Breakdown of PCAC in diffractive neutrino interactions

TL;DR

This paper investigates the validity of the PCAC hypothesis in high-energy diffractive neutrino interactions, revealing its breakdown at high energies on absorptive targets and restoration at lower energies with short-lived fluctuations.

Contribution

It provides a detailed analysis of PCAC breakdown and restoration in neutrino-induced pion production, highlighting the role of hadronic fluctuation lifetimes and nuclear effects.

Findings

PCAC breaks down at high energies on heavy nuclei due to unitarity saturation.

At lower energies, PCAC is restored when heavy hadronic fluctuations have short lifetimes.

The study clarifies the energy-dependent behavior of diffractive neutrino interactions.

Abstract

We test the hypothesis of partially conserved axial current (PCAC) in high energy diffractive neutrino production of pions. Since the pion pole contribution to the Adler relation (AR) is forbidden by conservation of the lepton current, the heavier states, like the a_1 pole, \rho-\pi-cut, etc., control the lifetime of the hadronic fluctuations of the neutrino. We evaluate the deviation from the AR in diffractive neutrino-production of pions on proton and nuclear targets. At high energies, when all the relevant time scales considerably exceed the size of the target, the AR explicitly breaks down on an absorptive target, such as a heavy nucleus. In this regime, close to the black disc limit, the off-diagonal diffractive amplitudes vanish, while the diagonal one, \pi->\pi, which enters the AR, maximizes and saturates the unitarity bound. At lower energies, in the regime of short lifetime of heavy hadronic fluctuations the AR is restored, i.e. it is not altered by the nuclear effects.