  Studies of gamma-ray bursts (GRBs) and their multi-wavelength afterglows have
led to insights in electron acceleration and emission properties from
relativistic, high-energy astrophysical sources. Broadband modeling across the
electromagnetic spectrum has been the primary means of investigating the
physics behind these sources, although independent diagnostic tools have been
developed to inform and corroborate assumptions made in particle acceleration
simulations and broadband studies. We present a methodology to constrain three
physical parameters related to electron acceleration in GRB blast waves: the
fraction of shock energy in electrons, $\epsilon_e$; the fraction of electrons
that gets accelerated into a power-law distribution of energies, $\xi_e$; and
the minimum Lorentz factor of the accelerated electrons, $\gamma_m$. These
parameters are constrained by observations of the peaks in radio afterglow
light curves and spectral energy distributions. From a sample of 49 radio
afterglows, we are able to find narrow distributions for these parameters,
hinting at possible universality of the blast wave microphysics, although
observational bias could play a role in this. Using radio peaks and
considerations related to the prompt gamma-ray emission efficiency, we
constrain the allowed parameter ranges for both $\epsilon_e$ and $\xi_e$ to
within about one order of magnitude, $0.01\lesssim\epsilon_e\lesssim0.2$ and
$0.1\lesssim\xi_e\lesssim1$. Such stringent constraints are inaccessible for
$\xi_e$ from broadband studies due to model degeneracies.
