Gluon polarization contribution to the spin alignment of vector mesons from holography

We investigate the behavior of vector mesons <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ρ</a:mi></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ϕ</c:mi></c:math>, and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>J</e:mi><e:mo>/</e:mo><e:mi mathvariant="normal">Ψ</e:mi></e:math> in both nonrotating and rotating thermal media using the soft-wall holographic QCD model with four flavors. By incorporating anisotropic backgrounds derived from the Einstein-Maxwell-dilaton action, we incorporate rotational effects via a <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>U</h:mi><h:mo stretchy="false">(</h:mo><h:mn>1</h:mn><h:mo stretchy="false">)</h:mo></h:math> gauge field, and the induced polarization of gluons is described by a rotation dependent dilation field. Spectral function analysis reveals that <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>ρ</l:mi></l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>ϕ</n:mi></n:math> mesons exhibit broad peaks at lower temperatures, indicating their presence in the medium, while these peaks disappear at higher temperatures. Rotation delays this melting process, increasing the dissociation temperature. In contrast, the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>J</p:mi><p:mo>/</p:mo><p:mi mathvariant="normal">Ψ</p:mi></p:math> meson, owing to its heavy charm quark content, demonstrates its resilience to thermal effects. We further explore the global spin alignment of these mesons in the event plane frame. For the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>ϕ</s:mi></s:math> meson, the averaged <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> over the full range of azimuthal angles shows weak temperature dependence at low transverse momentum (<w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>p</w:mi><w:mi>T</w:mi></w:msub></w:math>) but significant suppression at high <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>p</y:mi><y:mi>T</y:mi></y:msub></y:math>, aligning with experimental observations. Rotation enhances <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>ρ</ab:mi><ab:mn>00</ab:mn></ab:msub></ab:math> at high <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>p</cb:mi><cb:mi>T</cb:mi></cb:msub></cb:math>, a phenomenon attributed to angular momentum transfer via spin-orbit coupling. The <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>J</eb:mi><eb:mo>/</eb:mo><eb:mi mathvariant="normal">Ψ</eb:mi></eb:math> meson, however, displays insensitivity to temperature and rotation up to <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>p</hb:mi><hb:mi>T</hb:mi></hb:msub><hb:mo>=</hb:mo><hb:mn>5</hb:mn><hb:mtext> </hb:mtext><hb:mtext> </hb:mtext><hb:mi>GeV</hb:mi></hb:math>, with a very small suppression observed at higher <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msub><jb:mi>p</jb:mi><jb:mi>T</jb:mi></jb:msub></jb:math>, likely due to its heavy quark nature. Although <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mi>ρ</lb:mi></lb:math> meson spin alignment is not yet experimentally measured, it exhibits behavior qualitatively similar to the <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>ϕ</nb:mi></nb:math> meson, with thermal fluctuations dampening alignment and rotation enhancing it.