On Neutrino Mixing in Matter and CP and T Violation Effects in Neutrino Oscillations

Abstract

Aspects of 3-neutrino mixing and oscillations in vacuum and in matter with constant density are investigated working with a real form of the neutrino Hamiltonian. We find the (approximate) equalities ${\theta }_{23}^m={\theta }_{23}$ and ${\delta }^m=\delta$, ${\theta }_{23}$ (${\theta }_{23}^m$) and $\delta$ (${\delta }^m$) being respectively the atmospheric neutrino mixing angle and the Dirac CP violation phase in vacuum (in matter) of the neutrino mixing matrix, which are shown to represent excellent approximations for the conditions of the T2K (T2HK), T2HKK, NO$\nu$A and DUNE neutrino oscillation experiments. A new derivation of the known relation $\sin 2{\theta }_{23}^m\sin {\delta }^m=\sin 2{\theta }_{23}\sin \delta$ is presented and it is used to obtain a correlation between the shifts of ${\theta }_{23}$ and $\delta$ due to the matter effect. A derivation of the relation between the rephasing invariants which determine the magnitude of CP and T violating effects in 3-flavour neutrino oscillations in vacuum, $J_{\mathrm{CP}}$, and of the T violating effects in matter with constant density, $J_{\mathrm{T}}^m\equiv J^m$, reported in \cite{Krastev:1988yu} without a proof, is presented. It is shown that the function $F$ which appears in this relation, $J^m=J_{\mathrm{CP}}F$, and whose explicit form was given in \cite{Krastev:1988yu}, coincides with the function $\tilde{F}$ in the similar relation $J^m=J_{\mathrm{CP}}\tilde{F}$ derived in \cite{Naumov:1991ju}, although $F$ and $\tilde{F}$ are expressed in terms of different sets of neutrino mass and mixing parameters and have completely different forms.

17 pages, 6 figures, refs added, published in PLB

References in corpus (10)

• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• Physics Potential of a Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• First combined analysis of neutrino and antineutrino oscillations at T2K
• Constraints on Oscillation Parameters from ${\nu }_e$ Appearance and ${\nu }_{\mu }$ Disappearance in NOvA
• First measurement of muon-neutrino disappearance in NOvA
• Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 1: The LBNF and DUNE Projects
• Neutrino Oscillation Physics Potential of the T2K Experiment
• A Generic Diagonalization of the 3X3 Neutrino Mass Matrix and Its Implications on the mu-tau Flavor Symmetry and Maximal CP Violation
• Three Neutrino Oscillations in Matter
• Proposal for an Extended Run of T2K to $20\times 10^{21}$ POT

Cited by in corpus (14)

• Signatures of the genuine and matter-induced components of the CP violation asymmetry in neutrino oscillations
• On the Properties of the Effective Jarlskog Invariant for Three-flavor Neutrino Oscillations in Matter
• Model-independent test of T violation in neutrino oscillations
• On T violation in non-standard neutrino oscillation scenarios
• Sum rules and asymptotic behaviors of neutrino mixing in dense matter
• Do T asymmetries for neutrino oscillations in uniform matter have a CP-even component?
• CP-Violation with Neutrino Disappearance Alone
• Impact of Neutrino Properties and Dark Matter on the Primordial Lithium Production
• T violation without complex entries in lepton mixing matrix
• Radiative corrections to the lepton flavor mixing in dense matter
• Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter
• Analytic formulae for T violation in neutrino oscillations
• Model-independent search for T violation with T2HK and DUNE
• T versus CP effects in DUNE and T2HK