Abstract
Double hard scattering in proton-proton collisions is described in terms of double parton distributions. We derive bounds on these distributions that follow from their interpretation as probability densities, taking into account all possible spin correlations between two partons in an unpolarized proton. These bounds constrain the size of the polarized distributions and can for instance be used to set upper limits on the effects of spin correlations in double hard scattering. We investigate the stability of the bounds under leading-order DGLAP evolution to higher scales.
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References
G. Calucci and D. Treleani, Mini-jets and the two-body parton correlation, Phys. Rev. D 57 (1998) 503 [hep-ph/9707389] [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].
A. Del Fabbro and D. Treleani, Scale factor in double parton collisions and parton densities in transverse space, Phys. Rev. D 63 (2001) 057901 [hep-ph/0005273] [INSPIRE].
C. Flensburg, G. Gustafson, L. Lönnblad and A. Ster, Correlations in double parton distributions at small x, JHEP 06 (2011) 066 [arXiv:1103.4320] [INSPIRE].
T. Rogers and M. Strikman, Multiple hard partonic collisions with correlations in proton-proton scattering, Phys. Rev. D 81 (2010) 016013 [arXiv:0908.0251] [INSPIRE].
R. Corke and T. Sjöstrand, Multiparton interactions with an x-dependent proton size, JHEP 05 (2011) 009 [arXiv:1101.5953] [INSPIRE].
S. Domdey, H.-J. Pirner and U.A. Wiedemann, Testing the scale dependence of the scale factor σ eff in double dijet production at the LHC, Eur. Phys. J. C 65 (2010) 153 [arXiv:0906.4335] [INSPIRE].
M. Rinaldi, S. Scopetta and V. Vento, Double parton correlations in constituent quark models, arXiv:1302.6462 [INSPIRE].
M. Mekhfi, Correlations in color and spin in multiparton processes, Phys. Rev. D 32 (1985) 2380 [INSPIRE].
M. Mekhfi, Multiparton processes: an application to double Drell-Yan, Phys. Rev. D 32 (1985) 2371 [INSPIRE].
M. Diehl and A. Schäfer, Theoretical considerations on multiparton interactions in QCD, Phys. Lett. B 698 (2011) 389 [arXiv:1102.3081] [INSPIRE].
M. Diehl, D. Ostermeier and A. Schäfer, Elements of a theory for multiparton interactions in QCD, JHEP 03 (2012) 089 [arXiv:1111.0910] [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].
T. Kasemets and M. Diehl, Angular correlations in the double Drell-Yan process, JHEP 01 (2013) 121 [arXiv:1210.5434] [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].
J. Soffer, Positivity constraints for spin dependent parton distributions, Phys. Rev. Lett. 74 (1995) 1292 [hep-ph/9409254] [INSPIRE].
A. Bacchetta, M. Boglione, A. Henneman and P. Mulders, Bounds on transverse momentum dependent distribution and fragmentation functions, Phys. Rev. Lett. 85 (2000) 712 [hep-ph/9912490] [INSPIRE].
M. Diehl and P. Hägler, Spin densities in the transverse plane and generalized transversity distributions, Eur. Phys. J. C 44 (2005) 87 [hep-ph/0504175] [INSPIRE].
M. Diehl, Generalized parton distributions, Phys. Rept. 388 (2003) 41 [hep-ph/0307382] [INSPIRE].
M. Diehl, Generalized parton distributions with helicity flip, Eur. Phys. J. C 19 (2001) 485 [hep-ph/0101335] [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
X. Artru and M. Mekhfi, Transversely polarized parton densities, their evolution and their measurement, Z. Phys. C 45 (1990) 669 [INSPIRE].
L. Durand and W. Putikka, Probabilistic derivation of parton splitting functions, Phys. Rev. D 36 (1987) 2840 [INSPIRE].
J.C. Collins and J.-W. Qiu, A new derivation of the Altarelli-Parisi equations, Phys. Rev. D 39 (1989) 1398 [INSPIRE].
V. Barone, On the QCD evolution of the transversity distribution, Phys. Lett. B 409 (1997) 499 [hep-ph/9703343] [INSPIRE].
C. Bourrely, J. Soffer and O. Teryaev, The Q 2 evolution of Soffer inequality, Phys. Lett. B 420 (1998) 375 [hep-ph/9710224] [INSPIRE].
G. Altarelli, S. Forte and G. Ridolfi, On positivity of parton distributions, Nucl. Phys. B 534 (1998) 277 [hep-ph/9806345] [INSPIRE].
W. Vogelsang, Next-to-leading order evolution of transversity distributions and Soffer’s inequality, Phys. Rev. D 57 (1998) 1886 [hep-ph/9706511] [INSPIRE].
O. Martin, A. Schäfer, M. Stratmann and W. Vogelsang, Soffer’s inequality and the transversely polarized Drell-Yan process at next-to-leading order, Phys. Rev. D 57 (1998) 3084 [hep-ph/9710300] [INSPIRE].
R. Kirschner, Generalized Lipatov-Altarelli-Parisi equations and jet calculus rules, Phys. Lett. B 84 (1979) 266 [INSPIRE].
V. Shelest, A. Snigirev and G. Zinovev, The multiparton distribution equations in QCD, Phys. Lett. B 113 (1982) 325 [INSPIRE].
A. Snigirev, Double parton distributions in the leading logarithm approximation of perturbative QCD, Phys. Rev. D 68 (2003) 114012 [hep-ph/0304172] [INSPIRE].
J.R. Gaunt and W.J. Stirling, Double parton distributions incorporating perturbative QCD evolution and momentum and quark number sum rules, JHEP 03 (2010) 005 [arXiv:0910.4347] [INSPIRE].
F.A. Ceccopieri, An update on the evolution of double parton distributions, Phys. Lett. B 697 (2011) 482 [arXiv:1011.6586] [INSPIRE].
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ArXiv ePrint: 1303.0842
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Diehl, M., Kasemets, T. Positivity bounds on double parton distributions. J. High Energ. Phys. 2013, 150 (2013). https://doi.org/10.1007/JHEP05(2013)150
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DOI: https://doi.org/10.1007/JHEP05(2013)150