Impact of anisotropy on the QCD phase structure and transport coefficients of quark matter

Employing the Polyakov chiral SU(3) mean field (PCQMF) model, we investigate how momentum-space anisotropy, characteristic of quark-gluon plasma (QGP) in ultrarelativistic heavy-ion collisions (uRHIC), impacts the thermodynamic behavior and transport coefficients of strongly interacting quark matter. The momentum anisotropy is introduced via a small deformation in the momentum distribution, quantified by a spheroidal parameter <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ξ</a:mi> </a:math> , which deforms the distribution functions and captures anisotropic effects to linear order. The PCQMF model captures key non-perturbative aspects of QCD, such as chiral symmetry breaking or deconfinement dynamics through Polyakov loop potential, and is extended here to accommodate momentum-space anisotropy. We compute the modifications induced by momentum-space anisotropy to key thermodynamic observables including pressure <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>p</c:mi> </c:math> , energy density <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ε</e:mi> </e:math> , entropy density <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>s</g:mi> </g:math> , speed of sound squared <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi>c</i:mi> <i:mi>s</i:mi> <i:mn>2</i:mn> </i:msubsup> </i:math> , and specific heat <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>c</k:mi> <k:mi>v</k:mi> </k:msub> </k:math> , alongside key transport coefficients such as shear viscosity <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>η</m:mi> </m:math> , bulk viscosity <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>ζ</o:mi> <o:mi>b</o:mi> </o:msub> </o:math> , and electrical conductivity <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>σ</q:mi> <q:mrow> <q:mi>el</q:mi> </q:mrow> </q:msub> </q:math> . These coefficients are derived using the relativistic Boltzmann equation (RBE) under the relaxation time approximation (RTA). We find that even a weak anisotropy can lead to significant modifications in the thermodynamic response and transport behavior of quark matter. This underscores the importance of including momentum anisotropy for realistic modeling of the QCD medium across all energy regimes, from current studies at RHIC and LHC to future explorations of the high-density frontier at FAIR, NICA, and J-PARC.