Gluon dipole factorisation for diffractive dijets

Within the colour dipole picture for deep inelastic scattering at small Bjorken $x$, we study the production of a pair of relatively hard jets via coherent diffraction. By "relatively hard" we mean that the transverse momenta of the two jets -- the quark ($q$) and the antiquark ($\bar{q}$) generated by the decay of the virtual photon -- are much larger than the target saturation momentum $Q_s(Y_{\mathbb{P}})$ evaluated at the rapidity gap $Y_{\mathbb{P}}$. We argue that the typical final-state configurations are such that the hard $q\bar q$ dijets are accompanied by a semi-hard gluon jet, with a transverse momentum of the order of $Q_s(Y_{\mathbb{P}})$. The presence of this third jet ensures that the scattering is strong and thus avoids the strong suppression of exclusive (hard) dijet production due to colour transparency. For such "2+1" jet configurations, we demonstrate that both the emission of the semi-hard gluon and its scattering with the hadronic target can be factorised in terms of an effective gluon-gluon dipole. This effective description, originally proposed in [1-4], builds a bridge between the colour dipole picture and collinear factorisation: the cross-section for diffractive 2+1 jets can be written as the product between a hard factor describing the $q\bar{q}$ dijets and a semi-hard factor expressing the unintegrated gluon distribution of the Pomeron. The latter is controlled by gluon dipole scattering in the black disk limit and hence is strongly sensitive to gluon saturation. By integrating out the kinematics of the 3 jets, we obtain the $q\bar{q}g$ contribution to the diffractive structure function in collinearly-factorised form.