Therefore, the azimuthal asymmetry 〈 cos φ 〉 eA in deep inelastic eA scattering is suppressed compared to that in eN scattering and the suppression is inversely proportional to the total transverse momentum broadening Δ$_{2}$$_{F}$ . The suppression is independent of the transverse momentum k$_{⊥}$ . However, in general, the twist-2 and twist-3 TMD quark distributions are not necessarily the same and their Gaussian ansatz might have different widths β = α . The nuclear modification factor for the azimuthal asymmetry will then have non-trivial k$_{⊥}$ dependence. Shown in Fig. 1 are the nuclear modification factors for the azimuthal asymmetry when β/α = 2 and 0.5, respectively, as functions of Δ$_{2}$$_{F}$ /α , at different transverse momentum k$_{⊥}$ . In the case β > α , we see that the azimuthal asymmetry is suppressed and the suppression increases with the transverse momentum k$_{⊥}$ . However, when β < α , the suppression actually decreases with increasing k$_{⊥}$ and the azimuthal asymmetry could be enhanced for large enough transverse momentum k$_{⊥}$ . Therefore, the nuclear modification of the azimuthal asymmetry and its transverse momentum dependence is a very sensitive probe of the twist-2 and twist-3 TMD quark distribution functions. 7 〈〈 cos φ 〉〉 eN = − 2(2 − y $_{)}$√$_{1}$ − y 1 + (1 − y ) 2 √$_{πβ}$ 2 Q x$_{B}$f N q $_{⊥}$( x ) f N q ( x ) , (51) FIG. 1: (color online) Ratio 〈 cos φ 〉 eA / 〈 cos φ 〉 eN as a function of Δ 2 F for different k$_{⊥}$ and the relative width β/α of twist-3 and 2 TMD quark distributions. If we integrate over the magnitude of the transverse momentum k$_{⊥}$ , the averaged azimuthal asymmetry will only depend on the shape of the twist-3 TMD quark distributions, 0 0.5 1 0 5 10 $_{2F}$/ <cos$^{φ}$ > eA /<cos$^{φ}$ > eN / =2.0 k =0.2 k =0.5 k =1.0 k =1.5 0 1 2 0 5 10 $_{2F}$/ <cos > eA /<cos > eN / =0.5 k =0.2 k =0.8 k =1.2 k =1.5