  Prompt and nonprompt productions of exotic multiquark states are studied
using the $\sim$10.4 fb$^{-1}$ data sample collected by the D0 experiment in
Tevatron $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The recent D0 results
on the prompt and nonprompt production of the $X(3872)$ and $Z_c^+(3900)$
states and the $P_c$ pentaquarks at the 4450 MeV region are reported. Signals
corresponding to these states are found in the nonprompt production, whereas
only the $X(3872)$ state is seen in the prompt production. The ratio of prompt
to nonprompt $X(3872)$ production is about three times larger in the D0
measurement than that obtained by the ATLAS experiment at 8 TeV. Theoretically,
the production, formation, coalescence, and disassociation processes are
expected to be quite different for conventional mesons with a spatial size of
(0.4-0.8) fm, compact multiquark states such as tetraquarks with a size of a
few fm, and spatially extended molecular states with a size of (4-10) fm. They
can be differently affected in prompt hadron-hadron collisions where there are
many additional particles emitted from the interaction point. Consequently, the
prompt to nonprompt production ratio of spatially extended exotic states can be
suppressed at LHC comparing with the Tevatron conditions, because of large
difference in the hadron-hadron collisions particle multiplicity. The prompt
production studies provide an opportunity to better understand the nature of
exotic states.
