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Fermi Interaction

The Fermi interaction describes the weak interaction between particles, mediated by the W and Z bosons, represented by a specific mathematical formula.
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The statement of the theorem

The effective low-energy Fermi interaction, describing weak processes at energy scales E≪MW,MZE \ll M_W, M_Z, is represented by the four-fermion Lagrangian density LFermi\mathcal{L}_{Fermi}: \nLFermi=−GF2[JCCμJCCμ+JNCμJNCμ]\mathcal{L}_{Fermi} = -\frac{G_F}{\sqrt{2}} \left[ J^{\mu}_{CC} J^{\mu}_{CC} + J^{\mu}_{NC} J^{\mu}_{NC} \right] \nWhere GFG_F is the Fermi constant, and the charged and neutral current four-fermion currents are defined as: \nJCCμ=νˉeγμ1−γ52e+μˉγμ1−γ52μ†+…J^{\mu}_{CC} = \bar{\nu}_e \gamma^{\mu} \frac{1 - \gamma_5}{2} e + \bar{\mu} \gamma^{\mu} \frac{1 - \gamma_5}{2} \mu^{\dagger} + \dots \nThis approximation arises from the WW and ZZ boson propagators being approximated by g2M2−q2≈g2M2\frac{g^2}{M^2 - q^2} \approx \frac{g^2}{M^2}.
Source: Wikipedia