Dirac Neutrino Mass Formula
The Dirac neutrino mass formula, \frac{eta^2}{2} m^2, relates the neutrino mass to the mixing angle \beta, a key parameter in neutrino physics.
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The statement of the theorem
For a Dirac neutrino mass term , the mass matrix is defined by the coupling between the left-handed and right-handed components of the neutrino field : \n\n$$ \mathcal{L}_{mass} = - \frac{1}{2} \bar{\nu} M \nu^c + \text{h.c.} \tag{10} \text{If the mass is parameterized by a mixing angle } \beta \text{ and mass } m \text{ such that } M \propto \frac{\beta^2}{2} m^2 \text{ (as specified), the effective mass term is:} \tag{11} \mathcal{L}_{eff} = - \frac{\beta^2}{2} m^2 \bar{\nu} \nu^c + \text{h.c.} \tag{12} \text{This structure relates the mass scale } m \text{ to the mixing parameter } \beta. \tag{13}
Source: Wikipedia