Abstract
We consider double parton distribution functions (dPDFs), essential quantities in double parton scattering (DPS) studies, which encode novel non perturbative insight on the partonic proton structure. We develop the formalism to extract this information from dPDFs and present results by using constituent quark model calculations within the Light-Front approach, focusing on radiatively generated gluon dPDFs. Moreover, we generalize the relation between the mean transverse partonic distance between two active partons in a DPS process and the so called σeff to include partonic correlations and the so called 2v1 mechanism contribution. Finally we investigate the impact of relativistic effects on digluon distributions and study the structure of the corresponding longitudinal and transverse correlations.
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References
N. Paver and D. Treleani, Multi-quark scattering and large p Tjet production in hadronic collisions, Nuovo Cim.A 70 (1982) 215 [INSPIRE].
T. Sjöstrand and M. van Zijl, Multiple parton-parton interactions in an impact parameter picture, Phys. Lett.B 188 (1987) 149 [INSPIRE].
T. Sjöstrand and M. van Zijl, A multiple interaction model for the event structure in hadron collisions, Phys. Rev.D 36 (1987) 2019 [INSPIRE].
T. Kasemets and S. Scopetta, Parton correlations in double parton scattering, Adv. Ser. Direct. High Energy Phys.29 (2018) 49 [arXiv:1712.02884] [INSPIRE].
C. Goebel, F. Halzen and D.M. Scott, Double Drell-Yan annihilations in hadron collisions: novel tests of the constituent picture, Phys. Rev.D 22 (1980) 2789 [INSPIRE].
M. Mekhfi, Multiparton processes: an application to double Drell-Yan, Phys. Rev.D 32 (1985) 2371 [INSPIRE].
M. Diehl and A. Schafer, Theoretical considerations on multiparton interactions in QCD, Phys. Lett.B 698 (2011) 389 [arXiv:1102.3081] [INSPIRE].
M. Diehl, D. Ostermeier and A. Schafer, Elements of a theory for multiparton interactions in QCD, JHEP03 (2012) 089 [Erratum ibid.03 (2016) 001] [arXiv:1111.0910] [INSPIRE].
G. Calucci and D. Treleani, Proton structure in transverse space and the effective cross-section, Phys. Rev.D 60 (1999) 054023 [hep-ph/9902479] [INSPIRE].
H.-M. Chang, A.V. Manohar and W.J. Waalewijn, Double parton correlations in the bag model, Phys. Rev.D 87 (2013) 034009 [arXiv:1211.3132] [INSPIRE].
M. Rinaldi, S. Scopetta and V. Vento, Double parton correlations in constituent quark models, Phys. Rev.D 87 (2013) 114021 [arXiv:1302.6462] [INSPIRE].
W. Broniowski, E. Ruiz Arriola and K. Golec-Biernat, Generalized valon model for double parton distributions, Few Body Syst.57 (2016) 405 [arXiv:1602.00254] [INSPIRE].
M. Rinaldi, S. Scopetta, M. Traini and V. Vento, Double parton correlations and constituent quark models: a light front approach to the valence sector, JHEP12 (2014) 028 [arXiv:1409.1500] [INSPIRE].
M. Rinaldi and F.A. Ceccopieri, Relativistic effects in model calculations of double parton distribution function, Phys. Rev.D 95 (2017) 034040 [arXiv:1611.04793] [INSPIRE].
M. Rinaldi, S. Scopetta, M. Traini and V. Vento, A model calculation of double parton distribution functions of the pion, Eur. Phys. J.C 78 (2018) 781 [arXiv:1806.10112] [INSPIRE].
S. Cotogno, T. Kasemets and M. Myska, Spin on same-sign W -boson pair production, Phys. Rev.D 100 (2019) 011503 [arXiv:1809.09024] [INSPIRE].
M.G. Echevarria, T. Kasemets, P.J. Mulders and C. Pisano, Polarization effects in double open-charm production at LHCb, JHEP04 (2015) 034 [arXiv:1501.07291] [INSPIRE].
M. Diehl and T. Kasemets, Positivity bounds on double parton distributions, JHEP05 (2013) 150 [arXiv:1303.0842] [INSPIRE].
T. Kasemets and M. Diehl, Angular correlations in the double Drell-Yan process, JHEP01 (2013) 121 [arXiv:1210.5434] [INSPIRE].
G.S. Bali et al., Two-current correlations in the pion on the lattice, JHEP12 (2018) 061 [arXiv:1807.03073] [INSPIRE].
ATLAS collaboration, Study of hard double-parton scattering in four-jet events in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS experiment, JHEP11 (2016) 110 [arXiv:1608.01857] [INSPIRE].
LHCb collaboration, Measurement of the J/ψ pair production cross-section in pp collisions at \( \sqrt{s} \) = 13 TeV, JHEP06 (2017) 047 [Erratum ibid.10 (2017) 068] [arXiv:1612.07451] [INSPIRE].
CMS collaboration, Study of double parton scattering using W + 2-jet events in proton-proton collisions at \( \sqrt{s} \) = 7 TeV, JHEP03 (2014) 032 [arXiv:1312.5729] [INSPIRE].
CMS collaboration, Constraints on the double-parton scattering cross section from same-sign W boson pair production in proton-proton collisions at \( \sqrt{s} \) = 8 TeV, JHEP02 (2018) 032 [arXiv:1712.02280] [INSPIRE].
ATLAS collaboration, Measurement of the prompt J/ψ pair production cross-section in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, Eur. Phys. J.C 77 (2017) 76 [arXiv:1612.02950] [INSPIRE].
J.-P. Lansberg and H.-S. Shao, J/ψ-pair production at large momenta: indications for double parton scatterings and large α 5s contributions, Phys. Lett.B 751 (2015) 479 [arXiv:1410.8822] [INSPIRE].
M. Rinaldi and F.A. Ceccopieri, Hadronic structure from double parton scattering, Phys. Rev.D 97 (2018) 071501 [arXiv:1801.04760] [INSPIRE].
A.M. Snigirev, Double parton distributions in the leading logarithm approximation of perturbative QCD, Phys. Rev.D 68 (2003) 114012 [hep-ph/0304172] [INSPIRE].
F.A. Ceccopieri, An update on the evolution of double parton distributions, Phys. Lett.B 697 (2011) 482 [arXiv:1011.6586] [INSPIRE].
B. Blok, Yu. Dokshitzer, L. Frankfurt and M. Strikman, The four jet production at LHC and Tevatron in QCD, Phys. Rev.D 83 (2011) 071501 [arXiv:1009.2714] [INSPIRE].
B. Blok, Yu. Dokshitser, L. Frankfurt and M. Strikman, pQCD physics of multiparton interactions, Eur. Phys. J.C 72 (2012) 1963 [arXiv:1106.5533] [INSPIRE].
B. Blok, Yu. Dokshitzer, L. Frankfurt and M. Strikman, Perturbative QCD correlations in multi-parton collisions, Eur. Phys. J.C 74 (2014) 2926 [arXiv:1306.3763] [INSPIRE].
J.R. Gaunt and W.J. Stirling, Double parton distributions incorporating perturbative QCD evolution and momentum and quark number sum rules, JHEP03 (2010) 005 [arXiv:0910.4347] [INSPIRE].
J.R. Gaunt, R. Maciula and A. Szczurek, Conventional versus single-ladder-splitting contributions to double parton scattering production of two quarkonia, two Higgs bosons and c \( \overline{c} \)c \( \overline{c} \), Phys. Rev.D 90 (2014) 054017 [arXiv:1407.5821] [INSPIRE].
D. Treleani and G. Calucci, About double parton scattering at short relative transverse distances, arXiv:1808.02337 [INSPIRE].
M.G. Ryskin and A.M. Snigirev, A fresh look at double parton scattering, Phys. Rev.D 83 (2011) 114047 [arXiv:1103.3495] [INSPIRE].
V.P. Shelest, A.M. Snigirev and G.M. Zinovev, The multiparton distribution equations in QCD, Phys. Lett.B 113 (1982) 325 [INSPIRE].
R. Kirschner, Generalized Lipatov-Altarelli-Parisi equations and jet calculus rules, Phys. Lett.B 84 (1979) 266 [INSPIRE].
V.L. Korotkikh and A.M. Snigirev, Double parton correlations versus factorized distributions, Phys. Lett.B 594 (2004) 171 [hep-ph/0404155] [INSPIRE].
T. Kasemets and P.J. Mulders, Constraining double parton correlations and interferences, Phys. Rev.D 91 (2015) 014015 [arXiv:1411.0726] [INSPIRE].
K. Golec-Biernat, E. Lewandowska, M. Serino, Z. Snyder and A.M. Stasto, Constraining the double gluon distribution by the single gluon distribution, Phys. Lett.B 750 (2015) 559 [arXiv:1507.08583] [INSPIRE].
K. Golec-Biernat and E. Lewandowska, How to impose initial conditions for QCD evolution of double parton distributions?, Phys. Rev.D 90 (2014) 014032 [arXiv:1402.4079] [INSPIRE].
I. Schmidt and M. Siddikov, Contribution of digluons to charmonia production, J. Phys.G 46 (2019) 065002 [arXiv:1801.09974] [INSPIRE].
E. Elias, K. Golec-Biernat and A.M. Stasto, Numerical analysis of the unintegrated double gluon distribution, JHEP01 (2018) 141 [arXiv:1801.00018] [INSPIRE].
M. Diehl, J.R. Gaunt, D. Ostermeier, P. Plößl and A. Schäfer, Cancellation of Glauber gluon exchange in the double Drell-Yan process, JHEP01 (2016) 076 [arXiv:1510.08696] [INSPIRE].
A.V. Manohar and W.J. Waalewijn, A QCD analysis of double parton scattering: color correlations, interference effects and evolution, Phys. Rev.D 85 (2012) 114009 [arXiv:1202.3794] [INSPIRE].
J.R. Gaunt and W.J. Stirling, Double parton scattering singularity in one-loop integrals, JHEP06 (2011) 048 [arXiv:1103.1888] [INSPIRE].
M. Diehl, T. Kasemets and S. Keane, Correlations in double parton distributions: effects of evolution, JHEP05 (2014) 118 [arXiv:1401.1233] [INSPIRE].
A.M. Snigirev, N.A. Snigireva and G.M. Zinovjev, Perturbative and nonperturbative correlations in double parton distributions, Phys. Rev.D 90 (2014) 014015 [arXiv:1403.6947] [INSPIRE].
M. Rinaldi, S. Scopetta, M.C. Traini and V. Vento, Correlations in double parton distributions: perturbative and non-perturbative effects, JHEP10 (2016) 063 [arXiv:1608.02521] [INSPIRE].
D0 collaboration, Observation and studies of double J/ψ production at the Tevatron, Phys. Rev.D 90 (2014) 111101 [arXiv:1406.2380] [INSPIRE].
J.-P. Lansberg, H.-S. Shao, N. Yamanaka and Y.-J. Zhang, Prompt J/ψ-pair production at the LHC: impact of loop-induced contributions and of the colour-octet mechanism, arXiv:1906.10049 [INSPIRE].
J.R. Gaunt, Glauber gluons and multiple parton interactions, JHEP07 (2014) 110 [arXiv:1405.2080] [INSPIRE].
M. Diehl, J.R. Gaunt and K. Schönwald, Double hard scattering without double counting, JHEP06 (2017) 083 [arXiv:1702.06486] [INSPIRE].
M. Diehl and R. Nagar, Factorisation of soft gluons in multiparton scattering, JHEP04 (2019) 124 [arXiv:1812.09509] [INSPIRE].
M.G.A. Buffing, M. Diehl and T. Kasemets, Transverse momentum in double parton scattering: factorisation, evolution and matching, JHEP01 (2018) 044 [arXiv:1708.03528] [INSPIRE].
F.A. Ceccopieri, A second update on double parton distributions, Phys. Lett.B 734 (2014) 79 [arXiv:1403.2167] [INSPIRE].
P. Faccioli, M. Traini and V. Vento, Polarized parton distributions and light front dynamics, Nucl. Phys.A 656 (1999) 400 [hep-ph/9808201] [INSPIRE].
M.M. Giannini, Electromagnetic excitations in the constituent quark model, Rept. Prog. Phys.54 (1991) 453 [INSPIRE].
M. Diehl, P. Plößl and A. Schäfer, Proof of sum rules for double parton distributions in QCD, Eur. Phys. J.C 79 (2019) 253 [arXiv:1811.00289] [INSPIRE].
F.A. Ceccopieri, M. Rinaldi and S. Scopetta, Parton correlations in same-sign W pair production via double parton scattering at the LHC, Phys. Rev.D 95 (2017) 114030 [arXiv:1702.05363] [INSPIRE].
M. Rinaldi, S. Scopetta, M. Traini and V. Vento, Double parton scattering: a study of the effective cross section within a light-front quark model, Phys. Lett.B 752 (2016) 40 [arXiv:1506.05742] [INSPIRE].
D. Treleani, Double parton scattering, diffraction and effective cross section, Phys. Rev.D 76 (2007) 076006 [arXiv:0708.2603] [INSPIRE].
J.R. Gaunt, Single perturbative splitting diagrams in double parton scattering, JHEP01 (2013) 042 [arXiv:1207.0480] [INSPIRE].
L. Frankfurt and M. Strikman, Two gluon form-factor of the nucleon and J/ψ photoproduction, Phys. Rev.D 66 (2002) 031502 [hep-ph/0205223] [INSPIRE].
M. Traini, M. Rinaldi, S. Scopetta and V. Vento, The effective cross section for double parton scattering within a holographic AdS/QCD approach, Phys. Lett.B 768 (2017) 270 [arXiv:1609.07242] [INSPIRE].
P.A.M. Dirac, Forms of relativistic dynamics, Rev. Mod. Phys.21 (1949) 392 [INSPIRE].
B.D. Keister and W.N. Polyzou, Relativistic Hamiltonian dynamics in nuclear and particle physics, Adv. Nucl. Phys.20 (1991) 225 [INSPIRE].
S.J. Brodsky, H.-C. Pauli and S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rept.301 (1998) 299 [hep-ph/9705477] [INSPIRE].
G.P. Lepage and S.J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev.D 22 (1980) 2157 [INSPIRE].
S. Boffi, B. Pasquini and M. Traini, Linking generalized parton distributions to constituent quark models, Nucl. Phys.B 649 (2003) 243 [hep-ph/0207340] [INSPIRE].
B. Pasquini, M. Traini and S. Boffi, Nonperturbative versus perturbative effects in generalized parton distributions, Phys. Rev.D 71 (2005) 034022 [hep-ph/0407228] [INSPIRE].
B. Pasquini, S. Cazzaniga and S. Boffi, Transverse momentum dependent parton distributions in a light-cone quark model, Phys. Rev.D 78 (2008) 034025 [arXiv:0806.2298] [INSPIRE].
M. Traini, Next-to-next-to-leading-order nucleon parton distributions from a light-cone quark model dressed with its virtual meson cloud, Phys. Rev.D 89 (2014) 034021 [arXiv:1309.5814] [INSPIRE].
H.J. Melosh, Quarks: currents and constituents, Phys. Rev.D 9 (1974) 1095 [INSPIRE].
D0 collaboration, Evidence for simultaneous production of J/ψ and ϒ mesons, Phys. Rev. Lett.116 (2016) 082002 [arXiv:1511.02428] [INSPIRE].
J.-P. Lansberg and H.-S. Shao, Associated production of a quarkonium and a Z boson at one loop in a quark-hadron-duality approach, JHEP10 (2016) 153 [arXiv:1608.03198] [INSPIRE].
J.-P. Lansberg, H.-S. Shao and N. Yamanaka, Indication for double parton scatterings in W+ prompt J/ψ production at the LHC, Phys. Lett.B 781 (2018) 485 [arXiv:1707.04350] [INSPIRE].
LHCb collaboration, Production of associated Y and open charm hadrons in pp collisions at \( \sqrt{s} \) = 7 and 8TeV via double parton scattering, JHEP07 (2016) 052 [arXiv:1510.05949] [INSPIRE].
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Rinaldi, M., Ceccopieri, F.A. Double parton scattering and the proton transverse structure at the LHC. J. High Energ. Phys. 2019, 97 (2019). https://doi.org/10.1007/JHEP09(2019)097
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DOI: https://doi.org/10.1007/JHEP09(2019)097