[Paper Review] Modelling nuclear effects in neutrino interactions in 1 GeV region

J. T. Sobczyk|ArXiv.org|Jul 11, 2003

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This paper presents a modified Marteau model to compute nuclear effects in neutrino-nucleus interactions at ~1 GeV, incorporating RPA correlations and Δ width modification in nuclear matter. The key result is that RPA reduces π-production cross sections by ~25%, with significant suppression of the transverse component at high energy transfer, while quasi-elastic cross sections remain largely unchanged.

ABSTRACT

We evaluate nuclear effects in neutrino reactions in a framework based on a model proposed by Marteau with quasi-elastic and $Δ$ production processes treated together. Nuclear effects include RPA corrections and $Δ$ width modification in nuclear matter.

Motivation & Objective

• To improve the description of nuclear effects in neutrino-nucleus interactions at ~1 GeV, particularly in the Δ excitation region.
• To address limitations in existing Monte Carlo codes that rely on factorized treatments of neutrino-nucleon interactions and final-state interactions.
• To implement a unified framework treating quasi-elastic and Δ-production processes on equal footing with nuclear medium effects.
• To quantify the impact of RPA correlations and Δ width modification in nuclear matter on inclusive and exclusive cross sections.
• To provide a model suitable for implementation in Monte Carlo event generators with minimal double-counting risk.

Proposed method

• Adopts a relativistic Fermi gas model with a fixed Fermi momentum of 225 MeV, simplifying local density dependence for later inclusion.
• Uses the hadronic tensor formalism with contributions from NN, NΔ, ΔN, and ΔΔ channels, derived from weak current matrix elements with standard form factors.
• Incorporates RPA corrections via imaginary parts of polarization functions, modeling two-body particle-hole excitations and pion/ρ-meson exchange.
• Applies Oset’s results for Δ width modification in nuclear matter, including Pauli blocking and self-energy corrections from πN, NNΔ, and NNN final states.
• Calculates differential and total cross sections for quasi-elastic and π-production processes, decomposing contributions by spin operator (longitudinal, transverse, charge).
• Excludes 2p-2h excitations due to unresolved theoretical challenges, focusing on dominant quasi-elastic and Δ-resonance contributions.

Experimental results

Research questions

• RQ1 How do RPA correlations affect the total and differential cross sections for quasi-elastic and π-production processes in neutrino-nucleus scattering at 1 GeV?
• RQ2 To what extent does the modification of the Δ width in nuclear matter, including Pauli blocking and self-energy shifts, alter the π-production cross section?
• RQ3 What is the relative contribution of longitudinal, transverse, and charge components to the differential cross section, and how are they modified by RPA?
• RQ4 Can the model’s predictions be reconciled with experimental data given the current precision of ~25% in neutrino cross section measurements?
• RQ5 How can this model be adapted for implementation in Monte Carlo event generators without double-counting final-state interactions?

Key findings

• RPA corrections reduce the total π-production cross section by approximately 25% in 16O at 1 GeV neutrino energy.
• The transverse component of the differential π-production cross section is most strongly suppressed by RPA, especially at high energy transfer.
• The longitudinal contribution is reduced by about 50% on average, though minor enhancements are observed at low energy transfer.
• Quasi-elastic total cross sections are only weakly affected by RPA, with no significant shift in the peak structure.
• The inclusion of Δ-h excitation channels increases the cross section above 0.8 GeV, counteracting RPA suppression and bringing results close to the Fermi gas baseline.
• The model shows that RPA and Δ width modification effects are non-trivial and not fully captured by standard final-state interaction models in existing Monte Carlo codes.