Neutrino-production of single pions: dipole description

TL;DR

This paper extends the dipole approach to neutrino-induced pion production down to low Q^2 using the instanton vacuum model, revealing significant deviations from the Adler relation due to absorptive effects.

Contribution

It derives light-cone distribution amplitudes within the instanton vacuum model, enabling the dipole approach to be applied at low Q^2 and analyzing the breakdown of the Adler relation in diffractive neutrino-production.

Findings

Confirmed sizable deviation from Adler relation at Q^2→0.

Showed diffractive cross section vanishes in the black-disc limit.

Validated dipole phenomenology against nonperturbative effects.

Abstract

The light-cone distribution amplitudes for the axial current are derived within the instanton vacuum model (IVM), which incorporates nonperturbative effects including spontaneous chiral symmetry breaking. This allows to extend applicability of the dipole approach, usually used in the perturbative domain, down to $Q^{2}\to0$, where partially conserved axial current (PCAC) imposes a relation between the neutrino-production cross section and the one induced by pions. A dramatic breakdown of the Adler relation (AR) for diffractive neutrino-production of pions, caused by absorptive corrections, was revealed recently in arXiv:1105.1711. Indeed, comparing with the cross section predicted by the dipole phenomenology at $Q^{2}\to0$ on a proton target we confirmed the sizable deviation from the value given by the AR, as was estimated in arXiv:1105.1711 within a simplified two-channel model. The dipole approach also confirms that in the black-disc limit, where the absorptive corrections maximize, the diffractive cross section ceases, on the contrary to the expectation based on PCAC.