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Factorization vs. Non-Factorization: S-Matrix Corrections for Precision Neutrino Physics

D. Delepine, A. Yebra

Abstract

The standard treatment of neutrino oscillations usually relies on factorization which assumes neutrino production, propagation, and detection are independent processes. As a consequence, the total probability is given by the product of production, oscillation and detection probabilities. As next-generation experiments are bringing neutrino physics to a high level of precision, the validity of this assumption must be checked. We present an S matrix treatment of the entire experimental chain, pion decay, neutrino propagation, and nucleon interaction, as a single, coherent quantum process. Our results reveal non-factorizable terms arising from spin and angular correlations between production and detection final states.In the $ΔL=0$ channel, these corrections introduce a $\sim 1\%$ systematic shift in the energy spectrum and a non-vanishing azimuthal asymmetry, important to be taken into account for precision measurements of $δ_{CP}$. For the $ΔL=2$ Majorana channel, we demonstrate that the S-matrix formalism is generating an azimuthal modulation that provides a direct way to access to the Majorana CP phases, which remain hidden in standard factorized effective mass approximations.

Factorization vs. Non-Factorization: S-Matrix Corrections for Precision Neutrino Physics

Abstract

The standard treatment of neutrino oscillations usually relies on factorization which assumes neutrino production, propagation, and detection are independent processes. As a consequence, the total probability is given by the product of production, oscillation and detection probabilities. As next-generation experiments are bringing neutrino physics to a high level of precision, the validity of this assumption must be checked. We present an S matrix treatment of the entire experimental chain, pion decay, neutrino propagation, and nucleon interaction, as a single, coherent quantum process. Our results reveal non-factorizable terms arising from spin and angular correlations between production and detection final states.In the channel, these corrections introduce a systematic shift in the energy spectrum and a non-vanishing azimuthal asymmetry, important to be taken into account for precision measurements of . For the Majorana channel, we demonstrate that the S-matrix formalism is generating an azimuthal modulation that provides a direct way to access to the Majorana CP phases, which remain hidden in standard factorized effective mass approximations.
Paper Structure (13 sections, 31 equations, 1 table)

This paper contains 13 sections, 31 equations, 1 table.

Table of Contents

  1. Introduction
  2. Factorizable vs. Non-factorizable
  3. The S-Matrix Formalism for $\Delta L=0$
  4. Separation between factorizable and non-factorizable terms
  5. Integrating the phase space
  6. S-formalism for $\Delta L=2$
  7. Experimental prospects
  8. Conclusion
  9. Nuclear form factors
  10. The Vector Form Factors ($F_1^V, F_2^V$)
  11. The Axial Form Factor ($F_A$)
  12. The pseudoscalar form factor $F_P(Q^2)$
  13. Structure Functions