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May 4, 20260 citationsOpen Access

An Empirical Mass Relation among Electroweak Bosons: mH mZ² ≈ 2 mW³

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TITadashige Iwao

Key Points

  • This research aims to explore an empirical mass relation among Standard Model electroweak bosons.
  • Utilized Particle Data Group values for mass calculations (m_H, m_Z, m_W).
  • Calculated the dimensionless ratio I and assessed numerical accuracy.
  • Discussed alternative theoretical frameworks to explain the observed mass relation.
  • The mass relation m_H × m_Z² ≈ 2 m_W³ holds with 0.16% accuracy.
  • The dimensionless ratio I_exp = 2.003 was derived from the empirical relation.
  • The relation connects to the Higgs self-coupling and provides insight into potential theoretical extensions.

Abstract

We report a numerical relation among the masses of the Standard Model electroweak bosons: mH × mZ² ≈ 2 mW³ Using the latest Particle Data Group values (mH = 125. 1 GeV, mZ = 91. 1876 GeV, mW = 80. 379 GeV), this relation is satisfied to 0. 16% accuracy, and the dimensionless ratio I ≡ mH mZ²/mW³ takes the value Iₑxp = 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 cos⁴θW / 2 (accurate at ~2. 4%), where λ is the Higgs self-coupling and θW 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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Cite This Study

Tadashige Iwao (2026) studied this question.

synapsesocial.com/papers/69f838453ed186a739982719https://doi.org/10.5281/zenodo.19962845
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