Bound states of massless fermions

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The discussion centers on the implications of massless fermions for bound states, specifically questioning whether the absence of a Higgs mechanism would eliminate bound states in systems like the hydrogen atom. It is suggested that without mass, bound states may not exist, raising concerns about the confinement of quarks if they were massless. The complexities of bound states involving highly relativistic particles are noted, with an emphasis on their potential instability and differing properties compared to conventional systems. Additionally, the conversation touches on chiral symmetry and mass gaps, highlighting the theoretical challenges in understanding these concepts in the context of fermions. Overall, the discussion reveals significant uncertainties in the physics of massless particles and their interactions.
JustinLevy
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If I look at the energy of the hydrogen atom, the energy is proportional to the mass of the electron (or more precisely, the reduced mass). Does this mean that without a Higgs mechanism, there are no bound states of the hydrogen atom? (Or is it just an artifact of a non-relativistic theory that I see no bound states when I let the mass -> 0?)

Second question, if there aren't bound states for that reason, how general is this? For example, if the quarks were truly massless, would that prevent bound states of quarks as well? Or would there still be confinement?
 
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It would certainly be a challenge to create a bound state with a massless particle. The mathematics of Bound states with highly relativistic particles is difficult and controversial and I don't believe there is agreement in the literature. Certainly it would have very different properties than hydrogen and would be highly unstable.

As for the quarks, well yea in reality even without a Higgs mechanism, you won't have exactly zero mass b/c of the chiral symmetry breaking and mass gap issues. But since the mass scales are completely different you'd have again, very different physics than you are used too.
 
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Haelfix said:
even without a Higgs mechanism, you won't have exactly zero mass b/c of the chiral symmetry breaking and mass gap issues.
I'm not sure what you are referring to here, would you mind explaining a bit more to help me understand?

By chiral, do you mean left/right handed? I thought that was not a good symmetry at any energy (ie. it is not a spontaneously broken symmetry). As for mass gap, I've never really understood what motivates that expectation theoretically. Bosons don't necessarily have a mass gap, why should the fermions?
 
It is a spontaneous broken symmetry since you only have pseudoscalar mesons in nature, and no real scalar ones (i.e no positive parity partners for e.g. the pions)

This is a quite good (maybe a bit too technical) article about this:

http://www.fuw.edu.pl/~dobaczew/maub-42w/node10.html
 

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