[Paper Review] Weak Pion and Photon Production off Nucleons in a Chiral Effective Field Theory

Brian D. Serot, Xilin Zhang|arXiv (Cornell University)|Nov 26, 2010

Particle physics theoretical and experimental studies9 references3 citations

TL;DR

This paper develops a Lorentz-covariant chiral effective field theory (EFT) including nucleons, pions, deltas, and vector mesons to study weak pion and photon production from nucleons at intermediate energies (E<1 GeV). By incorporating the Δ(1232) resonance explicitly and enforcing chiral symmetry and vector meson dominance, the model ensures current conservation and PCAC, achieving good agreement with bubble-chamber data for pion production at low energies, with next-to-leading-order corrections found to be small.

ABSTRACT

Neutrino-induced pion and photon production from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, and these processes are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo extit{et al.} (MiniBooNE Collaboration), Phys.\ Rev.\ Lett.\ {\bf 100}, 032301 (2008)]. Pion and photon production are investigated at intermediate energies, where the $Δ$ resonance becomes important. The Lorentz-covariant effective field theory contains nucleons, pions, Deltas, isoscalar scalar ($σ$) and vector ($ω$) fields, and isovector vector ($ρ$) fields. The lagrangian exhibits a nonlinear realization of (approximate) $SU(2)_L \otimes SU(2)_R$ chiral symmetry and incorporates vector meson dominance. Power counting for vertices and Feynman diagrams involving the $Δ$ is explained. Because of the built-in symmetries, the vector currents are automatically conserved, and the axial-vector currents satisfy PCAC. The irrelevance of so-called off-shell $Δ$ couplings and the structure of the dressed $Δ$ propagator, which has a pole only in the spin-3/2 channel, are discussed. To calibrate the axial-vector transition current $(N\! \leftrightarrow Δ)$, pion production from the nucleon is used as a benchmark and compared to bubble-chamber data from Argonne and Brookhaven National Laboratories. At low energies, the convergence of our power-counting scheme is investigated, and next-to-leading-order tree-level corrections are found to be very small.

Motivation & Objective

• To develop a consistent Lorentz-covariant effective field theory including the Δ(1232) resonance for weak pion and photon production from nucleons.
• To ensure vector current conservation and axial current PCAC through nonlinearly realized chiral symmetry and vector meson dominance.
• To use pion production as a benchmark to calibrate the axial-vector N→Δ transition current against experimental data.
• To investigate the convergence of the power-counting scheme in the low- and intermediate-energy regime.
• To lay the foundation for future many-body calculations in nuclear matter.

Proposed method

• The model employs a nonlinear realization of approximate SU(2)_L ⊗ SU(2)_R chiral symmetry with explicit nucleons, pions, Δ(1232), σ, ω, and ρ mesons.
• Electroweak currents are derived via the external field procedure, ensuring current conservation and PCAC.
• Vector meson dominance (VMD) generates form factors without phenomenological input, preserving gauge invariance.
• Feynman diagrams are computed through next-to-leading order using a consistent power-counting scheme for vertices and propagators.
• The dressed Δ propagator is constructed with a single pole in the spin-3/2 channel, avoiding off-shell pathologies.
• Cross sections for charged and neutral current pion and photon production are calculated in the lab frame using phase-space integration in terms of invariants Q² and M_πn.

Experimental results

Research questions

• RQ1 How well does a chiral EFT with explicit Δ(1232) resonance describe weak pion production from nucleons at low and intermediate energies?
• RQ2 What is the impact of next-to-leading-order corrections on the calculated cross sections?
• RQ3 How does the model’s power-counting scheme converge in the low-energy regime?
• RQ4 To what extent does the inclusion of VMD and chiral symmetry improve the description of electroweak currents compared to phenomenological models?
• RQ5 Can the model’s predictions for pion production be consistently calibrated to existing bubble-chamber data?

Key findings

• The model achieves good agreement with ANL and BNL bubble-chamber data for pion production at low energies, validating the axial-vector N→Δ transition current.
• Next-to-leading-order tree-level corrections to the pion production amplitude are found to be very small, indicating good convergence of the power-counting scheme.
• The vector currents are automatically conserved and the axial currents satisfy the PCAC condition due to the underlying symmetries of the Lagrangian.
• The dressed Δ propagator contains only a physical pole in the spin-3/2 channel, avoiding unphysical off-shell couplings.
• The use of VMD to generate form factors avoids the need for phenomenological form factors while maintaining current conservation.
• Phase-space boundaries are derived in terms of the invariants Q² and M_πn, enabling precise integration for cross-section calculations.