Explanation of quadratic divergence in higgs mechanism

In summary: This can lead to an additional term ##\delta m^2## in the mass of the scalar field, which is proportional to the energy scale and can have a significant impact on the overall mass. These terms are squared because of the nature of the integral.In summary, a quadratic divergence is a mathematical concept in quantum field theory where an integral diverges quadratically in the high energy limit. This can lead to an additional term in the mass of a scalar field, denoted as ##\delta m^2##, which is proportional to the energy scale and can greatly affect the overall mass. These terms are squared due to the nature of the integral. In terms of the standard model, this divergence can introduce a need for fine-tuning,
  • #1
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 [itex] m^2 = m^2_{0} + \delta m^2[/itex], 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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  • #2
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 [itex] m^2 = m^2_{0} + \delta m^2[/itex], 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.
 
  • #3
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?
 
  • #4
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.
 

1. What is the quadratic divergence in the Higgs mechanism?

The quadratic divergence in the Higgs mechanism refers to a mathematical term that arises when calculating the mass of the Higgs boson in the Standard Model of particle physics. It arises due to the interaction between the Higgs field and other particles, causing the mass of the Higgs boson to increase as the energy scale increases.

2. How does the Higgs mechanism explain the origin of mass?

The Higgs mechanism explains the origin of mass by proposing the existence of a field, called the Higgs field, that permeates the universe and interacts with particles to give them mass. The Higgs field is responsible for the Higgs boson, which is a fundamental particle that gives mass to other particles through their interactions with the Higgs field.

3. What is the role of the Higgs boson in the Higgs mechanism?

The Higgs boson is a fundamental particle that is responsible for giving mass to other particles through their interactions with the Higgs field. Without the Higgs boson, the Higgs mechanism would not be able to explain the origin of mass in the universe.

4. How does the quadratic divergence relate to the Higgs boson's mass?

The quadratic divergence arises in the calculation of the mass of the Higgs boson and is a consequence of its interactions with other particles. This divergence results in the mass of the Higgs boson increasing as the energy scale increases, which is a key feature of the Higgs mechanism.

5. What implications does the quadratic divergence have for the Higgs mechanism?

The quadratic divergence poses a challenge for the Higgs mechanism, as it leads to the prediction of very high masses for the Higgs boson at high energy scales. This is known as the hierarchy problem and is an active area of research in particle physics to find a solution or potential new theories that can address this issue.

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