Description
The discovery of rapidly growing cascade of gluons and sharp non-linear rise of its distributions in DIS experiments at HERA collider provides indirect experimental evidence that proton at high energy is a hugely complex many body quantum system where gluons are the dominant degrees of freedom. By now many studies have been performed in the theoretical front to develop frameworks that extend our understanding on the structure of proton beyond just one dimensional ordinary parton distribution functions (PDFs). The attempts are mostly based on considering other (than regular PDFs) relatively closer descendants of the original, yet unknown, Wigner distribution functions which presumably contain all the information.
Transverse momentum dependent parton distributions (TMDs) or unintegrated parton distribution functions (UPDFs) are such examples that provide, in addition to longitudinal momentum fraction x of the parton, details of transverse momentum distribution and therefore contain much more detailed information on the internal structure of protons relative to the ordinary PDFs.
In this work we derive analytical results for black-disk asymptotic behavior of the unintegrated dipole gluon distribution function. By Fourier transforming asymptotic form of the S-matrix, as given by the Levin-Tuchin solution of the Balitsky-Kovchegov equation, to transverse momentum space, we derive the result in the form of a series of Bells polynomials. Interestingly, when resummation is done for the series in leading log accuracy, the results showing up striking similarity with the Sudakov form factor with role play of coupling is being done by a constant that stems from the saddle point condition along the saturation line. We also would like to discuss possible connection of unintegrated dipole gluon distribution and the Weizs\"{a}cker-Williams gluon distribution in the small-x limit.
Ref. [1] Raktim Abir, K. Banu, T. Bhattacharyya, M. Siddiqah and N. Vasim, ``Black-disk asymptotics of unintegrated dipole gluon distribution,'' arXiv:1801.01637 [hep-ph].
