Static linear response of hot and dense QCD matter to electromagnetic fields: Leading hard and soft QCD corrections

We compute the static electromagnetic susceptibilities of a hot and dense quark-gluon plasma using perturbative Quantum Chromodynamics (QCD). Our evaluation includes the leading $\mathcal{O}({\alpha }_s)$ correction as well as the leading soft, resummed contribution of $\mathcal{O}({\alpha }_s^{3\mathrm{/}2})$ within electrostatic QCD. By matching to Lattice QCD at vanishing baryon chemical potential through Lattice perturbation theory, we establish a connection between perturbative results and Lattice simulations and assess the size of higher-order corrections. This extends the electromagnetic susceptibilities to finite baryon chemical potential, where Lattice methods are not applicable and establishes first-principle constraints on the quark-gluon plasma’s electromagnetic response at temperatures and densities relevant for intermediate-energy heavy-ion collisions.