Sivers Function in the Quasi-Classical Approximation

Abstract

We calculate the Sivers function in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY) by employing the quasi-classical Glauber-Mueller/ McLerran-Venugopalan approximation. Modeling the hadron as a large "nucleus" with non-zero orbital angular momentum (OAM), we find that its Sivers function receives two dominant contributions: one contribution is due to the OAM, while another one is due to the local Sivers function density in the nucleus. While the latter mechanism, being due to the "lensing" interactions, dominates at large transverse momentum of the produced hadron in SIDIS or of the di-lepton pair in DY, the former (OAM) mechanism is leading in saturation power counting and dominates when the above transverse momenta become of the order of the saturation scale. We show that the OAM channel allows for a particularly simple and intuitive interpretation of the celebrated sign flip between the Sivers functions in SIDIS and DY.

Figures (14)

• Figure 1: The physical mechanism of STSA in DY as envisioned in the text.
• Figure 2: The physical mechanism of STSA in SIDIS as envisioned in the text.
• Figure 3: The lowest-order SIDIS process in the usual $\alpha_s$ power-counting. A quark is ejected from a nucleon in the nucleus by the high-virtuality photon, which escapes without rescattering. Different solid horizontal lines represent valence quarks from different nucleons in the nuclear wave function, with the latter denoted by the vertical shaded oval.
• Figure 4: Space-time structure of quark production in the quasi-classical SIDIS process in the rest frame of the nucleus, overlaid with one of the corresponding Feynman diagrams. The shaded circle is the transversely polarized nucleus, with the vertical double arrow denoting the spin direction.
• Figure 5: Decomposition of the nuclear quark distribution $\Phi_A$ probed by the SIDIS virtual photon into mean-field wave functions $\psi, \psi^*$ of nucleons and the quark and gluon distributions $\phi_N$ and $\varphi_N$ of the nucleons.