All order resummed leading and next-to-leading soft modes of dense QCD pressure

TL;DR

This paper develops an all-order resummation of soft mode contributions in dense QCD pressure at high baryon chemical potential, improving the precision of the equation of state relevant for neutron star physics.

Contribution

It introduces a novel all-order resummation method for soft modes in dense QCD, extending previous calculations to include leading and next-to-leading logarithmic contributions.

Findings

Derived compact analytical expressions for soft mode contributions.

Observed deviations from previous state-of-the-art results.

Reduced residual scale dependence in the calculations.

Abstract

The cold and dense QCD equation of state (EoS) at high baryon chemical potential $\mu_B$ involves at order $\alpha^2_S$ an all-loop summation of the soft mode $m_E\sim \alpha_S^{1/2} \mu_B$ contributions. Recently, the complete soft contributions at order $\alpha^3_S$ were calculated, using the hard thermal loop (HTL) formalism. By identifying {\em massive} renormalization group (RG) properties within HTL, we resum to all orders $\alpha_S^p, p\ge 3$ the leading and next-to-leading logarithmic soft contributions. We obtain compact analytical expressions, that show visible deviations from the state-of-the art results, and noticeably reduced residual scale dependence. Our results should help to reduce uncertainties in extending the EoS in the intermediate $\mu_B$ regime, relevant in particular for the phenomenology of neutron stars.