Hadronization impact on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:math> energy correlators: A pythia8 study from partonic to hadronic observables

A comprehensive study of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> </a:math> energy correlator as a probe of nonperturbative hadronization in color-octet <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>c</c:mi> <c:mover accent="true"> <c:mi>c</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> </c:math> production is performed. The energy correlator measures the energy flow as a function of the angular distance ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>χ</g:mi> </g:math> ) from the identified <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>J</i:mi> <i:mo>/</i:mo> <i:mi>ψ</i:mi> </i:math> meson. Using the 8 Monte Carlo event generator, the correlator is computed at both parton and hadron levels. At high- <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>J</k:mi> <k:mo>/</k:mo> <k:mi>ψ</k:mi> </k:math> transverse momentum ( <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:mo>&gt;</m:mo> <m:mn>7</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>GeV</m:mi> <m:mo>/</m:mo> <m:mi>c</m:mi> </m:math> ), the parton-level correlator in the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>cos</o:mi> <o:mi>χ</o:mi> <o:mo>&gt;</o:mo> <o:mn>0</o:mn> </o:math> region is dominated by soft gluon emission during the hadronization of the color-octet state, a contribution clearly distinguishable from other partonic sources, such as underlying multiparton interactions. The transition to the hadron level, however, introduces substantial modifications, suppressing the correlator in this region by approximately an order of magnitude and underscoring the complexity of the hadronization mapping. Further analysis reveals that the hadron-level observable exhibits notable sensitivity to model parameters: increasing the mass splitting between colored <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>c</q:mi> <q:mover accent="true"> <q:mi>c</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> </q:math> pre-resonances and the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>J</u:mi> <u:mo>/</u:mo> <u:mi>ψ</u:mi> </u:math> meson from 0.2 to <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mn>0.8</w:mn> <w:mtext> </w:mtext> <w:mtext> </w:mtext> <w:mi>GeV</w:mi> <w:mo>/</w:mo> <w:msup> <w:mi>c</w:mi> <w:mn>2</w:mn> </w:msup> </w:math> enhances the correlator by up to 60%, while extending the color reconnection range yields a milder enhancement of about 10%. These findings demonstrate that precise measurements of the hadron-level <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>J</y:mi> <y:mo>/</y:mo> <y:mi>ψ</y:mi> </y:math> energy correlator, when interpreted within robust event-generator frameworks, can provide novel constraints on hadronization dynamics and help clarify the production mechanisms of the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>J</ab:mi> <ab:mo>/</ab:mo> <ab:mi>ψ</ab:mi> </ab:math> state.