Lattice QCD study of color correlations between static quarks with gluonic excitations

We study the color correlation between static quark and antiquark (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>q</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>) that is accompanied by gluonic excitations in the confined phase at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>T</e:mi><e:mo>=</e:mo><e:mn>0</e:mn></e:math> by constructing reduced density matrices <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>ρ</g:mi></g:math> in color space. We perform quenched lattice quantum chromodynamics (QCD) calculations with the Coulomb gauge adopting the standard Wilson gauge action, and the spatial volume is <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>L</i:mi><i:mn>3</i:mn></i:msup><i:mo>=</i:mo><i:mn>3</i:mn><i:msup><i:mn>2</i:mn><i:mn>3</i:mn></i:msup></i:math> at <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>β</k:mi><k:mo>=</k:mo><k:mn>5.8</k:mn></k:math>, which corresponds to the lattice spacing <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>a</m:mi><m:mo>=</m:mo><m:mn>0.14</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>fm</m:mi></m:math> and the system volume <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>L</o:mi><o:mn>3</o:mn></o:msup><o:mo>=</o:mo><o:msup><o:mn>4.5</o:mn><o:mn>3</o:mn></o:msup><o:mtext> </o:mtext><o:mtext> </o:mtext><o:msup><o:mrow><o:mi>fm</o:mi></o:mrow><o:mrow><o:mn>3</o:mn></o:mrow></o:msup></o:math>. We evaluate the color density matrix <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ρ</q:mi></q:math> of static <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>q</s:mi><s:mover accent="true"><s:mi>q</s:mi><s:mo stretchy="false">¯</s:mo></s:mover></s:math> pairs in 6 channels (<w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msubsup><w:mi mathvariant="normal">Σ</w:mi><w:mi>g</w:mi><w:mo>+</w:mo></w:msubsup></w:math>, <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msup><z:msubsup><z:mi mathvariant="normal">Σ</z:mi><z:mi>g</z:mi><z:mo>+</z:mo></z:msubsup><z:mo>′</z:mo></z:msup></z:math>, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi mathvariant="normal">Π</cb:mi><cb:mi>u</cb:mi></cb:msub></cb:math>, <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msubsup><fb:mi mathvariant="normal">Π</fb:mi><fb:mi>u</fb:mi><fb:mo>′</fb:mo></fb:msubsup></fb:math>, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi mathvariant="normal">Δ</ib:mi><ib:mi>g</ib:mi></ib:msub></ib:math>, <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msubsup><lb:mi mathvariant="normal">Δ</lb:mi><lb:mi>g</lb:mi><lb:mo>′</lb:mo></lb:msubsup></lb:math>), and investigate the interquark-distance dependence of color correlations. We find that as the interquark distance increases, the color correlation quenches because of color leak into the gluon field and finally approaches the random color configuration in the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>q</ob:mi><ob:mover accent="true"><ob:mi>q</ob:mi><ob:mo stretchy="false">¯</ob:mo></ob:mover></ob:math> systems with and without gluonic excitations. For this color screening effect, we evaluate the “screening mass” to discuss its dependence on channels, the quantum number of the gluonic excitations.