Fermi's Pontecorvo Mechanism
This mechanism explains neutrino mixing and oscillations through a four-fermion interaction, initially proposed to account for observed neutrino behavior.
📜
The statement of the theorem
Let be the flavor eigenstate vector and be the mass eigenstate vector. The mixing is described by the unitary PMNS matrix : . The effective four-fermion interaction Lagrangian responsible for neutrino oscillations is given by:\n\n$$ \mathcal{L}_{eff} = \frac{G_{F}}{\sqrt{2}} \sum_{f, f'} ( \bar{\nu}_{f} \gamma^{\mu} \nu_{f} ) ( \bar{f} \gamma_{\mu} (1 - \sin^2\theta_W) \nu_{f'} ) + \text{h.c.} \quad \text{where } \nu_{f} = \sum_{i=1}^{3} U_{fi} \nu_{i} \text{ and } \nu_{i} \text{ are mass eigenstates.} \tag{1}