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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. 

<img src='content_image/443311.jpg'>

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, 

<img src='content_image/443308.jpg'>

