All Order Resummed Leading and Next-to-Leading Soft Modes of Dense QCD Pressure
Loïc Fernandez, Jean-Loı̈c Kneur
Abstract
The cold and dense QCD equation of state at high baryon chemical potential ${\ensuremath{\mu}}_{B}$ involves at order ${\ensuremath{\alpha}}_{s}^{2}$ an all-loop summation of the soft mode ${m}_{E}\ensuremath{\sim}{\ensuremath{\alpha}}_{s}^{1/2}{\ensuremath{\mu}}_{B}$ contributions. Recently, the complete soft contributions at order ${\ensuremath{\alpha}}_{s}^{3}$ were calculated using the hard thermal loop formalism. By identifying massive renormalization group properties of the hard thermal loop theory, we resum to all orders ${\ensuremath{\alpha}}_{s}^{p}$, $p\ensuremath{\ge}3$ 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 reduce residual scale dependence. Our results should help to reduce uncertainties in extending the equation of state in the intermediate ${\ensuremath{\mu}}_{B}$ regime, relevant in particular for the phenomenology of neutron stars.