Order $g^2$ susceptibilities in the symmetric phase of the Standard Model
Susceptibilities of conserved charges such as baryon minus lepton number enter baryogenesis computations, since they provide the relationship between conserved charges and chemical potentials. Their next-to-leading order corrections are of order $ g $, where $ g $ is a generic Standard Model coupling. They are due to soft Higgs boson exchange, and have been calculated recently, together with some order $ g ^ 2 $ corrections. Here we compute the complete $ g ^ 2 $ contributions. Close to the electroweak crossover the soft Higgs contribution is of order $ g ^ 2 $, and is determined by the non-perturbative physics at the magnetic screening scale.