8 〈〈 cos φ 〉〉 eA = − 2(2 − y $_{)}$√$_{1}$ − y 1 + (1 − y ) 2 √$_{πβ}$ 2 $_{Q}$√$_{β}$ + Δ$_{2}$$_{F}$ x$_{B}$f N q $_{⊥}$( x ) f N q ( x ) , (52) 〈〈 cos φ 〉〉 eA cos φ eN = √ β β + Δ$_{2}$$_{F}$ . (53) 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}$$_{F}$ . To take into account of the transverse momentum during the quark fragmentation process and its effect on the azimuthal asymmetry, we take another Gaussian smearing dσ eN → ehX = ∫ dσ eN → $^{eqX}$D q → h F ( z, ⃗ k$_{F}$$_{⊥}$ ) dzd $^{2}$k$_{F}$$_{⊥}$ δ $^{(3)}$( ⃗ p$_{h}$ − z ⃗ k ′ − k$_{F}$$_{⊥}$ ) d $^{3}$p$_{h}$ , (54) D q → h F ( z, ⃗ k$_{F}$$_{⊥}$ ) = D q → h F ( z ) 1 πα$_{F}$ e − ⃗ k 2 F $_{⊥}$/α F . (55) for the k$_{F}$$_{⊥}$ -dependence in the fragmentation function D q → h F ( z, ⃗ k$_{F}$$_{⊥}$ ), i.e. , Consider the case that α = β and one has the azimuthal asymmetry for the hadron production cross section We compare the above results with those obtained without fragmentation, Eqs. (48) and (49), and see that we have a clear smearing effect on the azimuthal asymmetry in both e $^{−}$N and e $^{−}$A -scatterings. The smearing factors are given by, The suppression factor in eA compared to eN is given by, After integrated over the magnitude of the transverse momentum, we have, Within the generalized factorization, we have calculated the SIDIS cross sections in terms of the TMD quark dis- tributions in a nucleon or nucleus up to twist-3. The azimuthal asymmetry 〈 cos φ 〉 in the small transverse momentum region depends on both twist-2 and 3 TMD quark distributions. By considering nuclear broadening of both twist-2 and 3 TMD quark distributions due to multiple scattering between the struck quark and nucleons inside the nucleus, 〈 cos φ$_{h}$ 〉 eN cos φ eN ∣ | ⃗p h $_{⊥}$| = z | ⃗ k$_{⊥}$ | = βz 2 βz 2 + α$_{F}$ , (58) 〈 cos φ$_{h}$ 〉 eA cos φ eA ∣ | ⃗p h $_{⊥}$| = z | ⃗ k$_{⊥}$ | = ( β + Δ$_{2}$$_{F}$ ) z 2 ( β + Δ$_{2}$$_{F}$ ) z 2 + α$_{F}$ . (59) 〈 cos φ$_{h}$ 〉 eA cos φ$_{h}$ eN = βz 2 + α$_{F}$ ( β + Δ$_{2}$$_{F}$ ) z 2 + α$_{F}$ . (60) 〈〈 cos φ$_{h}$ 〉〉 eA cos φ$_{h}$ eN = √ βz 2 + α$_{F}$ ( β + Δ$_{2}$$_{F}$ ) z 2 + α$_{F}$ . (61) IV. SUMMARY AND DISCUSSIONS 〈 cos φ$_{h}$ 〉 eN = − 2(2 − y $_{)}$√$_{1}$ − y 1 + (1 − y ) 2 βz βz 2 + α$_{F}$ | ⃗ p$_{h}$$_{⊥}$ | Q x$_{B}$f N q $_{⊥}$( x ) f N q ( x ) , (56) 〈 cos φ$_{h}$ 〉 eA = − 2(2 − y $_{)}$√$_{1}$ − y 1 + (1 − y ) 2 βz ( β + Δ$_{2}$$_{F}$ ) z 2 + α$_{F}$ | ⃗ p$_{h}$$_{⊥}$ | Q x$_{B}$f N q $_{⊥}$( x ) f N q ( x ) . (57)