Why is the mass gap of QCD so important?

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Discussion Overview

The discussion revolves around the significance of the mass gap in Quantum Chromodynamics (QCD) and its implications for understanding the strong nuclear force. Participants explore the necessity of proving the existence of a mass gap, its connection to confinement, and the potential consequences if such a gap did not exist.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question the importance of the mass gap in QCD, asking whether the successes of QCD would remain intact without the existence of glueballs.
  • Others express a desire for mathematical proofs of physical theories, specifically regarding the mass gap in QCD.
  • There is a discussion about the implications of a mass gap, with questions raised about what would happen if QCD lacked a mass gap.
  • One participant provides an explanation that links the mass gap to confinement, suggesting that the existence of a mass gap indicates that gluons cannot propagate long distances, thereby leading to a short-ranged force.
  • A request for references on the QCD mass gap indicates a desire for deeper understanding and further reading on the topic.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the necessity and implications of the mass gap in QCD. Participants express uncertainty and seek clarification on the connections between the mass gap and the properties of the strong nuclear force.

Contextual Notes

Participants note that the motivations for the mass gap problem are not fully addressed in existing literature, leading to further questions about the relationship between the mass gap and the short-range nature of the nuclear force.

franoisbelfor
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Ed Witten was essential in organizing the 1 million dollar prize for clarification of the mass gap in QCD that is offered by the Clay institute.

But why is this issue so important? Wouldn't all the successes of QCD stay also if no glueballs existed?

Can somebody explain why Witten wants the existence of a mass gap proven?

François
 
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One would of course like to have the mathematical theories of physics mathematically proven.
 
malawi_glenn said:
One would of course like to have the mathematical theories of physics mathematically proven.

Ok, but why do we *need* a mass gap in QCD? What are its implications?
What would happen if QCD had no mass gap?

François
 
franoisbelfor said:
Ok, but why do we *need* a mass gap in QCD? What are its implications?
What would happen if QCD had no mass gap?

François

have you read the formulation and motivation for the problem given on the clay inst. homepage??
 
malawi_glenn said:
have you read the formulation and motivation for the problem given on the clay inst. homepage??

Yes, the only hint I got was that the mass gap is "necessary to explain why the nuclear force is strong but shortranged". (The rest of the text is not about motivation, but only about why the problem is hard.)

But why is QCD shortranged only if there is a mass gap? How do the two aspects connect?

François
 
Here's a slightly oversimplified answer:

The statement that there is a "mass gap" is the statement that the lowest eigenstates of the QCD Hamiltonian are the vacuum and a massive state (that is, state with finite nonzero energy; a glueball) - there is nothing in between. However, the degrees of freedom in QCD are the gluons, which are massless (this is PURE Yang-Mills, no fermions).

SO: proving that there is a mass gap in the spectrum is a proof of confinement: that is, the (massless) gluon states are NOT stationary states of the Hamiltonian, and therefore cannot propagate long distances at the speed of light, like the photons of QED. This is the "proof" that a mass gap in QCD implies a short-ranged force, even though the gluons are massless. The effective "strong nuclear force" would be mediated by glueballs in a sort-of Yukawa-like interaction, with an exponentially suppressed potential.

Hope that gives you at least SOME motivation. It's a little sloppy, but perhaps a good first start.
 
Do you know any good reference where I could read more about the QCD mass gap in more detail? (Book, chapter, revieiw?)

Thanks a lot! :)
 

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