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Register a new userNeutrino amplitude decomposition in matter
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Authors
Hisakazu Minakata
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Observation of the interference between the atmospheric-scale and solar-scale oscillations is one of the challenging and tantalizing goals of the ongoing and upcoming neutrino experiments. An inevitable first step required for such analyses is to establish the way of how the oscillation $S$ matrix can be decomposed into the atmospheric and solar waves, the procedure dubbed as the amplitude decomposition. In this paper, with use of the perturbative framework proposed by Denton et al. (DMP), we establish the prescription for amplitude decomposition which covers the whole kinematical region of the terrestrial neutrino experiments. We analyze the limits to the atmospheric- and solar-resonance regions to argue that the dynamical two modes of the DMP decomposition can be interpreted as the matter-dressed atmospheric and solar oscillations. The expressions of the oscillation probability, which are decomposed into the non-interference and interference terms, are derived for all the relevant flavor oscillation channels. Through construction of the DMP decomposition, we reveal the nature of $psi$ ($theta_{12}$ in matter) symmetry as due to the $S$ matrix rephasing invariance. A new picture of the DMP perturbation theory emerged, a unified perturbative framework for neutrino oscillation in earth matter.
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Observation of the interference between the atmospheric and solar oscillation waves with the correct magnitude would provide another manifestation of the three-generation structure of leptons. As a prerequisite for such analyses we develop a method for decomposing the oscillation $S$ matrix into the atmospheric and solar amplitudes. Though the similar method was recently proposed successfully in vacuum, once an extension into the matter environment is attempted, it poses highly nontrivial problems. Even for an infinitesimal matter potential, inherent mixture of the atmospheric and solar oscillation waves occurs, rendering a simple extension of the vacuum definition untenable. We utilize general kinematic structure as well as analyses of the five perturbative frameworks, in which the nature of matter-dressed atmospheric and solar oscillations are known, to understand the origin of the trouble, how to deal with the difficulty, and to grasp the principle of decomposition. Then, we derive the amplitude decomposition formulas in these frameworks, and discuss properties of the decomposed probabilities. We mostly discuss the $ u_{mu} rightarrow u_{e}$ channel, but a comparison with the $ u_{mu} rightarrow u_{tau}$ channel reveals an interesting difference.
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.
We review the propagation of light neutrinos in matter assuming that their mixing with heavy neutrinos is close to present experimental limits. The phenomenological implications of the non-unitarity of the light neutrino mixing matrix for neutrino oscillations are discussed. In particular we show that the resonance effect in neutrino propagation in matter persists, but for slightly modified values of the parameters and with the maximum reduced by a small amount proportional to the mixing between light and heavy neutrinos squared.
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.
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