Optimizing the description of the Delta region in the Ghent Hybrid model for single-pion production

Abstract

Single-pion production is an important contribution to the total neutrino-nucleus interaction cross section in accelerator-based neutrino oscillation experiments. The goal of this paper is to improve the Ghent model in the Delta resonance region by incorporating as many physical constraints as possible while keeping the number of fitted parameters as low as possible. A multipole decomposition of the model is performed allowing the use of $K$-matrix theory to unitarize the background contributions. Watson's theorem is enforced by consistently modifying both the Delta and background contributions across all multipoles. Furthermore, the decay width and form factors of the Delta contribution are modified to ensure compliance with Watson's theorem, while the model is extended to include $ρ$- and $ω$-exchange diagrams. These adjustments are compared with other pion production models, as well as with CLAS pion electroproduction data on the nucleon. The results show considerable improvement in the description of the Delta peak region.

Figures (12)

• Figure 1: Schematic representation of single-pion production in the CMS.
• Figure 2: $s$-channel (left) and $u$-channel (right) diagrams of the resonances in the Ghent model.
• Figure 3: Background terms computed from the Chiral Perturbation Theory Lagrangian of Ref. Hernandez_HNVoffnucleon. The diagrams in the top row represent the $s$-channel (left) nucleon pole and the $u$-channel (right) crossed nucleon pole. The bottom row shows the contact term (left), pion pole (central) and $t$-channel or pion-in-flight contribution (right).
• Figure 4: $t$-channel meson-exchange diagrams for the $\rho$ (left) and $\omega$ meson (right).
• Figure 5: The phase $\delta_{\Delta}$ computed with the fit of $\Gamma_{\Delta}$ of Eq. (\ref{['eq: width delta from P33']}) in function of $W$. The green dashed line is the phase obtained with the original Ghent model Raul_Hybrid_model. The data for the pion-nucleon scattering phase is identical to that used for the unitarization of the background diagrams.