Energy dependence of detection cross section affects oscillation suppression.
- Method simplifies calculations by using plane waves for initial and final states.

## Abstract

We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most known processes of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes requires one to adjust the rules of passing to the momentum representation in the Feynman diagram technique in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets, both initial and final particle states are described by plane waves, which simplifies the calculations considerably. We consider neutrino oscillation processes, where the neutrinos are produced in three-particle weak decays of nuclei and detected in the charged-current interaction with nuclei or in the charged- and neutral-current interactions with electrons. Particular examples are considered and it is shown that the momentum spread of the produced neutrinos and the energy dependence of the differential cross section of the detection process result in the suppression of neutrino oscillation, which is characterized by a coherence length specific for a pair of production and detection processes. This coherence length turns out to be much less than the coherence length in the standard quantum-mechanical approach defined by the quantum uncertainty of neutrino momentum.