Time Evolution of Lepton Number Carried by Majorana Neutrinos
Abstract
We revisit the time evolution of the lepton family number for a SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the lefthanded current of the neutrino family. For this work we assume the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number is evolved. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and nonrelativistic neutrinos. The nonrelativistic region is of particular interest for the Cosmic Neutrino Background predicted from big bang models. In that region we find the lepton family numbers are sensitive to Majorana and Dirac phases, the absolute mass, and mass hierarchy of neutrinos.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 DOI:
 10.48550/arXiv.2101.07751
 arXiv:
 arXiv:2101.07751
 Bibcode:
 2021arXiv210107751S
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Experiment
 EPrint:
 20 pages, 7 figures. arXiv admin note: text overlap with arXiv:2004.07664. In v3,references are corrected. In v4, Fig.7 is added. In v6,the typos in Eq.(24),(2933), and (90) are corrected. In v7,Eq.(20) and an author address are corrected