  In a recent letter [Phys. Rev. Lett. 108, 172003 (2012), arXiv:1109.2480] we
have reported on a lattice QCD calculation of the heavy-hadron axial couplings
$g_1$, $g_2$, and $g_3$. These quantities are low-energy constants of
heavy-hadron chiral perturbation theory (HH$\chi$PT) and are related to the
$B^*B\pi$, $\Sigma_b^*\Sigma_b\pi$, and $\Sigma_b^{(*)}\Lambda_b\pi$ couplings.
In the following, we discuss important details of the calculation and give
further results. To determine the axial couplings, we explicitly match the
matrix elements of the axial current in QCD with the corresponding matrix
elements in HH$\chi$PT. We construct the ratios of correlation functions used
to calculate the matrix elements in lattice QCD, and study the contributions
from excited states. We present the complete numerical results and discuss the
data analysis in depth. In particular, we demonstrate the convergence of
$SU(4|2)$ HH$\chi$PT for the axial-current matrix elements at pion masses up to
about 400 MeV and show the impact of the nonanalytic loop contributions.
Finally, we present additional predictions for strong and radiative decay
widths of charm and bottom baryons.
