pQCD physics of multiparton interactions

Abstract

We study production of two pairs of jets in hadron-hadron collisions in view of extracting contribution of double hard interactions of three and four partons (3 → 4, 4 → 4). Such interactions, in spite of being power suppressed at the level of the total cross section, become comparable with the standard hard collisions of two partons, 2 → 4, in the back-to-back kinematics when the transverse momentum imbalances of two pairing jets are relatively small.We express differential and total cross sections for two-dijet production in double parton collisions through the generalized two-parton distributions, 2GPDs [1], that contain large-distance two-parton correlations of non-perturbative origin as well as small-distance correlations due to parton evolution. We find that these large-and small-distance correlations participate in different manner in 4-jet production, and treat them in the leading logarithmic approximation of pQCD that resums collinear logarithms in all orders.A special emphasis is given to 3 → 4 double hard interaction processes that occur as an interplay between large-and short-distance parton correlations and were not taken into consideration by approaches inspired by the parton model picture. We demonstrate that the 3 → 4 mechanism, being of the same order in αs as the 4 → 4 process, turns out to be geometrically enhanced compared to the latter and should contribute significantly to 4-jet production.The framework developed here takes into systematic consideration perturbative Q 2 evolution of 2GPDs. It can be used as a basis for future analysis of NLO corrections to multi-parton interactions (MPI) at LHC and Tevatron colliders, in particular for improving evaluation of QCD backgrounds to new physics searches.

Perturbative and nonperturbative correlations in double parton distributions

“…Later on, similar results were also obtained in Ref. [39], with an emphasis on the differential cross sections, and were partly corroborated in Refs. [40,41], albeit with some distinctions attributed mainly to the terminology.…”

“…Note that the particular solutions (10) of nonhomogeneous equations contribute to the inclusive cross section of DPS with a larger weight (different effective cross section) [38,39,41,42,50,57] as compared to the solutions (9) of homogeneous equations. The latter solutions are usually approximated by a factorized form if the initial nonperturbative correlations are absent.…”

Relativistic effects in model calculations of double parton distribution functions

“…It should be noticed that dPDFs, calculated in momentum space, describe a system where two partons have a relative transverse momentum (± k ⊥ ). This unbalance physically arises since the difference of parton transverse momenta is not conserved between the amplitude and its complex conjugate [34,35]. Due to this unbalance, the dPDFs are not densities in this representation and they can not be interpreted as probabilistic distributions.…”

“…Such a factorized ansatz is nevertheless valuable since, under a number of approximations, it allows to relate the double gluon distribution functions to the gluon GPDs, exactly in the kinematic range of small x where CQM model are difficult to extend and the corresponding theoretical predictions for T (b ⊥ ) are lacking, see Refs. [34,35]. On the perturbative side, the evolution effects on such a factorized b-space ansatz have been investigated in Ref.…”

Double parton scattering in the ultraviolet: addressing the double counting problem

“…(1.1) using dimensional regularisation. This also avoids double counting with the SPS, but a drawback is that one loses the concept of the DPD of an individual hadron -the appropriate operators for DPS then involve both hadrons at once.A further past suggestion [6] is somewhat similar to [4], but involves including the 1v1 contribution with an ad-hoc lower cut-off in the y integral at values of order 1/Q (in [6] the cut-off is actually imposed in the Fourier conjugate space, but the principle is the same). This renders the DPS contribution finite.…”