Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSymmetries of neutrino oscillations in vacuum, matter, and approximation schemes
121
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries. We elucidate the $2^7=128$ symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an additional set of $2^7=128$ symmetries exist of the matter parameters for a total of $2^{14}=16,384$ symmetries of the vacuum and/or matter parameters in the oscillation probabilities in matter. Due to the complexity of the exact expressions for neutrino oscillations in matter, we show that under certain assumptions, approximate expressions have at most $2^6=64$ additional symmetries of the matter parameters for a total of $2^{13}=8,192$ symmetries. We investigate which of these symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.
rate research
Read More
In a previous paper, the author proposed Symmetry Finder (SF) method for hunting symmetries in neutrino oscillation in matter, which essentially identifies a symmetry in the diagonalized Hamiltonian in matter. It was successfully applied to Denton {it et al.} (DMP) perturbation theory to identify the eight 1-2 state exchange symmetries. In this paper, we apply the SF method to the atmospheric-resonance perturbation theory and uncover the sixteen 1-3 state exchange symmetries. Meanwhile, an alternative method for finding symmetry has been discussed. If a symmetry in the vacuum part of the Hamiltonian is found, it can be regarded as the symmetry of the total Hamiltonian because the matter term is invariant, the vacuum symmetry (VS) approach. We discuss the relationship between these two methods. One of the key questions is whether the VS method can reproduce the symmetries obtained by the SF method, to which several counter arguments are presented. Moreover, we argue that the newly found 1-3 state exchange symmetries add even more difficulties. The way how the VS method could make the goal are discussed.
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{alpha i}$ (for $alpha = e, mu, tau$ and $i = 1, 2, 3$). When the matter parameter $a equiv 2sqrt{2} G^{}_{rm F} N^{}_e E$ is taken as an independent variable, a complete set of first-order ordinary differential equations for $widetilde{m}^2_i$ and $|V^{}_{alpha i}|^2$ have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the continuous symmetries characterized by one-parameter Lie groups and the discrete symmetry associated with the permutations of three neutrino mass eigenstates. The implications of these symmetries for solving the differential equations and looking for differential invariants are discussed.
We comment on the paper On application of the time-energy uncertainty relation to Mossbauer neutrino experiments (see arXiv: 0803.1424) in which our paper Time-energy uncertainty relations for neutrino oscillation and Mossbauer neutrino experiment (see arXiv: 0803.0527) has been criticized. We argue that this critique is a result of misinterpretation: The authors of (arXiv: 0803.1424) do not take into account (or do not accept) the fact that at present there exist different schemes of neutrino oscillations which can not be distinguished in usual neutrino oscillation experiments. We stress that a recently proposed Mossbauer neutrino experiment provides the unique possibility to discriminate basically different approaches to oscillations of flavor neutrinos.
We study neutrino oscillations in a medium of dark matter which generalizes the standard matter effect. A general formula is derived to describe the effect of various mediums and their mediators to neutrinos. Neutrinos and anti-neutrinos receive opposite contributions from asymmetric distribution of (dark) matter and anti-matter, and thus it could appear in precision measurement of neutrino or anti-neutrino oscillations. Furthermore, the standard neutrino oscillation can occur from the symmetric dark matter effect even for massless neutrinos.
Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2x2 matrices. The final result for the oscillation probabilities is obtained directly in the conventional parametric form as in the vacuum but with explicit simple modification of two mixing angles ($theta_{12}$ and $theta_{13}$) and mass eigenvalues.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
