content_image/432056.jpg content_image/432057.jpg content_image/432060.jpg content_image/432061.jpg content_image/432073.jpg content_image/432074.jpg content_image/432068.jpg content_image/432069.jpg content_image/432070.jpg content_image/432071.jpg
<img src='content_image/432056.jpg'>

<img src='content_image/432057.jpg'>

We see again that 〈〈 cos φ 〉〉 eA is suppressed compared to 〈〈 cos φ 〉〉 $_{eN}$, and the suppression factor is inversely proportional to the square-root of the total transverse momentum broadening Δ$_{2}$$_{F}$ . 

To take into account of the transverse momentum during the quark fragmentation process and its effect on the azimuthal asymmetry, we take another Gaussian smearing 

<img src='content_image/432060.jpg'>

for the k$_{F}$$_{⊥}$ -dependence in the fragmentation function D q → h F ( z, ⃗ k$_{F}$$_{⊥}$ ), i.e. , 

<img src='content_image/432061.jpg'>

Consider the case that α = β and one has the azimuthal asymmetry for the hadron production cross section 

<img src='content_image/432073.jpg'>

<img src='content_image/432074.jpg'>

We compare the above results with those obtained without fragmentation, Eqs. (48) and (49), and see that we have a clear smearing effect on the azimuthal asymmetry in both e $^{−}$N and e $^{−}$A -scatterings. The smearing factors are given by, 

<img src='content_image/432068.jpg'>

<img src='content_image/432069.jpg'>

The suppression factor in eA compared to eN is given by, 

<img src='content_image/432070.jpg'>

After integrated over the magnitude of the transverse momentum, we have, 

<img src='content_image/432071.jpg'>

## IV. SUMMARY AND DISCUSSIONS 

Within the generalized factorization, we have calculated the SIDIS cross sections in terms of the TMD quark dis- tributions in a nucleon or nucleus up to twist-3. The azimuthal asymmetry 〈 cos φ 〉 in the small transverse momentum region depends on both twist-2 and 3 TMD quark distributions. By considering nuclear broadening of both twist-2 and 3 TMD quark distributions due to multiple scattering between the struck quark and nucleons inside the nucleus, 

