Chiral phase transition and spin alignment of vector mesons with chiral imbalance in a rotating QCD medium

We study the two-flavor Nambu-Jona-Lasinio model under the rotation and chiral chemical potential <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>μ</a:mi><a:mn>5</a:mn></a:msub></a:math>. First, the influence of chiral imbalance on the chiral phase transition in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mrow><c:mi>p</c:mi><c:mi>c</c:mi></c:mrow></c:msub><c:mo>−</c:mo><c:mi>ω</c:mi></c:math> plane is investigated. Research manifests that, as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>μ</e:mi><e:mn>5</e:mn></e:msub></e:math> increases, the critical point of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>T</g:mi><g:mrow><g:mi>p</g:mi><g:mi>c</g:mi></g:mrow></g:msub><g:mo>−</g:mo><g:mi>ω</g:mi></g:math> plane chiral phase transition will move closer to the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>T</i:mi></i:math> axis. This means that the chiral chemical potential <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>μ</k:mi><k:mn>5</k:mn></k:msub></k:math> can significantly affect the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>T</m:mi><m:mrow><m:mi>p</m:mi><m:mi>c</m:mi></m:mrow></m:msub><m:mo>−</m:mo><m:mi>ω</m:mi></m:math> phase diagram and phase transition behavior. While discussing the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>T</o:mi><o:mrow><o:mi>p</o:mi><o:mi>c</o:mi></o:mrow></o:msub><o:mo>−</o:mo><o:mi>ω</o:mi></o:math> phase diagram, we also study the spin alignment of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ρ</q:mi></q:math> vector meson under rotation. In the study of the spin alignment of the vector meson <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>ρ</s:mi></s:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>ρ</u:mi><u:mn>00</u:mn></u:msub></u:math> is the 00 element of the spin density matrix of vector mesons. At high temperatures, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>ρ</w:mi><w:mn>00</w:mn></w:msub></w:math> is close to <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mn>1</y:mn><y:mo>/</y:mo><y:mn>3</y:mn></y:math>, which indicates that the spin alignment of the vector meson <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>ρ</ab:mi></ab:math> is isotropic. The study found that, under finite rotation, increasing the chiral chemical potential <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>μ</cb:mi><cb:mn>5</cb:mn></cb:msub></cb:math> can significantly enhance <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>ρ</eb:mi><eb:mn>00</eb:mn></eb:msub></eb:math> around the phase transition temperature. When rotational angular velocity is zero, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>ρ</gb:mi><gb:mn>00</gb:mn></gb:msub></gb:math> is close to <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mn>1</ib:mn><ib:mo>/</ib:mo><ib:mn>3</ib:mn></ib:math>, but as <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>ω</kb:mi></kb:math> increases, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>ρ</mb:mi><mb:mn>00</mb:mn></mb:msub></mb:math> significantly decreases and deviates <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mn>1</ob:mn><ob:mo>/</ob:mo><ob:mn>3</ob:mn></ob:math>, indicating that rotation can significantly cause polarization characteristics. The <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msub><qb:mi>ρ</qb:mi><qb:mn>00</qb:mn></qb:msub><qb:mo>−</qb:mo><qb:mi>r</qb:mi></qb:math> relationship near the phase transition temperature is studied. It is found that the farther away from the center of rotation, the lower the degree of spin polarization of the system. It is also found that the influence of chiral imbalance on the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msub><sb:mi>ρ</sb:mi><sb:mn>00</sb:mn></sb:msub><sb:mo>−</sb:mo><sb:mi>r</sb:mi></sb:math> relationship is also significant.