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Basic Concepts in Nuclear Physics: Theory, Experiments and Applications pp 3–54Cite as

Neutrinos in Nuclear Physics: RPA, MEC, 2p2h (Pionic Modes of Excitation in Nuclei)

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 182))

Abstract

This chapter is devoted to the study of weak interactions on nucleons and nuclei. I pay a special attention to the study of neutrino and antineutrino quasi-elastic reactions in nuclei , which are of the greatest importance for neutrino oscillation experiments, and crucial to achieve the precision goals required to make new discoveries, like the CP violation in the leptonic sector, possible. In particular, I discuss RPA correlations and 2p2h (multi-nucleon) effects on charged-current neutrino-nucleus reactions, and the influence of these nuclear effects on the recently measured MiniBooNE flux folded differential cross sections, and on the so-called nucleon axial mass puzzle. The modification of the nucleon-nucleon interaction inside of a nuclear medium , specially in the spin-isospin channel, will be also studied, since it plays a central role in understanding these nuclear effects. Other physical processes involving electrons and muons which are sensitive to this part of the interaction are also discussed, underlying the importance of the medium corrections also in these systems.

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Notes

  1. 1.

    The value of \(M_A\) extracted from early CCQE measurements on deuterium and, to a lesser extent, hydrogen targets is \(M_A = 1.016 \pm 0.026\) GeV [10], which is in excellent agreement with the pion electro-production result, \(M_A = 1.014 \pm 0.016\) GeV, obtained from the nucleon axial radius [7, 11]. Furthermore, NOMAD also reported in 2008 a small value of \(M_A = 1.05 \pm 0.02~(\mathrm{stat})~\pm 0.06~ \mathrm{(syst)}\) GeV [12].

  2. 2.

    Medium polarization or collective RPA correlations account for the change of the electroweak coupling strengths, from their free nucleon values, due to the presence of strongly interacting nucleons [16, 17].

  3. 3.

    A useful expression needed to evaluate the pion self-energy through \(\varDelta h\) excitation is given by the closure property,

    figure a

    in Cartesian basis.

  4. 4.

    Note that the lowest order contribution to \(\varGamma \) is essentially given by the imaginary part of the first \(\mu \)-selfenergy diagram depicted in Fig. 13, when the ph excitation and the outgoing neutrino are put on shell. Up to some kinematical corrections, this imaginary part is given by the imaginary part of the Lindhard function \(\bar{U}(p_\nu -p_\mu )\), which accounts for the ph excitation, and by \(\overline{\sum }\sum |T|^2\) which accounts for transition squared operator [51].

  5. 5.

    Note that in (53) the second term of (9) has not been included because it does not provide imaginary part for \(q^0=E_\mu -E_\nu > 0\).

  6. 6.

    This is taken into account by means of the factor \(1-n_2(k)\) in the Lindhard function of (53).

  7. 7.

    See [30] for more details, both of the model and its comparison to experimental data.

  8. 8.

    The elementary pion production cross sections \(\sigma _{ep}\) and \(\sigma _{en}\) can be found for instance in [68].

  9. 9.

    Neutral current driven QE processes were studied in [65].

  10. 10.

    Theoretical uncertainties of the model are estimated in [95], where the deviations of the predictions of the many body framework of [17] from those obtained within a simple Fermi gas model are also quantified.

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Acknowledgments

This research has been supported by the Spanish Ministerio de Economía y Competitividad and European FEDER funds under the contracts FIS2011-28853-C02-02, FIS2014-51948-C2-1-P, FIS2014-57026-REDT and SEV-2014-0398 (MINECO), by Generalitat Valenciana under contract PROMETEOII/2014/0068 and by the EU HadronPhysics3 project, grant agreement no. 283286.

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  1. Instituto de Física Corpuscular (IFIC), Institutos de Investigación de Paterna, Centro Mixto CSIC-Universidad de Valencia, Aptd. 22085, 46071, Valencia, Spain

    J. Nieves

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  1. Faculty of Experimental Sciences, University of Huelva, Huelva, Spain

    José-Enrique García-Ramos

  2. Faculty of Physics, University of Seville, Seville, Spain

    Clara E. Alonso

  3. Faculty of Physics, University of Seville, Seville, Spain

    María Victoria Andrés

  4. Faculty of Experimental Sciences, University of Huelva, Huelva, Spain

    Francisco Pérez-Bernal

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Nieves, J. (2016). Neutrinos in Nuclear Physics: RPA, MEC, 2p2h (Pionic Modes of Excitation in Nuclei). In: García-Ramos, JE., Alonso, C., Andrés, M., Pérez-Bernal, F. (eds) Basic Concepts in Nuclear Physics: Theory, Experiments and Applications. Springer Proceedings in Physics, vol 182. Springer, Cham. https://doi.org/10.1007/978-3-319-21191-6_1

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