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Twist-4 contributions to the azimuthal asymmetry in SIDIS

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering (SIDIS) process $e^-+N \to e^-+q+X$ in leading order (LO) of perturbative QCD and up to twist-4 in power corrections and study in particular the azimuthal asymmetry $<cos2ϕ>$. The final results are expressed in terms of transverse momentum dependent (TMD) parton matrix elements of the target nucleon up to twist-4. %Under the maximal two-gluon correlation approximation, these TMD parton matrix elements in a nucleus %can be expressed terms of a Gaussian convolution of that in a nucleon with the width given by the jet transport %parameter inside cold nuclei. We also apply it to $e^-+A \to e^-+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry $<cos2ϕ>$ by using a Gaussian ansatz for the TMD parton matrix elements.