Suppression of the jet quenching parameter near the critical temperature

In this work, we study the jet quenching parameter <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mover accent="true"> <a:mi>q</a:mi> <a:mo stretchy="false">^</a:mo> </a:mover> </a:math> by using a background field effective theory. Particular attention is paid to its behavior near the critical temperature where nonperturbative effects induced by the deconfining phase transition are taken into account through a self-consistently introduced background field <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="script">Q</e:mi> </e:math> . We adopt a theoretical approach in which the interaction rate between the energetic jet and medium partons is computed diagrammatically and the hard-thermal-loop resummed propagator is used to regulate the infrared divergence. In the presence of a background field, its influence on the jet quenching parameter manifests in two aspects. One is the modification on the screening mass in the resummed propagator, which leads to an enhanced <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mover accent="true"> <h:mi>q</h:mi> <h:mo stretchy="false">^</h:mo> </h:mover> </h:math> . The other corresponds to the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi mathvariant="script">Q</l:mi> </l:math> -modified parton distribution function which is dominant and leads to a suppression of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mover accent="true"> <o:mi>q</o:mi> <o:mo stretchy="false">^</o:mo> </o:mover> </o:math> . Decreasing the temperature <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>T</s:mi> </s:math> , our result shows a nonmonotonic <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>T</u:mi> </u:math> dependence of the dimensionless <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mover accent="true"> <w:mrow> <w:mi>q</w:mi> </w:mrow> <w:mrow> <w:mo stretchy="false">^</w:mo> </w:mrow> </w:mover> <w:mo>/</w:mo> <w:msup> <w:mrow> <w:mi>T</w:mi> </w:mrow> <w:mrow> <w:mn>3</w:mn> </w:mrow> </w:msup> </w:mrow> </w:math> . In the high temperature region, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mover accent="true"> <ab:mi>q</ab:mi> <ab:mo stretchy="false">^</ab:mo> </ab:mover> <ab:mo>/</ab:mo> <ab:msup> <ab:mi>T</ab:mi> <ab:mn>3</ab:mn> </ab:msup> </ab:math> shows an increase with decreasing <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>T</eb:mi> </eb:math> due to the running coupling effect. Near the critical temperature, the background field plays a significant role and a dramatic suppression of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mover accent="true"> <gb:mi>q</gb:mi> <gb:mo stretchy="false">^</gb:mo> </gb:mover> <gb:mo>/</gb:mo> <gb:msup> <gb:mi>T</gb:mi> <gb:mn>3</gb:mn> </gb:msup> </gb:math> is found which qualitatively agrees with the lattice simulation. In addition, the background field modification on the jet quenching parameter which is characterized by the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mover accent="true"> <kb:mi>q</kb:mi> <kb:mo stretchy="false">^</kb:mo> </kb:mover> </kb:math> ratio can be simply parametrized by a polynomial expression depending only on the background field. This expression is expected to be useful for phenomenological applications in jet physics.