Roles of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>U</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> axial anomaly effects in cold and dense two-

We explore phase structures and hadron mass spectra in cold and dense two-color quantum chromodynamics (QCD) with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>2</a:mn> </a:math> flavors where the sign problem disappears. We particularly focus on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>U</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>1</c:mn> <c:mo stretchy="false">)</c:mo> </c:math> axial anomaly effects. We employ an <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>N</g:mi> <g:mi>f</g:mi> </g:msub> <g:mo>=</g:mo> <g:mn>2</g:mn> <g:mo>+</g:mo> <g:mn>2</g:mn> </g:math> linear sigma model based on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>S</i:mi> <i:mi>U</i:mi> <i:mo stretchy="false">(</i:mo> <i:mn>8</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> Pauli-Gürsey symmetry to describe negative-parity as well as positive-parity hadrons, for which low-energy excitations are appropriately described particularly in the baryon superfluid phase with light diquark condensates. As a result, the strange chiral condensate is found to be enhanced in the superfluid phase owing to the flavor-mixing structure of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>U</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>1</m:mn> <m:mo stretchy="false">)</m:mo> </m:math> axial anomaly effects. We also confirm this enhancement by means of the Nambu–Jona-Lasinio model. Besides, our present analysis predicts the existence of a novel superfluid phase where heavy diquarks condense in dense regime. The topological susceptibility with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mn>2</q:mn> <q:mo>+</q:mo> <q:mn>2</q:mn> </q:math> flavors from the viewpoints of the anomaly effects and chiral-symmetry restoration is investigated. Furthermore, we derive a complete inverse mass hierarchy for negative-parity diquarks with sufficient anomaly effects. Our findings are expected to provide future lattice simulations with useful information on flavor-symmetry violation from the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>U</s:mi> <s:mo stretchy="false">(</s:mo> <s:mn>1</s:mn> <s:mo stretchy="false">)</s:mo> </s:math> axial anomaly aspects in cold and dense two-color QCD medium.