Instanton effects on condensates: (pseudo)scalars, (pseudo)vectors, tensor

Question

I have heard that the instanton effect in quark matter causes the di-quark condensate to be Lorentz scalar. As opposed to the Lorentz scalar, there are possibilities that the condensates are Lorentz pseudoscalars, Lorentz vectors, Lorentz pseudovectors, or Lorentz tensors. It could also possibly break the Lorentz symmetry.

So what is the physical intuition or math reasoning behind that instanton effect favor Lorentz scalar, but does not favor (pseudoscalars) that breaks parity $P$? How about other cases?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart

Comments

What do you understand by the "di-quark condensate"?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY

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It could be $<qq>, <\bar{q}q>$ and there are issues of their quantum numbers, such as spin $s$, angular momentum $L$, charge, color, parity, Lorentz [(pseudo)scalars, (pseudo)vectors, tensor], etc.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart

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By di-quark condensate, usually people mean $<qq>$. People may call $<q¯q>$ as anti-quark-quark condensate.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart

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You, of course, don't mean the realistic QCD quark condensate causing the SSB in the QCD, right?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY

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$ <q¯q> \neq 0$ in chiral symmetry breaking. $<qq> \neq 0$ in superconducting phase. I am talking about the superconducting phase.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart

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But how this "di-quark condensate" can be the scalar? It is non-invariant by the construction.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY

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Do you agree that meson is $q¯q$ pair but it can be a pseudo-scalar? In fact, it can be (Pseudo)-scalar/vector meson and Tensor meson. If so what leaves the constraints for writing $qq$, and for writing $q¯q$?

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart

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My understanding is that you can insert $\gamma^5$ and $\gamma^\mu$ into the condensate (what it means implicitly in the condensate shorthand).

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart

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The condensate itself has nothing to do with the vector, tensor and scalar mesons.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user Name YYY

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No, that was not what I mean. The instanton may favor certain channels such that only certein (pseudo)scalars, (pseudo)vectors, tensor tend to condense. I am asking which and what instanton causes this effect, what do they favor others.

This post imported from StackExchange Physics at 2020-10-29 11:44 (UTC), posted by SE-user annie marie heart