  New hidden particles could potentially be emitted and discovered in rare
nuclear transitions. In this work we investigate the production of hidden
vector bosons with primarily axial couplings to light quarks in nuclear
transitions, and we apply our results to the recent anomaly seen in $^8$Be
decays. The relevant matrix elements for $^8{\rm Be}^*(1^+) \rightarrow ^8{\rm
Be} (0^+)$ transitions are calculated using ${\it ab \, initio}$ methods with
inter-nucleon forces derived from chiral effective field theory and the
in-medium similarity renormalization group. We find that the emission of a
light axial vector with mass $m_X \simeq 17\, {\rm MeV}$ can account for the
anomaly seen in the $1^+\to 0^+$ isoscalar transition together with the absence
of a significant anomaly in the corresponding isovector transition. We also
show that such an axial vector can be derived from an anomaly-free
ultraviolet-complete theory that is consistent with current experimental data.
