We report a mass relation for electroweak bosons, suggesting paths for theoretical investigation.
We report a numerical relation among the masses of the Standard Model electroweak bosons: m_H × m_Z² ≈ 2 m_W³ Using the latest Particle Data Group values (m_H = 125.1 GeV, m_Z = 91.1876 GeV, m_W = 80.379 GeV), this relation is satisfied to 0.16% accuracy, and the dimensionless ratio I ≡ m_H m_Z²/m_W³ takes the value I_exp = 2.003. We emphasize that this relation is NOT a theoretical identity of the Standard Model: it is equivalent to the empirical near-equality λ ≈ g² cos⁴θ_W / 2 (accurate at ~2.4%), where λ is the Higgs self-coupling and θ_W is the Weinberg angle. The relation is therefore analogous in status to the Koide formula for charged-lepton masses---a precise empirical regularity awaiting theoretical explanation. We document the numerical accuracy, the equivalent forms, and discuss possible theoretical avenues including extended custodial symmetry, gauge-Higgs unification, and conformal extensions of the Standard Model.
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Tadashige Iwao (2026) studied this question.
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