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More about vacuum structure of Linear Sigma Model

In the study of critical phenomena of QCD, a linear sigma model (LSM) is often analyzed as it shares many properties with QCD. Motivated by recent arguments on effective restoration of the U_A(1) symmetry around the critical temperature, the renormalization group flow of U(2)$\otimes$U(2) LSM with a small violation of the U_A(1) symmetry is examined in the traditional epsilon expansion in threedimensions. With a mass-dependent renormalization scheme, we investigate the attractive basin flowing into the O(4) LSM in the parameter space and its dependence on the size of the U_A(1) breaking. Special emphasis is put on how the decoupling of the heavier degrees of freedom occur as approaching the O(4) LSM.