  We introduce the notions of quasi-Laurent and Laurent families of simple
modules over quiver Hecke algebras of arbitrary symmetrizable types. We prove
that such a family plays a similar role of a cluster in the quantum cluster
algebra theory and exhibits a quantum Laurent positivity phenomenon for the
basis of the quantum unipotent coordinate ring
$\mathcal{A}_q(\mathfrak{n}(w))$, coming from the categorification. Then we
show that the families of simple modules categorifying GLS-clusters are Laurent
families by using the PBW-decomposition vector of a simple module $X$ and
categorical interpretation of (co-)degree of $[X]$. As applications of such
$\mathbb{Z}$-vectors, we define several skew symmetric pairings on arbitrary
pairs of simple modules, and investigate the relationships among the pairings
and $\Lambda$-invariants of R-matrices in the quiver Hecke algebra theory.
