Saturation and Wilson line distribution

We introduce a Wilson line distribution function (W) over bar (tau)(v) to study gluon saturation at small Feynman x(F), or large tau=ln(1/x(F)). This new distribution can be obtained from the distribution W-tau(alpha) of the color glass condensate model and the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) renormalization group equation. (W) over bar (tau)(v) is physically more relevant, and mathematically simpler to deal with because of unitarity of the Wilson line v. A JIMWLK equation is derived for (W) over bar (tau)(v); its properties are studied. These properties are used to complete Mueller's derivation of the JIMWLK equation, though for (W) over bar (tau)(v) and not W-tau(alpha). They are used to derive a generalized Balitsky-Kovchegov equation for higher multipole amplitudes. They are also used to compute the unintegrated gluon distribution at x(F)=0, yielding a completely flat spectrum in transverse momentum squared k(2), with a known height. This is similar but not identical to the mean field result at small k(2).