  The azimuthal correlation angle, $\Delta\phi$, between the scattered lepton
and the leading jet in deep inelastic $e^{\pm}p$ scattering at HERA has been
studied using data collected with the ZEUS detector at a centre-of-mass energy
of $\sqrt{s} = 318 \;\mathrm{GeV}$, corresponding to an integrated luminosity
of $326 \;\mathrm{pb}^{-1}$. A measurement of jet cross sections in the
laboratory frame was made in a fiducial region corresponding to photon
virtuality $10 \;\mathrm{GeV}^2 < Q^2 < 350 \;\mathrm{GeV}^2$, inelasticity
$0.04 < y < 0.7$, outgoing lepton energy $E_e > 10 \;\mathrm{GeV}$, lepton
polar angle $140^\circ < \theta_e < 180^\circ$, jet transverse momentum $2.5
\;\mathrm{GeV} < p_\mathrm{T,jet} < 30 \;\mathrm{GeV}$, and jet pseudorapidity
$-1.5 < \eta_\mathrm{jet} < 1.8$. Jets were reconstructed using the
$k_\mathrm{T}$ algorithm with the radius parameter $R = 1$. The leading jet in
an event is defined as the jet that carries the highest $p_\mathrm{T,jet}$.
Differential cross sections, $d\sigma/d\Delta\phi$, were measured as a function
of the azimuthal correlation angle in various ranges of leading-jet transverse
momentum, photon virtuality and jet multiplicity. Perturbative calculations at
$\mathcal{O}(\alpha_{s}^2)$ accuracy successfully describe the data within the
fiducial region, although a lower level of agreement is observed near
$\Delta\phi \rightarrow \pi$ for events with high jet multiplicity, due to
limitations of the perturbative approach in describing soft phenomena in QCD.
The data are equally well described by Monte Carlo predictions that supplement
leading-order matrix elements with parton showering.
