  The relation between halo mass, M, and concentration, c, is a critical
component in our understanding of the structure of dark matter halos. While
numerous models for this relation have been proposed, almost none of them
attempt to derive the evolution of the relation analytically. We build on
previous efforts to model the c-M relation as a function of physical parameters
such as the peak height, $\nu$, and the effective power spectrum slope, $n_{\rm
eff}$, which capture the dependence of $c$ on halo mass, redshift, and
cosmology. We present three major improvements over previous models. First, we
derive an analytical expression for the c-M relation that is valid under the
assumption of pseudo-evolution, i.e., assuming that the density profiles of
halos are static in physical coordinates while the definition of their boundary
evolves. We find that this ansatz is highly successful in describing the
evolution of the low-mass end of the c-M relation. Second, we employ a new
physical variable, the effective exponent of linear growth, $\alpha_{\rm eff}$,
to parameterize deviations from an Einstein-de Sitter expansion history. Third,
we combine an updated definition of $n_{\rm eff}$ with the additional
dependence on $\alpha_{\rm eff}$ and propose a phenomenological extension of
our analytical framework to include all halo masses. This semianalytical model
matches simulated concentrations in both scale-free models and LambdaCDM to 5%
accuracy with very few exceptions and differs significantly from all previously
proposed models. We present a publicly available code to compute the
predictions of our model in the python toolkit Colossus, including updated
parameters for the model of Diemer and Kravtsov.
