Proof of sum rules for double parton distributions in QCD

Diehl, Markus; Plößl, Peter; Schäfer, Andreas

doi:10.1140/epjc/s10052-019-6777-5

Cited by 30 publications

(40 citation statements)

References 40 publications

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“…This avoids complications of bottom-up attempts in constructing dPDFs from known sPDFs, which cannot be unique and where one encounters problems [48,50]. Also, note a recent study [51] devoted to a verification of the GS sum rules in covariant perturbation theory and in light-cone perturbation theory.…”

Section: Basic Definitions and Propertiesmentioning

confidence: 97%

Double parton distribution of valence quarks in the pion in chiral quark models

Broniówski

Arriola

2020

Phys. Rev. D

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The valence double parton distribution of the pion is analyzed in the framework of chiral quark models, where in the chiral limit factorization between the longitudinal and transverse degrees of freedom occurs. This feature leads, at the quark-model scale, to a particularly simple distribution of the form D(x1, x2, y) = δ(1−x1 −x2)F (y), where x1,2 are the longitudinal momentum fractions carried the valence quark and antiquark, and y is the separation of their transverse positions. For y = 0 this result complies immediately to the Gaunt-Sterling sum rules. The DGLAP evolution to higher scales is carried out in terms of the Mellin moments. We then explore its role on the longitudinal correlation quantified with the ratio of the double distribution to the product of single distributions, D(x1, x2, y)/D(x1)D(x2). We point out that the ratios of moments x n 1 x m 2 / x n 1 x m 2 are independent of the evolution, providing particularly suitable measures to be tested in the upcoming lattice simulations. The transverse form factor F (y) is obtained in variants of the Nambu-Jona-Lasinio model with the spectral and Pauli-Villars regularizations. Interestingly, with the spectral regularization of the model, the effective cross section for the double parton scattering of pions is exactly equal to the geometric cross section, σ eff = π y 2 and yields about 20 mb.

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Section: Basic Definitions and Propertiesmentioning

confidence: 97%

Double parton distribution of valence quarks in the pion in chiral quark models

Broniówski

Arriola

2020

Phys. Rev. D

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“…For J/ψ-pair production, the main feeddown sources are the χ c and ψ . The feed-down from χ c is expected to be small, as gg → J/ψ + χ c and gg → ψ + χ c 1 Theory DPS studies advance [73][74][75][76], but not yet as to provide quantitative inputs to predict DPS cross sections as done for SPS. As such, one usually assumes the DPS contributions to be independent.…”

Section: Other Contributions To Quarkonium-pair Productionmentioning

confidence: 99%

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC

et al. 2020

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J/ψ-or Υ -pair production at the LHC are promising processes to study the gluon transverse momentum distributions (TMDs) which remain very poorly known. In this article, we improve on previous results by including the TMD evolution in the computation of the observables such as the pair-transverse-momentum spectrum and asymmetries arising from the linear polarization of gluons inside unpolarized protons. We show that the azimuthal asymmetries generated by the gluon polarization are reduced compared to the tree level case but are still of measurable size (in the 5%-10% range). Such asymmetries should be measurable in the available data sets of J/ψ pairs and in the future data sets of the high-luminosity LHC for Υ pairs. arXiv:1909.05769v1 [hep-ph]

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“…The general form of the convolution integrals in (5) was already given in [43] and follows from boost invariance and dimensional analysis. The splitting mechanism expressed in (5) also induces an inhomogeneous term in the evolution equation for momentum space DPDs, which reads [54]…”

Section: Basic Definitions and Notationmentioning

confidence: 99%

“…A description of DPS in terms of momentum space DPDs is considered in a number of works [12,13,56,61,66]. Furthermore, the momentum-space DPDs at ∆ = 0 are the objects that satisfy the number and momentum sum rules of [53], as was discussed in [54]. Similarly to the position space DPDs at small y, momentum space DPDs at large ∆ can be matched onto PDFs with perturbative kernels W a 1 a 2 ,a 0 (x 1 , x 2 , ∆).…”

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confidence: 99%

Two-loop splitting in double parton distributions

et al. 2019

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Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 → 2 splitting functions appearing in the evolution of momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 → 2 splitting functions are consistent with the number and momentum sum rules for DPDs.

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Proof of sum rules for double parton distributions in QCD

Cited by 30 publications

References 40 publications

Double parton distribution of valence quarks in the pion in chiral quark models

Double parton distribution of valence quarks in the pion in chiral quark models

Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC

Two-loop splitting in double parton distributions

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