Twist-4 contributions to the azimuthal asymmetry in semi-inclusive deeply inelastic scattering

Abstract

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering process ${e}^{\ensuremath{-}}+N\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+q+X$ in leading order of perturbative QCD and up to twist-4 in power corrections and study, in particular, the azimuthal asymmetry $⟨\mathrm{cos}2\ensuremath{\phi}⟩$. The final results are expressed in terms of transverse momentum dependent parton matrix elements of the target nucleon up to twist-4. We also apply it to ${e}^{\ensuremath{-}}+A\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ by using a Gaussian ansatz for the transverse momentum dependent parton matrix elements.