Long-range spatial correlation of neutrino in pion decay

TL;DR

This paper theoretically investigates the position-dependent properties of neutrinos from pion decay, revealing a universal finite-distance correction to neutrino flux influenced by neutrino mass and coherence length.

Contribution

It introduces a wave packet formalism to show a universal finite-distance correction in neutrino flux due to interference effects in pion decay.

Findings

Neutrino flux has a positive correction at finite distances.

The correction depends on neutrino mass and energy.

Flux decreases slowly with distance in a universal manner.

Abstract

Position-dependent property of the neutrino produced in high-energy pion decay is studied theoretically using a wave packet formalism. It is found that the neutrino probability has a universal finite-distance correction if the pion has a long coherence length. This correction has origins in the interference of the neutrino that is caused by the small neutrino mass and a light-cone singularity of the pion and muon system. This term is positive definite and leads excess to the neutrino flux over the in-coherent value at macroscopic distance of near detector region. The flux decreases slowly with distance in a universal manner that is determined by the absolute value of the neutrino mass and energy. Absolute value of the neutrino mass is expected to be measured indirectly from the neutrino detection probability at finite distance.