Search for decays of the $^{9}$B nucleus and Hoyle state in $^{14}$N nucleus dissociation
First results of an analysis to determine contribution of decays of the unstable $^{8}$Be and $^{9}$B nuclei and the Hoyle 3$\alpha$-state to dissociation of $^{14}$N $\to$ 3He (+H) are presented. As the research material, layers of nuclear track emulsion longitudinally exposed to 2.9 $A$ GeV/$c$ $^{14}$N nuclei with at the JINR Nuclotron. Under the assumption that the He and H fragments retain momentum per nucleon of the primary nucleus, these unstable states are identified by the invariant mass calculated from the emission angles of the fragments.