# Why is the mass gap of QCD so important?

## Main Question or Discussion Point

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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malawi_glenn
Homework Helper
One would of course like to have the mathematical theories of physics mathematically proven.

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

malawi_glenn
Homework Helper
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??

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

blechman

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 propogate 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! :)