  We prove that the zero-fiber of the moment map of a totally negative quiver
has rational singularities. Our proof consists in generalizing dimension bounds
on jet spaces of this fiber, which were introduced by Budur. We also transfer
the rational singularities property to other moduli spaces of objects in
2-Calabi-Yau categories, based on recent work of Davison. This has interesting
arithmetic applications on quiver moment maps and moduli spaces of objects in
2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptotic
behaviour of counts of jets of quiver moment maps over finite fields. Moreover,
we interpret the limit of counts of jets on a given moduli space as its p-adic
volume under a canonical measure analogous to the measure built by Carocci,
Orecchia and Wyss on certain moduli spaces of coherent sheaves.
