The quantum evolutions of the diffractive transverse-momentum dependent gluon distribution

Abstract

Using the Colour Glass Condensate description of electron-nucleus collisions at high energy, we study the diffractive production of a pair of jets with transverse momenta much larger than the nuclear saturation momentum $Q_s$. At leading order in the QCD coupling, the di-jet cross-section exhibits transverse-momentum dependent (TMD) factorisation, with a gluon diffractive TMD distribution (DTMD) which is controlled by gluon saturation and describes the transverse-momentum imbalance between the produced jets. The next-to-leading corrections generate the various quantum evolutions of the diffractive gluon distribution. We focus on the Collins-Soper-Sterman (CSS) evolution which describes the change in the gluon DTMD when increasing the ''hard scale'' (the typical transverse momentum of the di-jets). We consider two different representations for this equation, one in transverse-momentum space, the other one in transverse-coordinate space. They are not fully equivalent with each other (despite being related by a Fourier transform) because of the respective boundary conditions. These conditions encode the essential physics of gluon saturation together with the effects of two other types of quantum evolution: the BK/JIMWLK evolution over the rapidity gap (''inside the Pomeron'') and the DGLAP evolution outside the rapidity gap (''within the diffractive system''). We demonstrate that, due to gluon saturation, one can compute both the boundary conditions and the CSS solutions fully from first principles, without reference to non-perturbative physics. We numerically find a good agreement between the CSS solutions in the two aforementioned representations.