  We reanalyze the $\Lambda_b\to p$ transition form factors in the perturbative
QCD (PQCD) approach by including higher-twist light-cone distribution
amplitudes (LCDAs) of a $\Lambda_b$ baryon and a proton. The previous PQCD
evaluation performed decades ago with only the leading-twist $\Lambda_b$ baryon
and proton LCDAs gave the form factors, which are two orders of magnitude
smaller than indicated by experimental data. We find that the twist-4
$\Lambda_b$ baryon LCDAs and the twist-4 and -5 proton LCDAs contribute
dominantly, and the enhanced form factors become consistent with those from
lattice QCD and other nonperturbative methods. The estimated branching ratios
of the semileptonic decays $\Lambda_b\to p\ell\bar{\nu}_\ell$ and the hadronic
decay $\Lambda_b\to p\pi$ are also close to the data. It implies that the $b$
quark mass is not really heavy enough, and higher-power contributions play a
crucial role, similar to the observation made in analyses of $B$ meson
transition form factors. With the formalism established in this work, we are
ready to study various exclusive heavy baryon decays systematically in the PQCD
approach.
