Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model

We investigate the thermal properties of hadrons in two-color quantum chromodynamics ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:msub> <a:mrow> <a:mi>QC</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> <a:mi mathvariant="normal">D</a:mi> </a:mrow> </a:math> ) using the functional renormalization group method, with particular focus on modifications of the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>U</d:mi> <d:mo stretchy="false">(</d:mo> <d:mn>1</d:mn> <d:mo stretchy="false">)</d:mo> </d:math> axial anomaly effects. The hadrons are described by a linear sigma model based on the Pauli-Gürsey <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>S</h:mi> <h:mi>U</h:mi> <h:mo stretchy="false">(</h:mo> <h:mn>4</h:mn> <h:mo stretchy="false">)</h:mo> </h:math> symmetry, which incorporates both low-lying <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msup> <l:mn>0</l:mn> <l:mo>±</l:mo> </l:msup> </l:math> mesons and diquark baryons. We find that all quartic couplings are comparably suppressed when physical values of the pion mass and decay constant are taken as inputs, for which a reasonably smooth chiral symmetry restoration at finite temperature is reproduced. Consequently, mass differences among chiral partners remain small. Despite these tiny mass differences, mass degeneracies of chiral partners in the hot medium are clearly demonstrated, consistent with chiral symmetry restoration. Moreover, we find that the couplings responsible for the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>U</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>1</n:mn> <n:mo stretchy="false">)</n:mo> </n:math> axial anomaly are enhanced upon entering the finite-temperature regime. Baryonic fluctuations also provide sizable contributions to these enhancements. Finally, the fate of the topological susceptibility in the hot <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:mrow> <r:msub> <r:mrow> <r:mi>QC</r:mi> </r:mrow> <r:mrow> <r:mn>2</r:mn> </r:mrow> </r:msub> </r:mrow> <r:mi mathvariant="normal">D</r:mi> </r:mrow> </r:math> medium is examined.