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Torsional modulation of atmospheric neutrino oscillation

Riya Barick, Amitabha Lahiri

Abstract

Fermions act as sources of spacetime torsion. However, this torsion is non-dynamical and can be eliminated using its equations of motion. The resulting theory features an effective four-fermion interaction in a torsion-free background. Generically this interaction is non-universal and violates parity. When neutrinos propagate through matter, they experience the effect of this geometrical interaction, which is similar to the MSW effect, but diagonal in the mass basis. Since this quartic interaction term varies linearly with matter density, its effect will be more prominent for atmospheric neutrinos specially for upward going atmospheric neutrinos. We investigate the effect of spacetime geometry on $ν_μ\to ν_τ$ and $ν_μ\to ν_e$ conversion probability and $ν_μ$ survival probability, by solving the Schrödinger equation using the {Preliminary Reference Earth Model (PREM)} density profile of the Earth. We also study the dependence of atmospheric neutrino oscillation probability on the CP phase angle in presence of this effect. We further provide a discussion of the MSW and parametric resonances in presence of the geometrical interaction.

Torsional modulation of atmospheric neutrino oscillation

Abstract

Fermions act as sources of spacetime torsion. However, this torsion is non-dynamical and can be eliminated using its equations of motion. The resulting theory features an effective four-fermion interaction in a torsion-free background. Generically this interaction is non-universal and violates parity. When neutrinos propagate through matter, they experience the effect of this geometrical interaction, which is similar to the MSW effect, but diagonal in the mass basis. Since this quartic interaction term varies linearly with matter density, its effect will be more prominent for atmospheric neutrinos specially for upward going atmospheric neutrinos. We investigate the effect of spacetime geometry on and conversion probability and survival probability, by solving the Schrödinger equation using the {Preliminary Reference Earth Model (PREM)} density profile of the Earth. We also study the dependence of atmospheric neutrino oscillation probability on the CP phase angle in presence of this effect. We further provide a discussion of the MSW and parametric resonances in presence of the geometrical interaction.

Paper Structure

This paper contains 14 sections, 53 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Fermions and torsion
  3. Neutrino oscillation due to torsional interaction
  4. Effect of the torsional interaction on oscillograms
  5. $P(\nu_\mu \to \nu_e)$
  6. $P(\nu_\mu \to \nu_\mu)$
  7. $P(\nu_\mu \to \nu_\tau)$
  8. Changes in probabilities
  9. MSW and Parametric resonances
  10. Mikheyev-Smirnov-Wolfenstein resonance
  11. Parametric resonance
  12. Resonance for three flavors
  13. Summary and outlook
  14. Analytical expressions

Figures (8)

  • Figure 1: Oscillograms for the $\nu_\mu \to \nu_e$ conversion probability for NH and IH. The values of $\lambda^2$ used for these are mentioned at the top of the oscillograms.
  • Figure 2: Oscillograms for $\nu_\mu$ survival probability for SI and including the effect of the geometrical quartic interaction for both NH and IH.
  • Figure 3: Oscillograms for $\nu_\mu \to \nu_\tau$ conversion probability for SI and including the effect of torsional four-fermion interaction for both NH and IH.
  • Figure 4: The difference in the $\nu_\mu$ survival probability $\Delta P_{\mu \mu}=P^{\lambda\neq0}_{\mu \mu}-P^{\lambda=0}_{\mu \mu}$ in the $(E,\theta_\nu)$ plane for $\lambda^2=0.1~ G_F$ and $-0.1~ G_F\,.$
  • Figure 5: The difference in the $\nu_\mu \to \nu_e$ conversion probability $\Delta P_{\mu e}=P^{\lambda\neq0}_{\mu e}-P^{\lambda=0}_{\mu e}$ in the $(E,\theta_\nu)$ plane for $\lambda^2=0.1~ G_F$ and $-0.1~ G_F\,.$
  • ...and 3 more figures