Nuclear dependence of azimuthal asymmetry in semi-inclusive deep inelastic scattering arXiv:1001.3146v1 [hep-ph] 18 Jan 2010 I. INTRODUCTION Jian-Hua Gao 1 , 2 , 3 Zuo-tang Liang $^{2}$, Xin-Nian Wang3 $^{1}$Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China $^{2}$Department of Physics, Shandong University, Jinan, Shandong 250100, China and $^{3}$Nuclear Science Division, MS 70R0319, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (Dated: October 30, 2018) Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse- momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry 〈 cos φ 〉 of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of the azimuthal asymmetry 〈 cos φ 〉 is studied. It is shown that the azimuthal asymmetry is suppressed by multiple parton scattering and the transverse momentum dependence of the suppression depends on the relative shape of the twist-2 and 3 quark distributions in the nucleon. A Gaussian ansatz for TMD twist-2 and 3 quark distributions in nucleon is used to demonstrate the nuclear dependence of the azimuthal asymmetry and to estimate the smearing effect due to fragmentation. PACS numbers: 25.75.-q, 13.88.+e, 12.38.Mh, 25.75.Nq In high-energy nuclear collisions, from deeply inelastic scattering (DIS) off a nuclear target to hadron-nucleus and nucleus-nucleus collisions, multiple parton scattering plays an important role in the reaction dynamics and the final hadron spectra. It not only causes the transverse momentum broadening of the propagating parton but also leads to parton energy loss due to induced gluon bremsstrahlung. A direct consequence of the transverse momentum broadening is the so-called Cronin effect or the broadening of the final hadron spectra in transverse momentum in both DIS off nuclear targets [1, 2] and hadron-nucleus collisions [3, 4]. Gluon bremsstrahlung induced by multiple parton scattering on the other hand leads to parton energy loss [5–8] and medium modification of the parton fragmentation functions [9, 10], a phenomenon known as jet quenching which is observed as the suppression of the leading hadron yields from parton fragmentation. The radiative parton energy loss and medium modification to parton fragmentation functions are also determined by the jet transport parameter or the average squared transverse momentum broadening per unit distance experienced by the propagating parton, which is related to the gluonic structure of the scattering centers in the medium [6, 11]. Therefore, extraction of the jet transport parameter through experimental measurements of transverse momentum broadening and jet quenching can provide important information about the properties of the medium, either cold nuclei or hot and dense QCD matter, as probed by energetic partons. The jet quenching phenomenon has been seen in high-energy heavy-ion collisions via strong suppression of not only the large transverse momentum single hadron spectra [12, 13] but also the back-to-back dihadron correlation [14]. The extracted jet transport parameter is found to be much larger than that in large cold nuclei as obtained by phenomenological studies of jet quenching in DIS [15, 16], indicating much higher gluonic density in the initial stage of high-energy heavy-ion collisions. Much efforts have also been devoted to the study of transverse momentum broadening in DIS off nuclear targets [6, 9, 10, 17, 18, 20–24] and the Drell-Yan dilepton production in proton-nucleus collisions [25–27] within different approaches such as the color dipole model[17–19] and higher-twist expansion in the generalized collinear factorization formalism [20, 21]. It has been shown recently [24] that the gauge invariant transverse momentum dependent (TMD) quark distributions in nucleons and nuclei can be expressed as a sum of higher-twist collinear parton matrix elements, where ⃗ D$_{⊥}$ ( y $^{−}$) = ⃗ ∂$_{⊥}$ + ig ⃗ A$_{⊥}$ ( y $^{−}$) is the covariant derivative. For brevity of presentation, we have used the light-cone gauge and all the transverse coordinates have been set to ⃗ y$_{⊥}$ = ⃗ 0$_{⊥}$ in the above. Since the above expression is valid ⃗ W$_{⊥}$ ( y $^{−}$) ≡ i ⃗ D$_{⊥}$ ( y $^{−}$) + g ∫ y − −∞ dξ − ⃗ F$_{+}$$_{⊥}$ ( ξ $^{−}$) , (2) in terms of the parton transport operator