Incurable Adler relation for soft neutrino interactions

TL;DR

This paper demonstrates that the Adler relation, which connects neutrino and pion interactions, breaks down due to absorptive corrections, especially in coherent neutrino-induced pion production on nuclei across all energies.

Contribution

It reveals the limitations of the Adler relation in soft neutrino interactions and predicts its breakdown in nuclear coherent pion production due to absorptive effects.

Findings

The Adler relation does not hold universally for neutrino interactions.

Absorptive corrections significantly break the Adler relation.

A dramatic breakdown of the Adler relation is predicted for coherent pion production on nuclei.

Abstract

The Adler relation (AR), which bridges soft interactions of neutrinos and pions, might look as a manifestation of pion dominance. However neutrino cannot fluctuate to a pion because of lepton current conservation, instead it interacts via much heavier hadronic components. This fact leads to nontrivial relations between interaction amplitudes of different hadronic species, in particular, it links diagonal and off-diagonal diffractive interactions of pions. Absorptive corrections break these relations making the AR impossible to hold universally, i.e. for any target and at any energy. We predict a dramatic breakdown of the AR for coherent neutrino-production of pions on nuclei at all energies.