Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution

We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) using the tools of saturation physics. By generalizing the quasi-classical Glauber-Gribov-Mueller/McLerran-Venugopalan approximation to allow for the possibility of spin-orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large "nucleus." To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer-Mulders distribution. We observe that spin-orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.

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