Comparison of improved TMD and CGC frameworks in forward quark dijet production

Abstract

For studying small-x gluon saturation in forward dijet production in high-energy dilute-dense collisions, the improved TMD (ITMD) factorization formula was recently proposed. In the Color Glass Condensate (CGC) framework, it represents the leading term of an expansion in inverse powers of the hard scale. It contains the leading-twist TMD factorization formula relevant for small gluon’s transverse momentum kt, but also incorporates an all-order resummation of kinematical twists, resulting in a proper matching to high-energy factorization at large kt. In this paper, we evaluate the accuracy of the ITMD formula quantitatively, for the case of quark dijet production in high-energy proton-proton(p+p) and proton-nucleus (p+A) collisions at LHC energies. We do so by comparing the quark-antiquark azimuthal angle ∆ϕ distribution to that obtained with the CGC formula. For a dijet with each quark momentum pt much larger than the target saturation scale, Qs, the ITMD formula is a good approximation to the CGC formula in a wide range of azimuthal angle. It becomes less accurate as the jet pt’s are lowered, as expected, due to the presence of genuine higher-twists contributions in the CGC framework, which represent multi-body scattering effects absent in the ITMD formula. We find that, as the hard jet momenta are lowered, the accuracy of ITMD start by deteriorating at small angles, in the high-energy-factorization regime, while in the TMD regime near ∆ϕ = π, very low values of pt are needed to see differences between the CGC and the ITMD formula. In addition, the genuine twists corrections to ITMD become visible for higher values of pt in p + A collisions, compared to p+p collisions, signaling that they are enhanced by the target saturation scale.

Mining for Gluon Saturation at Colliders

“…This is an active area of research which has resulted in the development of improved TMD framework [159,160,198] and the CGC/TMD equivalence [201,254,255]. For comprehensive numerical studies both in pA and eA we refer the reader to the works in [203,256].…”

Low-x improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair

“…In [40], the γ * A → qqX ITMD expression (2.27) is compared to the full CGC expression, similarly to what was done in [18] for the gA → qqX case, in order to study the genuine twists contributions, which are parametrically suppressed by powers of Q 2 s /P 2 and neglected in the ITMD framework but included in the CGC.…”

“…where H ij (c) (k = 0) are the on-shell 'collinear' hard factors that appear at leading-twist. What is not included in the ITMD formula (but is in the full dilute-dense CGC expressions [8,9,17]) are the so-called genuine higher twists O(Q 2 s /P 2 ) [5,18]. For completeness, let us add that neglecting kinematical twists by replacing the hard factors H ij (c) with their collinear limit in (1.1) yields TMD factorization (to be precise, TMD factorization in which only the small-x gluon possesses nonzero transverse momentum).…”

Inclusive prompt photon-jet correlations as a probe of gluon saturation in electron-nucleus scattering at small x

“…Much of the discussion on azimuthal angle correlations at small x in the CGC and related frameworks has been restricted to dijet/dihadron production in p(d) + A collisions [41,[43][44][45][46][47][48][49][50][51][52][53][54][55]. Similar studies have been performed for the case of e + A scattering for the production of dijets/dihadrons [42,[56][57][58] and trijets 3 [61].…”