A study of the corrections to factorization in $\bar{B}^0 \to D^{* +} \omega \pi^-$

A factorization hypothesis is tested by examining a form factor of the $\omega\pi$ production in hadronic $B^0 \to D^{\ast \pm}\omega\pi^\mp$ decays. The form factor is compared to that from available $\tau$-lepton as well as $e^+e^-$ data using the conserved vector current hypothesis. The difference of normalizations of form factor shapes from $B$ and $\tau~(e^+e^-)$ data indicates the important role of the large $N_c$ limit in QCD. Moreover, the growth of the difference between the form factors with the $\omega\pi$ invariant mass is related to the perturbative QCD corrections of factorization. The current precision of $B$ data does not allow one to find any evidence of corrections to factorization. A promising study could be performed with the Belle II and LHCb data sets.