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  The skyrmion as the baryon in realistic QCD

+ 5 like - 0 dislike

The chiral perturbation theory arise as QCD with spontaneously breaking of $SU_{L}(3)\times SU_{R}(3)$ global symmetry down to $SU_{V}(3)$. Since $\pi_{3}(SU_{L}(3)\times SU_{R}(3)/SU_{V}(3)) = Z$, nontrivial solutions called skyrmions arise. They are fermions, and their baryon number coincides with the winding number. Thus they may represent the baryons. The state of chiral perturbation theory is organized as follows. Starting from the skyrmion ground state, we investigate fluctuations around it, which are represented by the massless degrees of freedom - scalar mesons. We obtain then, for example, results of low-energy theorems (such as chiral coupling etc.)

There are, however, such problems. In the minimal chiral perturbation theory (only the term with two derivatives ) skyrmion size is shrinked to zero since corresponding energy doesn't have an extremum (Derrick theorem). If we add nonminimal terms, then we may stabilize it, but chiral perturbation theory doesn't distinct many order derivative terms, so that by adding 4-derivative term theory becomes unpredictable.

The solution of the problem arise since we expect that the baryon mass is of order of $\text{GeV}$. For correctness of description we need to introduce vector mesons into chiral perturbation theory. This can be done by gauging global symmetry (its part which is unbroken by the global anomaly), and then mininally breaking it by adding gauge bosons mass term. It can be shown that $\omega$-meson stabilizes the skyrmion.

By using such construction, may we completely identify the skyrmion with the baryon? Does some problem exists which makes such identification impossible?

asked Feb 28, 2016 in Theoretical Physics by NAME_XXX (1,060 points) [ no revision ]

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