Jet transport coefficients by elastic and radiative scatterings in the strongly interacting quark-gluon plasma

We extend the investigation of jet transport coefficients within the effective dynamical quasiparticle model (DQPM)—constructed to describe nonperturbative QCD phenomena of the strongly interacting quark-gluon plasma (sQGP) in line with the lattice QCD equation of state—by accounting for inelastic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>2</a:mn><a:mo>→</a:mo><a:mn>3</a:mn></a:mrow></a:math> reactions with gluon radiation in addition to the elastic scattering of partons. The elastic and inelastic reactions are calculated explicitly within leading-order Feynman diagrams with effective propagators and vertices from the DQPM by accounting for all channels and their interferences. We present the results for the jet transport coefficients such as the transverse momentum transfer squared <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mover accent="true"><b:mi>q</b:mi><b:mo>̂</b:mo></b:mover></b:math> per unit length as well as the energy loss <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>d</d:mi><d:mi>E</d:mi><d:mo>/</d:mo><d:mi>d</d:mi><d:mi>x</d:mi></d:mrow></d:math> per unit length in the sQGP and investigate their dependence on the temperature <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>T</e:mi></e:math> and momentum of the jet parton depending on the choice of the strong coupling constant <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>α</f:mi><f:mi>s</f:mi></f:msub></f:math> in thermal, jet parton, and radiative vertices. For the latter, we consider different scenarios used in the literature and find a very strong dependence of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mover accent="true"><g:mi>q</g:mi><g:mo>̂</g:mo></g:mover></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>d</i:mi><i:mi>E</i:mi><i:mo>/</i:mo><i:mi>d</i:mi><i:mi>x</i:mi></i:mrow></i:math> on the choice of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>α</j:mi><j:mi>s</j:mi></j:msub></j:math>. Moreover, we explore the relation of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mover accent="true"><k:mi>q</k:mi><k:mo>̂</k:mo></k:mover><k:mo>/</k:mo><k:msup><k:mi>T</k:mi><k:mn>3</k:mn></k:msup></k:mrow></k:math> to the ratio of specific shear viscosity to entropy density <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>η</m:mi><m:mo>/</m:mo><m:mi>s</m:mi></m:mrow></m:math> and show that the ratio <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mrow><n:msup><n:mi>T</n:mi><n:mn>3</n:mn></n:msup><n:mo>/</n:mo><n:mover accent="true"><n:mi>q</n:mi><n:mo>̂</n:mo></n:mover></n:mrow></n:math> to <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mrow><p:mi>η</p:mi><p:mo>/</p:mo><p:mi>s</p:mi></p:mrow></p:math> has a strong <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mi>T</q:mi></q:math> dependence—especially when approaching <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:msub><r:mi>T</r:mi><r:mi>c</r:mi></r:msub></r:math>—on the choice of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:msub><s:mi>α</s:mi><s:mi>s</s:mi></s:msub></s:math> in scattering vertices. Published by the American Physical Society 2024