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

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 $\epsilon$-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.

21 pages, 5 figures, more explanations and 4th possibility for PT in Nf=2 QCD added, no change in conclusion, version accepted in PRD

References in corpus (7)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The transition temperature in QCD
• Bootstrapping phase transitions in QCD and frustrated spin systems
• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• Critical endpoint of finite temperature phase transition for three flavor QCD
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group
• Renormalization group flow of linear sigma model with $U_A(1)$ anomaly

Cited by in corpus (2)

• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• Renormalization group flow of linear sigma model with $U_A(1)$ anomaly