Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model

Abstract

We construct an extended version of the linear sigma model in such a way as to describe spin-1 hadrons as well as spin-0 hadrons in two-color QCD (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><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:mi mathvariant="normal">D</a:mi></a:mrow></a:math>) by respecting the Pauli-Gürsey <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>S</d:mi><d:mi>U</d:mi><d:mo stretchy="false">(</d:mo><d:mn>4</d:mn><d:mo stretchy="false">)</d:mo></d:math> symmetry. Within a mean-field approximation, we therefrom examine a mass spectrum of the spin-1 hadrons at finite quark chemical potential (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>μ</h:mi><h:mi>q</h:mi></h:msub></h:math>) and zero temperature. Not only mean fields of scalar mesons and scalar-diquark baryons but also of vector mesons and vector-diquark baryons are incorporated. As a result, we find that, unless all of those four types of mean fields are taken into account, neither lattice result for the critical <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>μ</j:mi><j:mi>q</j:mi></j:msub></j:math> that corresponds to the onset of baryon superfluidity nor for <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>μ</l:mi><l:mi>q</l:mi></l:msub></l:math> dependence of the pion mass can be reproduced. We also find that a slight suppression of the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>ρ</n:mi></n:math> meson mass in the superfluid phase, which was suggested by the lattice simulation, is reproduced by subtle mixing effects between spin-0 and spin-1 hadrons. Moreover, we demonstrate the emergence of an axial-vector condensed phase and possibly of a vector condensed phase by identifying the values of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>μ</p:mi><p:mi>q</p:mi></p:msub></p:math> at which the corresponding hadron masses vanish. The possible presence of isotriplet <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mn>1</r:mn><r:mo>−</r:mo></r:msup></r:math> diquarks that may be denoted by a tensor-type quark bilinear field is also discussed. Published by the American Physical Society 2024

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