  By taking advantage of the natural stability of the high-energy resummation,
recently discovered in the context of heavy-flavor studies, we investigate the
inclusive hadroproduction of a neutral heavy-light, hidden-flavored tetraquark
($X_{cu\bar{c}\bar{u}}$ or $X_{bs\bar{b}\bar{s}}$ state), in association with a
heavy (single $c$- or $b$-flavored) hadron or a light jet at the (HL-)LHC. We
make use of the JETHAD multi-modular working package to provide predictions for
rapidity, azimuthal-angle and transverse-momentum distributions calculated via
the hybrid high-energy and collinear factorization, where the
Balitsky--Fadin--Kuraev--Lipatov resummation of energy logarithms is
supplemented by collinear parton densities and fragmentation functions. We rely
upon the single-parton fragmentation mechanism, valid in the large
transverse-momentum regime, to describe the tetraquark production. Our study
represents a first attempt at bridging the gap between all-order calculations
of high-energy QCD and the exotics.
