Explanation of quadratic divergence in higgs mechanism

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Discussion Overview

The discussion centers around the concept of quadratic divergence in the context of the Higgs mechanism and its implications for the mass of scalar fields within the Standard Model (SM). Participants explore the mathematical formulation of mass corrections and the potential issues of fine-tuning associated with these divergences.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants seek clarification on the nature of quadratic divergence and its effect on the mass of scalar fields, specifically questioning why mass corrections are expressed as squared terms.
  • There is mention of the Higgs mass being approximately 125 GeV, while the correction term ##\delta m^2## is suggested to be on the order of 1019 GeV, raising concerns about the necessity of fine-tuning the mass parameter ##m_0##.
  • One participant questions whether the small fine-tuning required implies that the Standard Model is invalid or if it could still be valid under the assumption of a higher energy theory, such as supersymmetry.
  • Another participant argues that fine-tuning does not imply invalidity of the Standard Model, noting that the Weinberg mixing angle contributes to this fine-tuning and is not derived from the Standard Model itself.
  • A quadratic divergence is described as being associated with an integral that diverges quadratically in the high-energy limit.

Areas of Agreement / Disagreement

Participants express differing views on the implications of fine-tuning for the validity of the Standard Model. Some suggest that it raises questions about the model's standalone nature, while others argue that it does not imply invalidity and point to potential extensions beyond the Standard Model.

Contextual Notes

There are unresolved assumptions regarding the implications of fine-tuning and the relationship between the Standard Model and potential higher energy theories. The discussion does not reach a consensus on the validity of the Standard Model in light of quadratic divergences.

pleasehelpmeno
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Hi can anyone explain what a quadratic divergence is? and if so how it effects the mass of the scalar field i.e why m^2 = m^2_{0} + \delta m^2, why are these things squared?

Also how would this divergence affect the standard model as a natural concept, because from reading books it would seem that this introduces an intolerable amount of fine tumning making the SM as a standalone seem ridiculous.
 
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pleasehelpmeno said:
Hi can anyone explain what a quadratic divergence is? and if so how it effects the mass of the scalar field i.e why m^2 = m^2_{0} + \delta m^2, why are these things squared?
How much do you know about quantum field theory?

Also how would this divergence affect the standard model as a natural concept, because from reading books it would seem that this introduces an intolerable amount of fine tumning making the SM as a standalone seem ridiculous.
Precision measurements and the newly found particle indicate a Higgs mass ##m \approx 125 GeV##, while ##\delta m^2## is of the order of 1019 GeV, and requires ##m_0## to be fine-tuned to get such a small difference.
 
I no a bit but not much, never covered this before though.

Since the fine tuning is so small then would it imply that the SM is invalid or does it imply that it is valid providing there is a higher energy e.g. super-symmetric model?
 
fine tuning is provided by weinberg mixing angle.it does not imply any invalidity of SM.however it is not a part of SM to derive the angle.beyond the standard model things like supersymmetry and GUT can yield this theoretically.A quadratic divergence is mainly associated with an integral which diverges quadratically in high energy limit.
 

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