Bulk viscosity of quark matter across the QCD phase transitions

Based on the kinetic theory with relaxation time approximation, we investigate the bulk viscosity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mo>(</a:mo> <a:mi>ζ</a:mi> <a:mo>)</a:mo> </a:math> and its ratio to shear viscosity <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mo>(</b:mo> <b:mi>ζ</b:mi> <b:mo>/</b:mo> <b:mi>η</b:mi> <b:mo>)</b:mo> </b:mrow> </b:math> of quark matter at finite temperature and chemical potential with the in-medium particle masses derived in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>2</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> flavor Polyakov-loop improved Nambu–Jona-Lasinio model. We explore the behaviors of specific bulk viscosity <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mo>(</d:mo> <d:mi>ζ</d:mi> <d:mo>/</d:mo> <d:mi>s</d:mi> <d:mo>)</d:mo> </d:mrow> </d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>ζ</e:mi> <e:mo>/</e:mo> <e:mi>η</e:mi> </e:mrow> </e:math> across different QCD phase transitions, including the Mott phase transition, the chiral crossover, and the first-order transition with the associated metastable phase. The calculation shows that both <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>ζ</f:mi> <f:mo>/</f:mo> <f:mi>s</f:mi> </f:mrow> </f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>ζ</g:mi> <g:mo>/</g:mo> <g:mi>η</g:mi> </g:mrow> </g:math> are extremely small at high temperatures, approaching the nature of a conformal theory. Larger <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>ζ</h:mi> <h:mo>/</h:mo> <h:mi>s</h:mi> </h:mrow> </h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>ζ</i:mi> <i:mo>/</i:mo> <i:mi>η</i:mi> </i:mrow> </i:math> are derived near the chiral phase transition at finite temperature. Along the chiral crossover line, <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi>ζ</j:mi> <j:mo>/</j:mo> <j:mi>s</j:mi> </j:mrow> </j:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mi>ζ</k:mi> <k:mo>/</k:mo> <k:mi>η</k:mi> </k:mrow> </k:math> generally increase with decreasing temperature, though <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mi>ζ</l:mi> <l:mo>/</l:mo> <l:mi>η</l:mi> </l:mrow> </l:math> exhibits a slight decline near the critical end point. On the boundary of the first-order transition, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>ζ</m:mi> <m:mo>/</m:mo> <m:mi>s</m:mi> </m:mrow> </m:math> shows a nonmonotonic variation with temperature. Furthermore, an additional peak structure emerges beyond the chiral phase boundary for both <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mi>ζ</n:mi> <n:mo>/</n:mo> <n:mi>s</n:mi> </n:mrow> </n:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mi>ζ</o:mi> <o:mo>/</o:mo> <o:mi>η</o:mi> </o:mrow> </o:math> , with magnitudes even exceeding those near the chiral crossover of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:mi>u</p:mi> <p:mo>,</p:mo> <p:mi>d</p:mi> </p:mrow> </p:math> quarks. Our analysis indicates this peak originates from the chiral crossover transformation of strange quark.