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Particle Mass Formula

The Standard Model predicts particle masses through equations involving Higgs boson interactions and gauge couplings, e.g., \frac{m_f}{2} = \frac{v^2}{2 an( heta_W)}.
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The statement of the theorem

For a fundamental fermion ff with corresponding Yukawa coupling yfy_f, the mass term mfm_f arises from the interaction Lagrangian LYukawa=−yfψˉLΦψR+h.c.\mathcal{L}_{Yukawa} = -y_f \bar{\psi}_L \Phi \psi_R + h.c.. After spontaneous symmetry breaking, the Higgs field Φ\Phi acquires a vacuum expectation value ⟨Φ⟩=v/2\langle \Phi \rangle = v / \sqrt{2}. The resulting mass formula is:\nmf=yfv2m_f = \frac{y_f v}{\sqrt{2}} \nFor charged leptons, me=yev/2m_e = y_e v / \sqrt{2}. For quarks, mq=yqv/2m_q = y_q v / \sqrt{2}. The coupling yfy_f is determined by the ratio of the mass to the vacuum expectation value.
Source: Wikipedia