Sudakov factor in deep inelastic scattering of a current off a large nucleus

We consider a gedanken experiment of the scattering of a current $j=-\frac{1}{4}{F}_{\mu \nu }^i{F}_{\mu \nu }^i$ off a large nucleus to study the gluon saturation at the small-$x$ limit and compute the Sudakov factor of this process through a one-loop calculation. The differential cross section is expressed in terms of the Sudakov resummation, in which the collinear and the rapidity divergences are subtracted.

Figure 1

Feynman diagram at leading order of deep inelastic scattering of the current off a large nucleus.

Figure 2

Radiating gluon happens between the multiply scattering, this process is neglected because the time for multiply scattering between the produced gluon and nucleus target is too short in the high-energy limit.

Figure 3

The real diagrams of deep inelastic scattering of the current off a large nucleus at one-loop order.

Figure 4

Virtual loop diagrams in deep inelastic scattering of the current off a large nucleus at one-loop order.