Gorda, Tyler; Kurkela, Aleksi; Paatelainen, Risto; Sappi, Saga; Vuorinen, Aleksi
(2021)
Accurate knowledge of the thermodynamic properties of zero-temperature, high-density quark matter plays an integral role in attempts to constrain the behavior of the dense QCD matter found inside neutronstar cores, irrespective of the phase realized inside the stars. In this Letter, we consider the weak-coupling expansion of the dense QCD equation of state and compute the next-to-next-to-next-to-leading-order contribution arising from the non-Abelian interactions among long-wavelength, dynamically screened gluonic fields. Accounting for these interactions requires an all-loop resummation, which can be performed using hard-thermal-loop (HTL) kinematic approximations. Concretely, we perform a full two-loop computation using the HTL effective theory, valid for the long-wavelength, or soft, modes. We find that the soft sector is well behaved within cold quark matter, contrary to the case encountered at high temperatures, and find that the new contribution decreases the renormalization-scale dependence of the equation of state at high density.