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In lecture today we were reviewing the QCD lagrangian, and discussing hadronic wavefunctions. My lecturer said that QCD alone allows for states of colored hadrons, however because we do not see anything like this in nature, we then also simply demand that every hadronic wavefunction be an $SU(3)$ colour singlet. For the same reason (we don't observe long range strong interactions) we deny the existance of the singlet gluon.

Is this QCD + this phenomenological-singlet-heuristic approach still the best way of understanding confinement, or is there a better way?

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  • $\begingroup$ have a look here hyperphysics.phy-astr.gsu.edu/hbase/Particles/quark.html#c6 $\endgroup$ – anna v Mar 15 at 5:13
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    $\begingroup$ @annav This link explains why confined quarks stay confined. It does not explain why free quarks don't exist in the first place, which I believe is what the OP is asking. $\endgroup$ – safesphere Mar 15 at 5:49
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    $\begingroup$ @s It explains how the potential grows with distance, and for quarks to be free they need measurable distance, where the attraction is enormous. Only in cosmological times can there be quark gluon plasma with the quarks an gluons "free", i.e not in a hadron. In LHC scatteirn with ions they claim quark gluon plasmal but for tiny delta(t) . it is not an answer, it is a relevant background $\endgroup$ – anna v Mar 15 at 6:11
  • $\begingroup$ This talk give a review arxiv.org/abs/1007.0531 "Understanding Confinement in QCD: Elements of a Big Picture" $\endgroup$ – anna v Mar 15 at 11:56
  • $\begingroup$ @anna v does the lagrangian itself lead to this potential? I was told that was a toy model $\endgroup$ – Craig Mar 15 at 15:31
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If the question is "Does QCD predict confinement?" then the answer seems to be yes, based on numerical studies. For example, https://arxiv.org/abs/1807.01673 says,

Lattice QCD simulations provided... overwhelming... numerical evidence that color confinement is encoded in the QCD Lagrangian. ...the field generated by two opposite static color sources [is] concentrated in a linear structure that connects the two static sources. ...The existence of the color flux tube provides an intuitive explanation for the linearly rising potential between two opposite static color sources...

If the question is "Do we understand why QCD predicts confinement?" then the answer is no, at least not completely. The status of this question is reviewed in Greensite (2011), An Introduction to the Confinement Problem, https://www.springer.com/us/book/9783642143816, which includes an in-depth discussion of various inequivalent definitions of confinement.

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