  In this letter, measurements of (anti)alpha production in central (0$-$10%)
Pb$-$Pb collisions at a center-of-mass energy per nucleon$-$nucleon pair of
$\sqrt{s_{\rm NN}}$ = 5.02 TeV are presented, including the first measurement
of an antialpha transverse-momentum spectrum. Owing to its large mass,
(anti)alpha production yields and transverse-momentum spectra are of particular
interest because they provide a stringent test of particle production models.
The averaged antialpha and alpha spectrum is included into a common blast-wave
fit with lighter particles, indicating that the (anti)alpha also participates
in the collective expansion of the medium created in the collision. A
blast-wave fit including only protons, (anti)alpha, and other light nuclei
results in a similar flow velocity as the fit that includes all particles. A
similar flow velocity, but a significantly larger kinetic freeze-out
temperature is obtained when only protons and light nuclei are included in the
fit. The coalescence parameter $B_4$ is well described by calculations from a
statistical hadronization model but significantly underestimated by
calculations assuming nucleus formation via coalescence of nucleons. Similarly,
the (anti)alpha-to-proton ratio is well described by the statistical
hadronization model. On the other hand, coalescence calculations including
approaches with different implementations of the (anti)alpha substructure tend
to underestimate the data.
