WeakMAID

Dual Unitary Isobar-Regge Model for Pion Neutrino-Production

Mikhail Gorshteyn, Institut für Kernphysik, Johannes-Gutenberg Universität Mainz

Motivation

Long-base neutrino oscillation experiments, such as DUNE, aim at determining neutrino masses and mixing parameters at an unprecedented level of precision. Born from charged pions decaying in flight, by the time they reach the far detector 1300 km away, the muon neutrinos will oscillate to electron or tau ones. To unravel the oscillation pattern, the energy of the neutrino beam has to be known to a good precision. For this purpose, close enough to the neutrino source - where no oscillation has occurred yet - the near detector is placed to study neutrino interactions with matter. An important mechanism in these interactions is the production of pions. This project is dedicated to developing a state-of-the-art  theoretical analysis for weak  pion production on the nucleon. Embedded in Monte Carlo simulation codes, it will lead to precise predictions of pion counts in the near detector, resulting in a reliable neutrino energy reconstruction.

Method and Background

Pion production in electromagnetic reactions has a long history. One of the leading efforts is due to the Mainz-based partial wave analysis tool MAID, a unitary isobar model that accounts for all known N* and Δ resonances, single-channel unitarity and over years has proven to be a valuable analysis tool for pion photo- and electroproduction. At present, MAID is further developed by the Mainz-Tuzla-Zagreb Collaboration.

MAID approach is suitable for the invariant mass of the πN-system W < 2 GeV and moderate photon virtualities. The project WeakMAID builds upon its predecessor while extending it in several ways. Firstly, weak interaction contains the axial current, additionally to the vector current readily contained in the electromagnetic case. Secondly, the energy spectrum of neutrinos at DUNE extends to 5-6 GeV, so that a connection to high-energy such as Regge theory is necessary. This can be correctly done by implementing  unitarity, analyticity and duality constraints.

Realization

As a partial wave analysis (PWA) tool, WeakMAID is based on the decomposition of scattering amplitudes for weak pion production into multipoles characterized by the angular momentum l, total spin J=l±1/2, total isospin I=1/2,3/2 of the πN-system, as well as the multipolarity (electric E, magnetic M, and longitudinal L) carried by the electro-weak probe. Two sets of multipoles describe the interaction with the hadronic vector and axial current. Additionally, two sets of invariant amplitudes V1-6 for vector and A1-6 for axial current are introduced, as well as center-of-mass CGLN F1-6 and G1-6, respectively, and helicity amplitudes H1-6. 

 

Vector Weak Multipoles (El±, Ml±, Ll±)

Vector Amplitudes (F1-6; V1-6; H1-6)

Axial Weak Multipoles (El±, Ml±, Ll±).

Axial Amplitudes (G1-6; A1-6; H1-6)

Total cross sections