Theoretical insights on nuclear double parton distributions

We consider the production of W-boson plus dijet, W-boson plus b-jets and same sign WW via double parton scattering (DPS) in pA collisions at the LHC and evaluate the corresponding cross sections. The impact of a novel DPS contribution pertinent to pA collisions is quantified. Exploiting the experimental capability of performing measurements differential in the impact parameter in pA collisions, we discuss a method to single out this novel DPS contribution. The method allows the subtraction of the leading twist (LT) single parton scattering background and it gives access in a very clean way to double parton distribution functions in the proton. We calculate leading twist and DPS cross sections and study the dependence of the observables on the cuts in the jets phase space. In the Wjj channel the observation of DPS is possible with data already accumulated in pA runs and the situation will greatly improve for the next high luminosity runs. For the Wb{bar{b}} final state, the statistics within the current data is too low, but there is possibility to observe DPS in this channel in future runs, albeit with much reduced sensitivity than in Wjj final state. Finally the DPS observation in the same sign WW channel will require either significant increase of integrated luminosity beyond that foreseen in next pA runs or improved methods for W reconstruction, along with its charge, in hadronic decay channels.

Double parton scattering (DPS) has become very relevant as a background to interesting analyses performed by the experiments at the LHC. It encodes knowledge of correlations between the proton constituents not accessible in single parton scattering. Within perturbative QCD DPS is described in terms of partonic subprocesses and double parton distributions (DPDs). There exists a large number of different DPDs describing the different possible states of two partons inside a proton. They include correlations between the two partons and interferences between the two hard subprocesses. Taking the probability interpretation of the DPDs as starting point, we derive limits on the interference DPDs and thereby constrain the size of correlations between two partons inside an unpolarized proton.

The high gluon density in the initial state of hadronic collisions at LHC energies implies that the probability of multiple parton interactions within one proton-proton collision increases. In particular, this motivates one to investigate the importance of Double Parton Scattering (DPS) processes at the LHC. In a DPS process one can have, from one proton-proton collision, two interacting partons coming from each colliding hadron. In this context, the relation between the double parton distribution functions (dPDF) and the usual parton distribution functions (PDF) is discussed, and some formulae for the DPS cross section are compared. Our results focus on the production of different final states related to two heavy quark-antiquark pairs. Those include [Formula: see text], which is called the golden channel of DPS, [Formula: see text] and [Formula: see text].

We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with focus on correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering (DPS) in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results gives insight to the strengths of correlations in different kinematical regions, which can help in constructing input DPDs in cross section calculations.

We present the construction of unintegrated double parton distribution\nfunctions which include dependence on transverse momenta of partons. We extend\nthe formulation which was used to obtain the single unintegrated parton\ndistributions from the standard, integrated parton distribution functions.\nStarting from the homogeneous part of the evolution equations for the\nintegrated double parton distributions, we construct the unintegrated double\nparton distributions as the convolutions of the integrated double distributions\nand the splitting functions, multiplied by the Sudakov form factors. We show\nthat there exist three domains of external hard scales which require three\ndistinct forms of the unintegrated double distributions. The additional\ntransverse momentum dependence which arises through the Sudakov form factors\nleads to non-trivial correlations in the parton momenta. We also discuss the\nnon-homogeneous contribution to the unintegrated double parton distributions,\nwhich arises due to the splitting of a single parton into daughter partons with\nhigh transverse momenta. We analyze two cases, the unfolding of the transverse\nmomenta dependence from the last step of the evolution of two partons, and the\ncase where the transverse momenta are generated directly from the single parton\nsplitting.\n

A bstract Reconstructing Mellin moments of double parton distributions from calculations on a Euclidean lattice requires taking an integral over a variable that may be regarded as a Ioffe time. The Fourier conjugate of this variable plays the role of a kinematic skewness in the double parton distributions. We discuss the skewness dependence of the relevant hadronic correlation functions. Using several models, we study the impact of this dependence on extracting moments of double parton distributions from existing lattice data.

We show how the double parton distributions may be obtained consistently from the many-body light-cone wave functions. We illustrate the method on the example of the pion with two Fock components. The procedure, by construction, satisfies the Gaunt-Stirling sum rules. The resulting single parton distributions of valence quarks and gluons are consistent with a phenomenological parametrization at a low scale.

Recent results on double parton scattering (DPS) studies using data collected during Run 1 and Run 2 of the LHC with the CMS experiment are presented. Double parton scattering is investigated in several final states including vector bosons and multi-jets. Measurements of observables designed to highlight the DPS contribution are shown and compared to MC predictions from models based on multiple partonic interactions (MPIs) phenomenology.

Double parton scattering is sensitive to correlations between the two partons\nin the hadron, including correlations in flavor, spin, color, momentum\nfractions and transverse separation. We obtain a first estimate of the size of\nthese correlations by calculating the corresponding double parton distribution\nfunctions in a bag model of the proton. We find significant correlations\nbetween momentum fractions, spin and flavor, but negligible correlations with\ntransverse separation. The model estimates of the relative importance of these\ncorrelations will help experimental studies disentangle them.\n

We briefly discuss the status of double parton scattering (DPS) on both theoretical and experimental sides and summarize the state of the naive DPS model, where the scatterers are taken completely independent. We then elaborate on some of the effects which are neglected in such an approach, and often ignored in phenomenological studies, with focus on polarization - which arises from the correlation between the spin of two partons inside a proton. Polarization is of particular interest, thanks to its direct and calculable connections to the distribution of particles in the final state. Although the physics described is different, there are strong similarities between polarization in DPS and in single partons scattering with measured transverse momentum, and several of the techniques and results from studies of transverse momentum dependent parton distributions can be translated into the setting of double parton scattering.

Structure functions and parton distributions

Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.

The production of fully-heavy tetraquark states in proton–proton (pp) and proton–nucleus (pA) collisions at the center-of-mass energies of the Large Hadron Collider (LHC) and at the Future Circular Collider (FCC) is investigated considering that these states are produced through the double parton scattering mechanism. We estimate the cross sections for the T4c,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c},$$\\end{document}T4b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4b}$$\\end{document} and T2b2c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{2b2c}$$\\end{document} states and present predictions for pp, pCa and pPb collisions considering the rapidity ranges covered by central and forward detectors. We demonstrate that the cross sections for pA collisions are enhanced in comparison to the pp predictions scaled by the atomic number. Moreover, our results indicate that a search of these exotic states is, in principle, feasible in the future runs of the LHC and FCC.

The ATLAS collaboration recently reported on the first observation of associated-production of a Z0 boson with a J/ψ. We recently claimed that the corresponding yield of the promptJ/ψ was dominated by double parton scatterings in the ATLAS acceptance with a somewhat small value of σeff. We also found out that single parton scatterings were only dominant at large transverse momenta. We present here the first phenomenological analysis of another part of the ATLAS data sample, namely of a Z0 boson plus a non-promptJ/ψ. Our study is performed at next-to-leading order in αs and includes parton-shower effects via the MadGraph5_aMC@NLO framework. We find out that the data, unlike the case of prompt J/ψ+Z0, do not hint at significant DPS contributions. Owing to the current experimental and theoretical uncertainties, there is still a room for these but with a lower limit of σeff close to 5 mb. We stress the importance of QCD corrections to account for the ATLAS data.

Quarkonium production has long been considered an ideal means of investigating QCD and other new phenomena. Measurements of simultaneous production of quarkonium and other states are important for the understanding of the production mechanism; e.g. SPS (single parton scattering) versus DPS (double parton scattering). Measurements from ATLAS, CMS, LHCb, and D0 are reported.