Generalized Lindblad master equation for neutrino evolution

A new theoretical framework, based on the quantum field theory of open systems applied to neutrinos, has been developed. This framework aims to describe the neutrino evolution in external environment, taking into account the effect of neutrino quantum decoherence. We have applied this approach to investigate a novel mechanism for neutrino quantum decoherence, which arises due to the neutrino decay into a lighter neutrino state and a massless particle, as well as the inverse process of absorption of a massless particle by a neutrino. We derived the new generalized Lindblad master equation for the neutrino evolution that accounts for neutrino transitions between states with different momenta. We also demonstrate that studying of neutrino quantum decoherence through this master equation provides a unique possibility to determine or limit the neutrino decay width. On this basis we obtained the constraint on neutrino lifetime <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mfrac><a:mrow><a:msub><a:mrow><a:mi>τ</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msub></a:mrow><a:mrow><a:msub><a:mrow><a:mi>m</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msub></a:mrow></a:mfrac><a:mo>&gt;</a:mo><a:mn>1.83</a:mn><a:mo>×</a:mo><a:msup><a:mrow><a:mn>10</a:mn></a:mrow><a:mrow><a:mo>−</a:mo><a:mn>10</a:mn></a:mrow></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mfrac><a:mrow><a:mi mathvariant="normal">s</a:mi></a:mrow><a:mrow><a:mi>eV</a:mi></a:mrow></a:mfrac></a:mrow></a:math> (for the case of the Dirac neutrino scalar decay and neutrino degenerate hierarchy).