Emergence of Koba-Nielsen-Olsen scaling in multiplicity distributions in jets produced at the LHC

In this work we study the multiplicity distributions (MDs) of charged particles within jets in proton-proton collisions, which were measured by the ATLAS Collaboration in 2011, 2016 and 2019. The first dataset refers to jets with smaller transverse momenta (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>4</a:mn><a:mo>&lt;</a:mo><a:msub><a:mrow><a:mi>p</a:mi></a:mrow><a:mrow><a:mi>T</a:mi></a:mrow></a:msub><a:mo>&lt;</a:mo><a:mn>40</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:mrow></a:math>) whereas the other two refer to higher <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>p</c:mi><c:mi>T</c:mi></c:msub></c:math> jets (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>0.1</e:mn><e:mo>&lt;</e:mo><e:msub><e:mrow><e:mi>p</e:mi></e:mrow><e:mrow><e:mi>T</e:mi></e:mrow></e:msub><e:mo>&lt;</e:mo><e:mn>2.5</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>TeV</e:mi></e:mrow></e:math>). We find that the lower <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>p</g:mi><g:mi>T</g:mi></g:msub></g:math> set shows no sign of KNO scaling and that the higher <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>p</i:mi><i:mi>T</i:mi></i:msub></i:math> sets gradually approach the scaling limit. For the lower <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>p</k:mi><k:mi>T</k:mi></k:msub></k:math> set the mean multiplicity as a function of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>p</m:mi><m:mi>T</m:mi></m:msub></m:math> can be well-described by expressions derived from QCD with different approximation schemes. For higher (<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo>&gt;</o:mo><o:mn>500</o:mn><o:mtext> </o:mtext><o:mtext> </o:mtext><o:mi>GeV</o:mi></o:math>) values of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>p</q:mi><q:mi>T</q:mi></q:msub></q:math> these expressions significantly overshoot the data. We show that the behavior of the MDs can be well-represented by a sub-Poisson distribution with energy dependent parameters. In the range <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>40</s:mn><s:mo>&lt;</s:mo><s:msub><s:mi>p</s:mi><s:mi>T</s:mi></s:msub><s:mo>&lt;</s:mo><s:mn>100</s:mn><s:mtext> </s:mtext><s:mtext> </s:mtext><s:mi>GeV</s:mi></s:math> there is a transition from sub to super Poissonian behavior and the MD evolves to a geometric distribution, which shows KNO scaling. In this way we fit the MDs in all transverse momentum intervals with one single expression. We discuss the implications of this phenomenological finding. Published by the American Physical Society 2024