  We calculate the axial couplings of mesons and baryons containing a heavy
quark in the static limit using lattice QCD. These couplings determine the
leading interactions in heavy hadron chiral perturbation theory and are central
quantities in heavy quark physics, as they control strong decay widths and the
light-quark mass dependence of heavy hadron observables. Our analysis makes use
of lattice data at six different pion masses, 227 MeV < m_\pi < 352 MeV, two
lattice spacings, a=0.085, 0.112 fm, and a volume of (2.7 fm)^3. Our results
for the axial couplings are g_1=0.449(51), g_2=0.84(20), and g_3=0.71(13),
where g_1 governs the interaction between heavy-light mesons and pions and
g_{2,3} are similar couplings between heavy-light baryons and pions. Using our
lattice result for g_3, and constraining 1/m_Q corrections in the strong decay
widths with experimental data for \Sigma_c^{(*)} decays, we obtain
\Gamma[\Sigma_b^{(*)} \to \Lambda_b \pi^\pm] = 4.2(1.0), 4.8(1.1), 7.3(1.6),
7.8(1.8) MeV for the \Sigma_b^+, \Sigma_b^-, \Sigma_b^{*+}, \Sigma_b^{*-}
initial states, respectively. We also derive upper bounds on the widths of the
\Xi_b^{\prime(*)} baryons.
