# What is a quark condensate?

1. What is a quark condensate? is it a bound state between 2 quarks? can we have 3(or more)-quarks condensate?
2. What mediates the interaction between the constituents of the condensate?
3. Are the constituents of the condensate always fermions?
-
I've been planning on asking about properties of QCD spectrum for some time now. It's good that someone else is asking this too so that I won't have to spam the site by dozens of questions :) +1 –  Marek Aug 18 '11 at 6:48
I believe the quark condensate is essentially analogous to a superconductor, or a superfluid of fermionic atoms. Your fermionic system has bosonic excitations which Bose-Einstein condense. The usual picture is that your fermions form bound pairs, which are bosons and these condense (but this is not always accurate - you can't always find well defined pairs). No 3-quark condensate because thats fermionic. The force involved in pairing is the strong force. You can have a bosonic condensate - thats just the usual superfluid or spontaneous symmetry breaking. –  BebopButUnsteady Aug 18 '11 at 13:33
@BebopButUnsteady Not sure I understood your explanation, but anyway, if no 3 quarks can form a condensate, can 4 quarks do ? –  Revo Aug 18 '11 at 14:15
@Revo: the explanation is that this should be similar to usual explanation of superconduction by B-E condensation of Cooper pairs. In QCD the role of Cooper pairs is taken on by pseudoscalar mesons ($\pi$ and the rest of the family). Now, B-E condensation requires (at least approximately) massless particles which is true for pseudoscalar mesons since they are Goldstone bosons (assuming chiral symmetry among flavors). My guess would be that exotic stuff such as tetraquarks etc. have masses that can't be neglected and so can't condense in this way. –  Marek Aug 18 '11 at 14:45

The quark condensate is the vacuum expectation $\langle 0|\bar{\psi}\psi|0\rangle$ responsible for the breakdown of the chiral symmetry in QCD. Its importance in QCD is by being one of the main contributrs to the Shifman, Vainshtein, Zakharov sum rule, please see for example equation 30 in the following review article by: Colangelo and Khodjamirian on QCD sum rules. It's value was already known in the pre-QCD era, please see equation 47 in the same article.