content_image/435222.jpg content_image/435223.jpg content_image/435240.jpg content_image/435239.jpg content_image/435238.jpg content_image/435232.jpg content_image/435231.jpg content_image/435233.jpg content_image/435234.jpg content_image/435235.jpg content_image/435236.jpg content_image/435237.jpg
multiply both sides of Eq. (38) by d αβ and obtain, 

<img src='content_image/435222.jpg'>

⊥ Given the twist-2 TMD quark distribution function f N q ( x, k$_{⊥}$ ) and the twist-3 quark distribution f N q $_{⊥}$( x, ℓ$_{⊥}$ ) in a nucleon and using the above convolution, Eqs.(3) and (40), one can then calculate the nuclear dependence of the azimuthal asymmetry 〈 cos φ 〉 and 〈〈 cos φ 〉〉 . In general, if the convoluted twist-3 TMD quark distribution is a decreasing function of the transverse momentum in the region of interest, the second term involving a derivative in the above equation will be negative. Therefore, one would expect the azimuthal asymmetry to decrease because of the multiple scattering in nuclei. 

<img src='content_image/435223.jpg'>

To illustrate the nuclear dependence of the azimuthal asymmetry qualitatively, we consider an ansatz of the Gaussian distributions in k$_{⊥}$ for both the twist-2 and 3 TMD quark distributions, 

<img src='content_image/435240.jpg'>

<img src='content_image/435239.jpg'>

The corresponding TMD distributions in nuclei are, 

<img src='content_image/435238.jpg'>

<img src='content_image/435232.jpg'>

One can then calculate the the azimuthal asymmetry for SIDIS off both nucleon 

<img src='content_image/435231.jpg'>

and nuclear targets 

<img src='content_image/435233.jpg'>

The nuclear modification factor for the azimuthal asymmetry is then, 

<img src='content_image/435234.jpg'>

In the special case when α = β , we have 

<img src='content_image/435235.jpg'>

<img src='content_image/435236.jpg'>

<img src='content_image/435237.jpg'>

