Thermal static potential and pseudoscalar quarkonium spectral functions from ( 2+1 )-flavor lattice QCD

Quarkonia, which are bound states of a heavy quark and antiquark, play a key role in probing the quark-gluon plasma (QGP). The dynamics of quarkonia in the QGP are encoded in their finite-temperature spectral functions. In this work, we estimate the quarkonium spectral functions in the pseudoscalar channel using (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-flavor lattice QCD with a pion mass of 320 MeV, at temperatures of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>220</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>MeV</c:mi><c:mo stretchy="false">(</c:mo><c:mn>1.2</c:mn><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 stretchy="false">)</c:mo></c:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>251</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>MeV</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1.4</g:mn><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 stretchy="false">)</g:mo></g:math>, and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>293</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>MeV</k:mi><k:mo stretchy="false">(</k:mo><k:mn>1.6</k:mn><k:msub><k:mi>T</k:mi><k:mrow><k:mi>p</k:mi><k:mi>c</k:mi></k:mrow></k:msub><k:mo stretchy="false">)</k:mo></k:math>. Reconstructing the spectral function from the Euclidean lattice correlator is a well-known ill-posed problem, requiring additional physics-motivated input. We address this by smoothly matching contributions from different frequency regions of the spectral function, using appropriate physics valid for each region. The spectral function around <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>ω</o:mi><o:mo>∼</o:mo><o:mn>2</o:mn><o:msub><o:mi>M</o:mi><o:mi>q</o:mi></o:msub></o:math> is obtained using a nonperturbative complex potential, while for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ω</q:mi><q:mo>≫</q:mo><q:mn>2</q:mn><q:msub><q:mi>M</q:mi><q:mi>q</q:mi></q:msub></q:math> it is modeled using results from vacuum perturbation theory. Since the pseudoscalar channel does not receive a transport contribution near <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>ω</s:mi><s:mo>∼</s:mo><s:mn>0</s:mn></s:math>, we find that the combination of these two regions already provides a good description of the relativistic lattice pseudoscalar correlator. We observe a substantial thermal width in the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>η</u:mi><u:mi>c</u:mi></u:msub><u:mo stretchy="false">(</u:mo><u:mn>1</u:mn><u:mi>S</u:mi><u:mo stretchy="false">)</u:mo></u:math> state, indicating that pseudoscalar charmonium (<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>η</y:mi><y:mi>c</y:mi></y:msub></y:math>) is nearing dissolution at the studied temperatures. In comparison, the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>η</ab:mi><ab:mi>b</ab:mi></ab:msub></ab:math> ground state exhibits little change and remains well defined.