Inverse magnetic catalysis and energy loss in a holographic QCD model

Abstract

In this paper, we consider the Einstein-Maxwell-dilaton holographic model for light quarks with nonzero magnetic field and chemical potential. First, we study the phase diagrams in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>T</a:mi> <a:mtext>−</a:mtext> <a:mi>μ</a:mi> </a:mrow> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>T</c:mi> <c:mtext>−</c:mtext> <c:mi>B</c:mi> </c:mrow> </c:math> planes. We observe inverse magnetic catalysis which is consistent with the lattice QCD results. We discuss the influence of the magnetic field and chemical potential on the location of the critical end point (CEP). It is found that the magnetic field increases the critical <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>μ</e:mi> <e:mrow> <e:mi>C</e:mi> <e:mi>E</e:mi> <e:mi>P</e:mi> </e:mrow> </e:msub> </e:math> of the CEP in the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>T</g:mi> <g:mtext>−</g:mtext> <g:mi>μ</g:mi> </g:mrow> </g:math> plane and the chemical potential increases the critical <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>B</i:mi> <i:mrow> <i:mi>C</i:mi> <i:mi>E</i:mi> <i:mi>P</i:mi> </i:mrow> </i:msub> </i:math> of the CEP in the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>T</k:mi> <k:mtext>−</k:mtext> <k:mi>B</k:mi> </k:mrow> </k:math> plane. Second, we discuss the equations of state (EOS) with nonzero magnetic field and chemical potential. We observe that the EOS near the phase transition temperature are nonmonotonic. Then we study the energy loss with a nonzero magnetic field and chemical potential. It is found that the drag force of the heavy quark and jet quenching parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo stretchy="false">^</m:mo> </m:mover> </m:math> show an enhancement near the phase transition temperature. The peak values of drag force and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mover accent="true"> <q:mi>q</q:mi> <q:mo stretchy="false">^</q:mo> </q:mover> </q:math> are pushed toward lower temperature with increasing <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>B</u:mi> </u:math> or <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>μ</w:mi> </w:math> . This phenomenon is consistent with the phase transition temperature decrease with increasing <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>B</y:mi> </y:math> or <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>μ</ab:mi> </ab:math> in this holographic model. Moreover, we find that the heavy quark may lose more energy when it is perpendicular to a magnetic field, which is consistent with the results of the jet quenching parameter. Published by the American Physical Society 2024

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