Abstract
The geometric phase for neutrinos propagating in an adiabatically varying magnetic field in matter is calculated. It is shown that for neutrino propagation in sufficiently large magnetic field the neutrino eigenstates develop a significant geometric phase. The geometric phase varies from 2$\pi$ for magnetic fields $\sim$ fraction of a micro gauss to $\pi$ for fields $\sim 10^7$ gauss or more. The variation of geometric phase with magnetic field parameters is shown and its phenomenological implications are discussed.
Highlights
The existence of non-zero neutrino mass is so far the only experimental proof [1] of physics beyond standard model
Many theoretical considerations [3,4,5,7] which utilize physics beyond minimally extended standard model put much more stronger upper bound on the neutrino magnetic moments, as large as ≈ 10−14μB for a Dirac neutrino and ≈ 10−12 − 10−10μB for a Majorana neutino
A particular case of interest is the transverse precession of the magnetic field, which contributes maximum to the geometric phase for a given field strength
Summary
The existence of non-zero neutrino mass is so far the only experimental proof [1] of physics beyond standard model. Okun et al [13] included matter effects and showed that it results in the suppression of νeL → νeR transitions It was soon realised [9,10,14] that the spin-flavor precession of the neutrinos can lead to resonant conversion νe → νμ,τ. Naumov [21] calculated Berry phase for a three-flavor Dirac neutrino system as the neutrino propagation occurs in a medium whose density and element composition varies cyclically with distance He et al [22] generalised [21] and studied Berry phase in neutrino oscillations for both Dirac and Majorana neutrinos including active and active-sterile neutrino mixing and non-standard interactions. We write transition probabilty P (νL → νR) in terms of geometric phase and analyse the values of geometric phase which lead to resonance
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