  The distribution of the azimuthal angle of charged and neutral hadrons
relative to the lepton plane has been studied for neutral current deep
inelastic $ep$ scattering using an integrated luminosity of 45 pb-1 taken with
the ZEUS detector at HERA. The measurements were made in the hadronic
centre-of-mass system. The analysis exploits the energy-flow method, which
allows the measurement to be made over a larger range of pseudorapidity
compared to previous results. The dependence of the moments of the azimuthal
distributions on the pseudorapidity and minimum transverse energy of the
final-state hadrons are presented. Although the predictions from
next-to-leading-order QCD describe the data better than do the Monte Carlo
models incorporating leading-logarithm parton showers, they still fail to
describe the magnitude of the asymmetries. This suggests that higher-order
calculations may be necessary to describe these data.
