- #1

paralleltransport

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- TL;DR Summary
- I would like to understand why people say higgs field solves giving mass to particles.

Here's my current understanding of mass terms.

For scalar fields, a mass term flows under RG to larger values in the IR. This implies having mass values in the theory is unnatural because it has to be fine tuned at the UV level to get the correct observed mass at low energy (the term I think is "relevant").

For dirac fermion fields, I am unsure.

For vector potentials that have gauge invariance, adding a mass term breaks the gauge symmetry.

The higgs field ϕϕϕϕ mechanism gives a mass to field αααα by coupling to it via. However, the coupling is relevant and one still has to tune the coupling to fix observables in the IR to the desired value. So in a sense I don't see how it solves the mass problem.

I do see how it solves the gauge invariance problem. Because the higgs breaks spontaneously, you don't need to explicitly break gauge invariance in the UV version of the theory. However, this is a matter of aesthetic, so I'm not sure why it's such a big deal that one needs to write a gauge invariant theory.

Could someone help clarify those 2 points?

ζζξξ

For scalar fields, a mass term flows under RG to larger values in the IR. This implies having mass values in the theory is unnatural because it has to be fine tuned at the UV level to get the correct observed mass at low energy (the term I think is "relevant").

For dirac fermion fields, I am unsure.

For vector potentials that have gauge invariance, adding a mass term breaks the gauge symmetry.

The higgs field ϕϕϕϕ mechanism gives a mass to field αααα by coupling to it via. However, the coupling is relevant and one still has to tune the coupling to fix observables in the IR to the desired value. So in a sense I don't see how it solves the mass problem.

I do see how it solves the gauge invariance problem. Because the higgs breaks spontaneously, you don't need to explicitly break gauge invariance in the UV version of the theory. However, this is a matter of aesthetic, so I'm not sure why it's such a big deal that one needs to write a gauge invariant theory.

Could someone help clarify those 2 points?

ζζξξ