Spin alignments of vector mesons in deeply inelastic lepton-nucleon scattering

We extend the calculations of the spin alignments of vector mesons in $e^+e^-$ annihilation in a recent Rapid Communication to deeply inelastic lepton-nucleon scatterings. We present the results for different mesons in the current fragmentation regions of $\mu^- N$$ \to$$ \mu^- VX$ at high energies and $\nu_\mu N $$\to$$ \mu^- VX$ at both high and low energies. We also present the predictions for $\nu_\mu N$$ \to$$ \mu^- VX$ at NOMAD energies in the target fragmentation region using a valence quark model.