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Register a new userGeometric phase of neutrinos: differences between Dirac and Majorana neutrinos
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We analize the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. Future experiments, based on interferometry, could reveal the nature of neutrinos.
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In this paper we reply to the comment presented in [1]. In that work the author raises several points about the geometric phase for neutrinos discussed in [2]. He affirms that the calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. He claims that the results are neither gauge invariant nor lepton field rephasing invariant and presents an alternative calculation, solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. Finally he claims that the nontrivial dependence of geometric phase on Majorana CP-violating phase presented in [2] is unphysical and thus unmeasurable. We discuss each of the points raised in [1] and show that they are incorrect. In particular, we introduce geometric invariants which are gauge and reparametrization invariants and show that the omitted term in the Wolfenstein effective Hamiltonian has no effect on them. We prove that the appearance of the Majorana phase cannot be ascribed to a lepton field rephasing transformation and thus the incorrectness of the claim of unphysicality and unmeasurability of the geometric phase. In the end we show that the calculation presented in [1] is inconsistent and based on the erroneous assumption and implementation of the wavefunction collapse. We remark that the geometric invariants defined in the present paper show a difference between Dirac and Majorana neutrinos, since they depend on the CP-violating Majorana phase.
Massive neutrinos can have helicity $s_{parallel} eq -1$. Neutrino helicity changes when the neutrino interacts with an external magnetic field and it is possible that the left-handed neutrinos born inside the Sun or a supernova could leave their sources with a different helicity. Since Dirac and Majorana neutrinos have different cross sections in the scattering on electrons for different neutrino helicities, a change in the final neutrino helicity may generate a different number of events and spectra in terrestrial detectors when astrophysical neutrinos have travelled regions with strong magnetic fields. In this work, we show that looking for these effects in solar neutrinos, it could be possible to set bounds in the neutrino properties such as the neutrino magnetic moment. Furthermore, for neutrinos coming from a supernova, we show that even in the case of an extremely small neutrino magnetic moment, $mu_ u sim 10^{-19}mu_B$, there will be measurable differences in both the number of events and in the spectra of Majorana and Dirac neutrinos.
It is well known that Majorana neutrinos have a pure axial neutral current interaction while Dirac neutrinos have the standard vector-axial interaction. In spite of this crucial difference, usually Dirac neutrino processes differ from Majorana processes by a term proportional to the neutrino mass, resulting in almost unmeasurable observations of this difference. In the present work we show that once the neutrino polarization evolution is considered, there are clear differences between Dirac and Majorana scattering on electrons. The change of polarization can be achieved in astrophysical environments with strong magnetic fields. Furthermore, we show that in the case of unpolarized neutrino scattering onto polarized electrons, this difference can be relevant even for large values of the neutrino energy.
Neutrinos may acquire small Dirac or Majorana masses by new low-energy physics in terms of the chiral gravitational anomaly, as proposed by Dvali and Funcke (2016). This model predicts fast neutrino decays, $ u_ito u_j+phi$ and $ u_itobar{ u}_j+phi$, where the gravi-majorons $phi$ are pseudoscalar Nambu-Goldstone bosons. The final-state neutrino and antineutrino distributions differ depending on the Dirac or Majorana mass of the initial state. This opens a channel for distinguishing these cases, for example in the spectrum of high-energy astrophysical neutrinos. In particular, we put bounds on the neutrino lifetimes in the Majorana case, ${tau_2}/{m_2}> 1.1times 10^{-3}(6.7times 10^{-4})~{rm s/eV}$ and ${tau_3}/{m_3}> 2.2times 10^{-5}(1.3times 10^{-4})~{rm s/eV}$ at 90% CL for hierarchical (degenerate) masses, using data from experiments searching for antineutrino appearance from the Sun.
We study the evolution of massive mixed Dirac and Majorana neutrinos in matter under the influence of a transversal magnetic field. The analysis is based on relativistic quantum mechanics. We solve exactly the evolution equation for relativistic neutrinos, find the neutrino wave functions, and calculate the transition probability for spin-flavor oscillations. We analyze the dependence of the transition probability on the external fields and compare the cases of Dirac and Majorana neutrinos. The evolution of Majorana particles in vacuum is also studied and correction terms to the standard oscillation formula are derived and discussed. As a possible application of our results we discuss the spin-flavor transitions in supernovae.
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