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

Abstract

The cold and dense QCD equation of state (EoS) at high baryon chemical potential ${\mu }_B$ involves at order ${\alpha }_S^2$ 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 ${\alpha }_S^3$ 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.

Comments: 5 pages + appendices, 2 figures. Eq.(22) corrected, changes in Fig.2, added content in appendices. To appear in PRL