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arXiv · 1412.8026

Linking $U(2)\times U(2)$ to $O(4)$ model via decoupling

Tomomi Sato·Norikazu Yamada
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Abstract

The nature of chiral phase transition of massless two flavor QCD depends on the fate of flavor singlet axial symmetry $U_A(1)$ at the critical temperature ($T_c$). Assuming that a finite $U_A(1)$ breaking remains at $T_c$, the corresponding three dimensional effective theory is composed of four massless and four massive scalar fields. We study the renormalization group flow of the effective theory in the $ε$-expansion, using a mass dependent renormalization scheme, and determine the region of the attractive basin flowing into the $O(4)$ fixed point with a focus on its dependence on the size of the $U_A(1)$ breaking. The result is discussed from a perspective of the decoupling of massive fields. It is pointed out that, although the effective theory inside the attractive basin eventually reaches the $O(4)$ fixed point, the approaching rate, one of the universal exponents, is different from that of the standard $O(4)$ model. We present the reason for this peculiarity, and propose a novel possibility for chiral phase transition in two-flavor QCD.

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Tomomi Sato, Norikazu Yamada. 2015-02-07. Linking $U(2)\times U(2)$ to $O(4)$ model via decoupling. https://doi.org/10.1103/physrevd.91.034025

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