  We review the semi-inclusive hadroproduction of a neutral hidden-flavor
tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by
another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0
determinations of leading-twist fragmentation functions to describe the
formation mechanism of a tetraquark state within the next-to-leading order
perturbative QCD. This framework builds on the basis of a spin-physics inspired
model, taken as a proxy for the lowest-scale input of the constituent
heavy-quark fragmentation channel. Then, all parton-to-tetraquark fragmentation
functions are consistently obtained via the above-threshold DGLAP evolution in
a variable-flavor number scheme. We provide predictions for a series of
differential distributions calculated by the hands of the JETHAD method
well-adapted to NLL/NLO+ hybrid-factorization studies, where the resummation of
next-to-leading energy logarithms and beyond is included in the collinear
picture. We provide corroborating evidence that high-energy observables
sensitive to semi-inclusive tetraquark emissions at the HL-LHC exhibit a fair
stability under radiative corrections as well as MHOU studies. Our analysis
constitutes a prime contact point between QCD resummations and the exotic
matter.
