The Effect of the Earth Matter on Three Neutrino Oscillations and Sensitivity to CP Phase Parameter

Abstract

We find an analytical expression of neutrino evolution operator in the Earth matter using perturbative approach in the context of three neutrino oscillations. We find that our analytical expression is highly accurate by comparing its results with the numerical solutions of neutrino evolution equation at energy scales relevant for solar, reactor, atmospheric, and accelerator neutrinos. Using our analytical approach we study the accuracy of hypothesis of treating the Earth density piecewise constant. We also study how the Earth matter effect can change the sensitivity to CP phase parameter ${\delta }_{CP}$. Through nadir angle averaged conversion probabilities of neutrino and anti-neutrino, we find that the sensitivity to ${\delta }_{CP}$ is maximum in the energy range 0.2 to 1 GeV and through energy averaged conversion probabilities, we find that the sensitivity is maximum about nadir angle $72.5^{\text{o}}$ for neutrinos oscillating in the Earth matter.

arXiv comment19 pages, 7 figures

References in corpus (9)

• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• Diffractive-Like (or Parametric-Resonance-Like?) Enhancement of the Earth (Day-Night) Effect for Solar Neutrinos Crossing the Earth Core
• Parametric resonance of neutrino oscillations and passage of solar and atmospheric neutrinos through the earth
• Atmospheric neutrinos at Super-Kamiokande and parametric resonance in neutrino oscillations
• Earth regeneration effect in solar neutrino oscillations: an analytic approach
• Atmospheric neutrino oscillations from upward throughgoing muon multiple scattering in MACRO
• Measurement of the ${\nu }_e$ and Total ${}^8$B Solar Neutrino Fluxes with the Sudbury Neutrino Observatory Phase-III Data Set
• A simple analytic three-flavour description of the day-night effect in the solar neutrino flux
• The Flavor Structure of the Three-Site Higgsless Model

Cited by in corpus (1)

• Fast Exact Algorithm for Neutrino Oscillation in Constant Matter Density