Pseudoscalar heavy quarkonium production in heavy ion ultraperipheral collision

The inclusive production of pseudoscalar heavy quarkonia (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>η</a:mi></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow></a:msub></a:mrow></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>η</c:mi></c:mrow><c:mrow><c:mi>b</c:mi></c:mrow></c:msub></c:mrow></c:math>, and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>B</e:mi><e:mi>c</e:mi></e:msub></e:math>) via photon-photon fusion in heavy ion ultraperipheral collision (UPC) are calculated to QCD next-to-leading order in the framework of nonrelativistic QCD (NRQCD). The total cross section of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>η</g:mi><g:mi>c</g:mi></g:msub></g:math> produced in Pb-Pb UPC is <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>194</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>nb</i:mi></i:mrow></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mn>1275</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>nb</k:mi></k:mrow></k:math> at nucleon-nucleon c.m. energies <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msqrt><m:msub><m:mi>S</m:mi><m:mi>NN</m:mi></m:msub></m:msqrt><m:mo>=</m:mo><m:mn>5.52</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>TeV</m:mi></m:math> and 39.4 TeV, respectively. The cross sections for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>η</o:mi><o:mi>b</o:mi></o:msub></o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>B</q:mi><q:mi>c</q:mi></q:msub></q:math> mesons are more than two to three orders of magnitude smaller. We make a detailed phenomenological analysis on the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>η</s:mi><s:mi>c</s:mi></s:msub></s:math> production; the uncertainties caused by the renormalization scale and the charm quark mass, the cross sections in other ultraperipheral nucleon-nucleon colliding systems, and the transverse momentum distribution are discussed. At the coming HL-LHC and future FCC, the heavy ion UPC opens another door of the study on the production of heavy quarkonium.