  We explore the on-shell recursion for tree-level scattering amplitudes with
massive spinning particles. Based on the factorization structure encoded in the
same way by two different recursion relations, we conjecture an
all-multiplicity formula for two gauged massive particles of arbitrary spin and
any number of identical-helicity gluons. Specializing to quantum chromodynamics
(QCD), we solve the on-shell recursion relations in the presence of two pairs
of massive quarks and an arbitrary number of identical-helicity gluons. We find
closed-form expressions for the two distinct families of color-ordered
four-quark amplitudes, in which all gluons comprise a single color-adjacent
set. We compare the efficiency of the numerical evaluation of the two resulting
analytic formulae against a numerical implementation of the off-shell
Berends-Giele recursion. We find the formulae for both amplitude families to be
faster for large multiplicities, while the simpler of the two is actually
faster for any number of external legs. Our analytic results are provided in a
computer-readable format as two ancillary files.
