Graduate Why is the Higgs mechanism needed?

[paralleltransport]

TL;DR

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?
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[valenumr]

I found this site to be easily digestible for almost anyone. There are several other articles the site introduce the necessary background topics as well.

 

[Gaussian97]

I think the fast answer is this:
Gauge bosons and Dirac fermions (which includes all vector bosons we know and all fermions except, maybe, the neutrino) need to be massless in order to maintain Gauge invariance, which is the fundamental principle we use to build the fundamental theories.
Because we know that some of those particles do have a mass, we must find a way to incorporate that into the theory without abandoning the Gauge principle, one of the solutions and the one that fits best with the experiments in the Higgs mechanism. Fine-tuning is another problem, for sure a theory without fine-tuning is usually better (as long as it agrees with the experiments) but without the Higgs field the problem is not fine-tuning, is that almost all particles we know have mass, which is impossible for the Gauge theories.

 

[paralleltransport]

Hi, thanks. So the short answer is aesthetics, correct? In other words, we like gauge invariant theories because they make pretty UV complete theories. I could easily reproduce all observables with effective theories that have fine tuned masses (so the number of fine tuned parameters is the same as the number of coupling strengths that are fine tuned in the gauge invariant theory with the higgs)

 

[ohwilleke]

Hi, thanks. So the short answer is aesthetics, correct?

More than just aesthetics.

In other words, we like gauge invariant theories because they make pretty UV complete theories. I could easily reproduce all observables with effective theories that have fine tuned masses (so the number of fine tuned parameters is the same as the number of coupling strengths that are fine tuned in the gauge invariant theory with the higgs)

If they have intrinsic masses not imparted by a field in theory, your theory won't be gauge invariant, and that causes all sorts of deep problems, not merely aesthetic ones. It isn't easy to come up with a good alternative to a gauge invariant theory that fits other experimental observations.

 

[paralleltransport]

More than just aesthetics.

If they have intrinsic masses not imparted by a field in theory, your theory won't be gauge invariant, and that causes all sorts of deep problems, not merely aesthetic ones. It isn't easy to come up with a good alternative to a gauge invariant theory that fits other experimental observations.

Thank you for the answer. Could you elaborate why not having a gauge invariant theory is a problem? I have access to all the standard textbooks (srednicki, peskin, zee, weinberg) for QFT so even better if you could refer me to introductory material on the literature that discuss this issue.