Why Higgs produces different masses for electron and muon

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Discussion Overview

The discussion centers around the mechanism by which the Higgs field imparts mass to elementary fermions, specifically focusing on the differing masses of the electron and muon. Participants explore theoretical implications and the nature of mass generation within the Standard Model, addressing both conceptual and technical aspects.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that while the electron and muon share the same charge and coupling to the electroweak interaction, their differing masses raise questions about the Higgs mechanism's role in mass generation.
  • Another participant states that the interaction terms between the Higgs field and fermions have independent coupling parameters, suggesting a complexity in the mass generation process.
  • A different viewpoint emphasizes that the common assertion that the Higgs field "gives mass" to fermions is misleading, arguing that the mass term is a product of the Higgs field's value and a constant unique to each particle, which remains of unknown origin.
  • Some participants express dissatisfaction with the current understanding, describing the situation as "ugly" and unsatisfactory, particularly regarding the implications of renormalization in the context of fermion masses.
  • One participant suggests that the Standard Model can accommodate fermion masses without the Higgs mechanism, but this leads to complications when renormalization is considered, ultimately preferring to view the mass as solely arising from the Higgs field.

Areas of Agreement / Disagreement

Participants express a range of views regarding the Higgs mechanism and its implications for mass generation, with no consensus reached on the nature of the mass terms or the role of the Higgs field. The discussion remains unresolved, highlighting differing perspectives on the theoretical framework.

Contextual Notes

Participants acknowledge limitations in the current understanding, including the dependence on unknown constants and the implications of renormalization on mass terms. The discussion reflects ongoing uncertainties in the theoretical landscape of particle physics.

bcrowell
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Elementary fermions get their mass from the Higgs field. The electron and the muon have the same charge, i.e., the same coupling to the electroweak interaction. If these two particles are identical except for mass, then how can the Higgs mechanism give rise to different masses for them?
 
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All interaction terms Higgs field <-> fermions have independent coupling parameters.
 
The popular notion that the Higgs field "gives mass" to fermions is misleading. The mass term is actually a product vC where v is the value of the Higgs field (246 GeV) and C is a constant different for each particle and of unknown origin. The Higgs field v only permits the masses to be nonzero. Their actual values depend on BSM physics which gives them mass, encapsulated in the C's.
 
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Thanks for the replies. That seems like an extremely ugly and unsatisfactory situation.
 
Ugly it is.

To be fair, the SM accommodates fermion masses even without the Higgs mechanism, provided you don't need to renormalize. When you renormalize, you get the condition that the mass from the Higgs mechanism is proportional to the de novo mass, which is even uglier, so most folks prefer to think that the non-Higgs component of the mass is zero, and the only mass comes from the Higgs.

So essentially, you replace a bunch of random masses in the theory with a bunch of random Yukawa couplings in the theory.
 

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