Probing the path-length dependence of parton energy loss via scaling properties in heavy ion collisions

The scaling property of large-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>p</a:mi><a:mo>⊥</a:mo></a:msub></a:math> hadron suppression, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>R</c:mi><c:mi>AA</c:mi></c:msub><c:mo stretchy="false">(</c:mo><c:msub><c:mi>p</c:mi><c:mo>⊥</c:mo></c:msub><c:mo stretchy="false">)</c:mo></c:math>, measured in heavy ion collisions at the relativistic heavy ion collider and at the large hadron collider (LHC) leads to the determination of the average parton energy loss <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo stretchy="false">⟨</g:mo><g:mi>ε</g:mi><g:mo stretchy="false">⟩</g:mo></g:math> in quark-gluon plasma produced in a variety of collision systems and centrality classes. Relating <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mo stretchy="false">⟨</k:mo><k:mi>ε</k:mi><k:mo stretchy="false">⟩</k:mo></k:math> to the particle multiplicity and collision geometry allows for probing the dependence of parton energy loss on the path length <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>L</o:mi></o:math>. We find that <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo stretchy="false">⟨</q:mo><q:mi>ε</q:mi><q:mo stretchy="false">⟩</q:mo><q:mo>∝</q:mo><q:msup><q:mi>L</q:mi><q:mi>β</q:mi></q:msup></q:math> with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mi>β</u:mi><u:mo>=</u:mo><u:msubsup><u:mn>1.02</u:mn><u:mrow><u:mo>−</u:mo><u:mn>0.06</u:mn></u:mrow><u:mrow><u:mo>+</u:mo><u:mn>0.09</u:mn></u:mrow></u:msubsup></u:mrow></u:math>, which is consistent with the perturbative quantum chromodynamics expectation of parton energy loss in a longitudinally expanding quark-gluon plasma. We then demonstrate that the azimuthal anisotropy coefficient divided by the collision eccentricity, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:msub><w:mrow><w:mi>v</w:mi></w:mrow><w:mn>2</w:mn></w:msub><w:mo>/</w:mo><w:mi mathvariant="normal">e</w:mi></w:mrow></w:math>, follows the same scaling property as <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>R</z:mi><z:mi>AA</z:mi></z:msub></z:math>. This scaling is observed in data, which are reproduced by the model at large <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>p</bb:mi><bb:mo>⊥</bb:mo></bb:msub></bb:math>. Finally, a linear relationship between <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mrow><db:msub><db:mrow><db:mi>v</db:mi></db:mrow><db:mn>2</db:mn></db:msub><db:mo>/</db:mo><db:mi mathvariant="normal">e</db:mi></db:mrow></db:math> and the logarithmic derivative of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>R</gb:mi><gb:mi>AA</gb:mi></gb:msub></gb:math> is found and confirmed in data, offering an additional way to probe the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>L</ib:mi></ib:math> dependence of parton energy loss using coming measurements from LHC run 3. Published by the American Physical Society 2024