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Δ-mediated pion production in nuclei

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Abstract
We present a fully relativistic formalism for describing neutrino-induced Δ -mediated single-pion production in nuclei. We assess the ambiguities stemming from the Δ interactions and quantify the uncertainties in the axial form-factor parameters by comparing with the available bubble-chamber neutrino-scattering data. To include nuclear effects, we turn to a relativistic plane-wave impulse approximation (RPWIA) using realistic bound-state wave functions derived in the Hartree approximation to the σ - ω Walecka model. For neutrino energies larger than 1 GeV, we show that a relativistic Fermi-gas model with appropriate binding-energy correction produces results that are comparable to the RPWIA that naturally includes Fermi motion, nuclear-binding effects, and the Pauli exclusion principle. Including Δ medium modifications roughly halves the RPWIA cross section. Calculations for primary (prior to undergoing final-state interactions) pion production are presented for both electron- and neutrino-induced processes, and a comparison with electron-scattering data and other theoretical approaches is included. We infer that the total Δ -production strength is underestimated by about 20 to 25%, a fraction that is due to the pionless decay modes of the Δ in a medium. The model presented in this work can be naturally extended to include the effect of final-state interactions in a relativistic and quantum-mechanical way.
Keywords
ENERGY, TRANSITION, FORM-FACTORS, NEUTRINO SCATTERING, PI(0) PRODUCTION, BEAM, NU

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MLA
Praet, Christophe, et al. “Δ-Mediated Pion Production in Nuclei.” PHYSICAL REVIEW C, vol. 79, no. 4, 2009, doi:10.1103/PhysRevC.79.044603.
APA
Praet, C., Lalakulich, O., Jachowicz, N., & Ryckebusch, J. (2009). Δ-mediated pion production in nuclei. PHYSICAL REVIEW C, 79(4). https://doi.org/10.1103/PhysRevC.79.044603
Chicago author-date
Praet, Christophe, Olga Lalakulich, Natalie Jachowicz, and Jan Ryckebusch. 2009. “Δ-Mediated Pion Production in Nuclei.” PHYSICAL REVIEW C 79 (4). https://doi.org/10.1103/PhysRevC.79.044603.
Chicago author-date (all authors)
Praet, Christophe, Olga Lalakulich, Natalie Jachowicz, and Jan Ryckebusch. 2009. “Δ-Mediated Pion Production in Nuclei.” PHYSICAL REVIEW C 79 (4). doi:10.1103/PhysRevC.79.044603.
Vancouver
1.
Praet C, Lalakulich O, Jachowicz N, Ryckebusch J. Δ-mediated pion production in nuclei. PHYSICAL REVIEW C. 2009;79(4).
IEEE
[1]
C. Praet, O. Lalakulich, N. Jachowicz, and J. Ryckebusch, “Δ-mediated pion production in nuclei,” PHYSICAL REVIEW C, vol. 79, no. 4, 2009.
@article{692818,
  abstract     = {{We present a fully relativistic formalism for describing neutrino-induced Δ -mediated single-pion production in nuclei. We assess the ambiguities stemming from the Δ interactions and quantify the uncertainties in the axial form-factor parameters by comparing with the available bubble-chamber neutrino-scattering data. To include nuclear effects, we turn to a relativistic plane-wave impulse approximation (RPWIA) using realistic bound-state wave functions derived in the Hartree approximation to the σ - ω Walecka model. For neutrino energies larger than 1 GeV, we show that a relativistic Fermi-gas model with appropriate binding-energy correction produces results that are comparable to the RPWIA that naturally includes Fermi motion, nuclear-binding effects, and the Pauli exclusion principle. Including Δ medium modifications roughly halves the RPWIA cross section. Calculations for primary (prior to undergoing final-state interactions) pion production are presented for both electron- and neutrino-induced processes, and a comparison with electron-scattering data and other theoretical approaches is included. We infer that the total Δ -production strength is underestimated by about 20 to 25%, a fraction that is due to the pionless decay modes of the Δ in a medium. The model presented in this work can be naturally extended to include the effect of final-state interactions in a relativistic and quantum-mechanical way.}},
  articleno    = {{044603}},
  author       = {{Praet, Christophe and Lalakulich, Olga and Jachowicz, Natalie and Ryckebusch, Jan}},
  issn         = {{0556-2813}},
  journal      = {{PHYSICAL REVIEW C}},
  keywords     = {{ENERGY,TRANSITION,FORM-FACTORS,NEUTRINO SCATTERING,PI(0) PRODUCTION,BEAM,NU}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{12}},
  title        = {{Δ-mediated pion production in nuclei}},
  url          = {{http://doi.org/10.1103/PhysRevC.79.044603}},
  volume       = {{79}},
  year         = {{2009}},
}

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