Momentum sum rule and factorization of double parton distributions

Abstract

We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of the evolution scale Q. This is a somewhat surprising result since the momentum sum rule involves integration over all values of the momentum fraction. In essence, the momentum sum rule provides a proper relation between the double and single parton distributions, which is necessary for the small x factorization at large $Q$.

arXiv comment11 pages, 4 figures, version published in Phys. Rev. D

References in corpus (62)

• Parton distributions for the LHC
• Double Parton Distributions Incorporating Perturbative QCD Evolution and Momentum and Quark Number Sum Rules
• Measurement of hard double-parton interactions in W->lv+ 2 jet events at sqrt(s)=7 TeV with the ATLAS detector
• Elements of a theory for multiparton interactions in QCD
• pQCD Physics of multiparton interactions
• Double parton interactions in photon+3 jet events in ppbar collisions sqrt{s}=1.96 TeV
• Observation of $J/\psi$ pair production in pp collisions at $\sqrt{s}=7TeV$
• Theoretical considerations on multiparton interactions in QCD
• Observation of double charm production involving open charm in pp collisions at $\sqrt{s}$=7 TeV
• The four jet production at LHC and Tevatron in QCD
• Perturbative QCD correlations in multi-parton collisions
• A QCD Analysis of Double Parton Scattering: Color Correlations, Interference Effects and Evolution
• Study of double parton scattering using W + 2-jet events in proton-proton collisions at sqrt(s) = 7 TeV
• A fresh look at double parton scattering
• Measurement of the prompt $J/\psi$ pair production cross-section in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Double Parton Scattering Singularity in One-Loop Integrals
• Double parton distributions in the leading logarithm approximation of perturbative QCD
• Observation of Upsilon(1S) pair production in proton-proton collisions at sqrt(s) = 8 TeV
• Like-Sign W Boson Production at the LHC as a Probe of Double Parton Scattering
• Cancellation of Glauber gluon exchange in the double Drell-Yan process
• Single Perturbative Splitting Diagrams in Double Parton Scattering
• Observation and measurements of the production of prompt and non-prompt $J/\psi$ mesons in association with a $Z$ boson in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Double parton scattering in double logarithm approximation of perturbative QCD
• Measurement of the $J/\psi$ pair production cross-section in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$
• Double parton correlations versus factorized distributions
• Production of two $c\bar{c}$ pairs in double-parton scattering
• Double hard scattering without double counting
• Correlations in double parton distributions: effects of evolution
• Measurement of the production cross section of prompt J/psi mesons in association with a W boson in pp collisions at sqrt{s}=7 TeV with the ATLAS detector
• Conventional versus single-ladder-splitting contributions to double parton scattering production of two quarkonia, two Higgs bosons and $c\bar{c}c\bar{c}$
• An update on the evolution of double parton distributions
• Production of associated ${\rm Y}$ and open charm hadrons in $pp$ collisions at $\sqrt{s}=7$ and $8$TeV via double parton scattering
• Study of hard double-parton scattering in four-jet events in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS experiment
• Valence double parton distributions of the nucleon in a simple model
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• Correlations in Double Parton Distributions: Perturbative and Non-Perturbative effects
• Constraining the double gluon distribution by the single gluon distribution
• Parton correlations in same-sign $W$ pair production via double parton scattering at the LHC
• Study of the hard double-parton scattering contribution to inclusive four-lepton production in $pp$ collisions at $\sqrt{s}$ = 8 TeV with the ATLAS detector
• Evidence for WW production from double-parton interactions in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Single-parton scattering versus double-parton scattering in the production of two $c\bar{c}$ pairs and charmed meson correlations at the LHC
• Electroweak boson production in double parton scattering
• Prospects for observation of double parton scattering with four-muon final states at LHCb
• Hadronic structure from double parton scattering
• How to impose initial conditions for QCD evolution of double parton distributions?
• Double-parton scattering contribution to production of jet pairs with large rapidity separation at the LHC
• Perturbative and nonperturbative correlations in double parton distributions
• Generalized Valon Model for Double Parton Distributions
• A second update on double parton distributions
• Exclusive production of double $J/\psi$ mesons in hadronic collisions
• Double parton distribution of valence quarks in the pion in chiral quark models
• Two-loop splitting in double parton distributions
• Factorisation of soft gluons in multiparton scattering
• Double parton scattering and the proton transverse structure at the LHC
• Sum rule improved double parton distributions in position space
• Unintegrated double parton distributions
• Open charm production in Double Parton Scattering processes in the forward kinematics
• Combining single and double parton scatterings in a parton shower
• Two-loop splitting in double parton distributions: the colour non-singlet case
• Double parton distributions in the pion from lattice QCD
• Numerical analysis of the unintegrated double gluon distribution
• Double parton distributions out of bounds in colour space

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• Evolution and interpolation of double parton distributions using Chebyshev grids
• Quark mass effects in double parton distributions
• Two-loop evolution kernels for colour dependent double parton distributions
• Double parton distributions of the proton from basis light-front quantization
• Nonlinear Corrections to the Momentum Sum Rule
• Numerical Study of MRW-Type Unintegrated Double Parton Distribution Functions from Non-Factorized DPDFs