All Order Resummed Leading and Next-to-Leading Soft Modes of Dense QCD Pressure

The cold and dense QCD equation of state at high baryon chemical potential μ_{B} involves at order α_{s}^{2} an all-loop summation of the soft mode m_{E}∼α_{s}^{1/2}μ_{B} contributions. Recently, the complete soft contributions at order α_{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 α_{s}^{p}, p≥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 μ_{B} regime, relevant in particular for the phenomenology of neutron stars.