# Associated production of a quarkonium and a *Z* boson at one loop in a quark-hadron-duality approach

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## Abstract

In view of the large discrepancy about the associated production of a prompt *J/ψ* and a *Z* boson between the ATLAS data at \( \sqrt{s}=8 \) TeV and theoretical predictions for Single Parton Scattering (SPS) contributions, we perform an evaluation of the corresponding cross section at one loop accuracy (Next-to-Leading Order, NLO) in a quark-hadron-duality approach, also known as the Colour-Evaporation Model (CEM). This work is motivated by (i) the extremely disparate predictions based on the existing NRQCD fits conjugated with the absence of a full NLO NRQCD computation and (ii) the fact that we believe that such an evaluation provides a likely upper limit of the SPS cross section. In addition to these theory improvements, we argue that the ATLAS estimation of the Double Parton Scattering (DPS) yield may be underestimated by a factor as large as 3 which then reduces the size of the SPS yield extracted from the ATLAS data. Our NLO SPS evaluation also allows us to set an upper limit on *σ* _{eff} driving the size of the DPS yield. Overall, the discrepancy between theory and experiment may be smaller than expected, which calls for further analyses by ATLAS and CMS, for which we provide predictions, and for full NLO computations in other models. As an interesting side product of our analysis, we have performed the first NLO computation of *d*σ*/dP* _{ T } for prompt single-*J/ψ* production in the CEM from which we have fit the CEM non-pertubative parameter at NLO using the most recent ATLAS data.

## Keywords

NLO Computations QCD Phenomenology## Notes

**Open Access**

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## References

- [1]CDF collaboration, D. Acosta et al.,
*Search for associated production of*Y*and vector boson in*\( p\overline{p} \)*collisions at*\( \sqrt{s}=1.8 \)*TeV*,*Phys. Rev. Lett.***90**(2003) 221803 [INSPIRE]. - [2]CDF collaboration, T. Aaltonen et al.,
*Search for production of an*Y(1*S*)*meson in association with a W or Z boson using the full*1*.*96*TeV*\( p\overline{p} \)*collision data set at CDF*,*Phys. Rev.***D 91**(2015) 052011 [arXiv:1412.4827] [INSPIRE]. - [3]ATLAS collaboration,
*Measurement of the production cross section of prompt J/ψ mesons in association with a W*^{±}*boson in pp collisions at*\( \sqrt{s}=7 \)*TeV with the ATLAS detector*,*JHEP***04**(2014) 172 [arXiv:1401.2831] [INSPIRE]. - [4]ATLAS collaboration,
*Observation and measurements of the production of prompt and non-prompt J/ψ mesons in association with a Z boson in pp collisions at*\( \sqrt{s}=8 \)*TeV with the ATLAS detector*,*Eur. Phys. J.***C 75**(2015) 229 [arXiv:1412.6428] [INSPIRE]. - [5]D.P. Roy and K. Sridhar,
*J/ψ*+*γ production at the Tevatron energy*,*Phys. Lett.***B 341**(1995) 413 [hep-ph/9407390] [INSPIRE].ADSGoogle Scholar - [6]P. Mathews, K. Sridhar and R. Basu,
*J/ψ*+*γ production at the CERN LHC*,*Phys. Rev.***D 60**(1999) 014009 [hep-ph/9901276] [INSPIRE].ADSGoogle Scholar - [7]R. Li and J.-X. Wang,
*Next-to-leading-order QCD corrections to J/ψ*(Y) +*γ production at the LHC*,*Phys. Lett.***B 672**(2009) 51 [arXiv:0811.0963] [INSPIRE].ADSCrossRefGoogle Scholar - [8]J.P. Lansberg,
*Real next-to-next-to-leading-order QCD corrections to J/ψ and*Y*hadroproduction in association with a photon*,*Phys. Lett.***B 679**(2009) 340 [arXiv:0901.4777] [INSPIRE].ADSCrossRefGoogle Scholar - [9]R. Li and J.-X. Wang,
*Next-to-leading-order study of the associated production of J/ψ*+*γ at the LHC*,*Phys. Rev.***D 89**(2014) 114018 [arXiv:1401.6918] [INSPIRE].ADSGoogle Scholar - [10]M.A. Doncheski and C.S. Kim,
*Associated J/ψ*+*γ production as a probe of the polarized gluon distribution*,*Phys. Rev.***D 49**(1994) 4463 [hep-ph/9303248] [INSPIRE].ADSGoogle Scholar - [11]W.J. den Dunnen, J.P. Lansberg, C. Pisano and M. Schlegel,
*Accessing the transverse dynamics and polarization of gluons inside the proton at the LHC*,*Phys. Rev. Lett.***112**(2014) 212001 [arXiv:1401.7611] [INSPIRE].ADSCrossRefGoogle Scholar - [12]M.N. Doroshenko, V.G. Kartvelishvili, E.G. Chikovani and S.M. Esakiya,
*Vector quarkonium in decays of heavy Higgs particles*,*Yad. Fiz.***46**(1987) 864 [*Sov. J. Nucl. Phys.***46**(1987) 493] [INSPIRE]. - [13]G.T. Bodwin, F. Petriello, S. Stoynev and M. Velasco,
*Higgs boson decays to quarkonia and the*\( H\overline{c}c \)*coupling*,*Phys. Rev.***D 88**(2013) 053003 [arXiv:1306.5770] [INSPIRE].ADSGoogle Scholar - [14]ATLAS collaboration,
*Search for Higgs and Z boson decays to J/ψγ and*Y(*nS*)*γ with the ATLAS detector*,*Phys. Rev. Lett.***114**(2015) 121801 [arXiv:1501.03276] [INSPIRE]. - [15]S. Mao, M. Wen-Gan, L. Gang, Z. Ren-You and G. Lei,
*QCD corrections to J/ψ plus Z*^{0}*-boson production at the LHC*,*JHEP***02**(2011) 071 [*Erratum ibid.***12**(2012) 010] [arXiv:1102.0398] [INSPIRE]. - [16]B. Gong, J.-P. Lansberg, C. Lorce and J. Wang,
*Next-to-leading-order QCD corrections to the yields and polarisations of J/ψ and*Y*directly produced in association with a Z boson at the LHC*,*JHEP***03**(2013) 115 [arXiv:1210.2430] [INSPIRE].ADSCrossRefGoogle Scholar - [17]G. Li, M. Song, R.-Y. Zhang and W.-G. Ma,
*QCD corrections to J/ψ production in association with a W-boson at the LHC*,*Phys. Rev.***D 83**(2011) 014001 [arXiv:1012.3798] [INSPIRE].ADSGoogle Scholar - [18]J.P. Lansberg and C. Lorce,
*Reassessing the importance of the colour-singlet contributions to direct J/ψ*+*W production at the LHC and the Tevatron*,*Phys. Lett.***B 726**(2013) 218 [*Erratum ibid.***B 738**(2014) 529] [arXiv:1303.5327] [INSPIRE]. - [19]S. Leontsinis, private communication.Google Scholar
- [20]NA3 collaboration, J. Badier et al.,
*Evidence for ψψ production in π*^{−}*interactions at*150*GeV/c and*280*GeV/c*,*Phys. Lett.***B 114**(1982) 457 [INSPIRE]. - [21]NA3 collaboration, J. Badier et al.,
*ψψ production and limits on beauty meson production from*400*GeV/c protons*,*Phys. Lett.***B 158**(1985) 85 [INSPIRE]. - [22]LHCb collaboration,
*Observation of J/ψ pair production in pp collisions at*\( \sqrt{s}=7 \)*TeV*,*Phys. Lett.***B 707**(2012) 52 [arXiv:1109.0963] [INSPIRE]. - [23]CMS collaboration,
*Measurement of prompt J/ψ pair production in pp collisions at*\( \sqrt{s}=7 \)*TeV*,*JHEP***09**(2014) 094 [arXiv:1406.0484] [INSPIRE]. - [24]ATLAS collaboration,
*Measurement of the prompt J/ψ pair production cross-section in pp collisions at*\( \sqrt{s}=8 \)*TeV with the ATLAS detector*, ATLAS-CONF-2016-047, CERN, Geneva Switzerland (2016). - [25]D0 collaboration, V.M. Abazov et al.,
*Observation and studies of double J/ψ production at the Tevatron*,*Phys. Rev.***D 90**(2014) 111101 [arXiv:1406.2380] [INSPIRE]. - [26]J.-P. Lansberg and H.-S. Shao,
*Production of J/ψ*+*η*_{c}*versus J/ψ*+*J/ψ at the LHC: importance of real α*_{s}^{5}*corrections*,*Phys. Rev. Lett.***111**(2013) 122001 [arXiv:1308.0474] [INSPIRE].ADSCrossRefGoogle Scholar - [27]L.-P. Sun, H. Han and K.-T. Chao,
*Impact of J/ψ pair production at the LHC and predictions in nonrelativistic QCD*, arXiv:1404.4042 [INSPIRE]. - [28]A.K. Likhoded, A.V. Luchinsky and S.V. Poslavsky,
*Production of J/ψ*+*χ*_{c}*and J/ψ*+*J/ψ with real gluon emission at LHC*,*Phys. Rev.***D 94**(2016) 054017 [arXiv:1606.06767] [INSPIRE].Google Scholar - [29]J.-P. Lansberg and H.-S. Shao,
*J/ψ-pair production at large momenta: indications for double parton scatterings and large α*_{s}^{5}*contributions*,*Phys. Lett.***B 751**(2015) 479 [arXiv:1410.8822] [INSPIRE].ADSCrossRefGoogle Scholar - [30]Z.-G. He and B.A. Kniehl,
*Complete nonrelativistic-QCD prediction for prompt double J/ψ hadroproduction*,*Phys. Rev. Lett.***115**(2015) 022002 [arXiv:1609.02786] [INSPIRE].ADSCrossRefGoogle Scholar - [31]S.P. Baranov and A.H. Rezaeian,
*Prompt double J/ψ production in proton-proton collisions at the LHC*,*Phys. Rev.***D 93**(2016) 114011 [arXiv:1511.04089] [INSPIRE].ADSGoogle Scholar - [32]D0 collaboration, V.M. Abazov et al.,
*Evidence for simultaneous production of J/ψ and*Y*mesons*,*Phys. Rev. Lett.***116**(2016) 082002 [arXiv:1511.02428] [INSPIRE]. - [33]H.-S. Shao and Y.-J. Zhang,
*Complete study of hadroproduction of a*Y*meson associated with a prompt J/ψ*,*Phys. Rev. Lett.***117**(2016) 062001 [arXiv:1605.03061] [INSPIRE].ADSCrossRefGoogle Scholar - [34]LHCb collaboration,
*Observation of double charm production involving open charm in pp collisions at*\( \sqrt{s}=7 \)*TeV*,*JHEP***06**(2012) 141 [*Addendum ibid.***03**(2014) 108] [arXiv:1205.0975] [INSPIRE]. - [35]LHCb collaboration,
*Production of associated Y and open charm hadrons in pp collisions at*\( \sqrt{s}=7 \)*and*8*TeV via double parton scattering*,*JHEP***07**(2016) 052 [arXiv:1510.05949] [INSPIRE]. - [36]ATLAS collaboration,
*Measurement of hard double-parton interactions in W*(→*ℓν*) + 2*jet events at*\( \sqrt{s}=7 \)*TeV with the ATLAS detector*,*New J. Phys.***15**(2013) 033038 [arXiv:1301.6872] [INSPIRE]. - [37]A. Andronic et al.,
*Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions*,*Eur. Phys. J.***C 76**(2016) 107 [arXiv:1506.03981] [INSPIRE].ADSCrossRefGoogle Scholar - [38]LHCb collaboration,
*Measurement of the η*_{c}(1*S*)*production cross-section in proton-proton collisions via the decay η*_{c}(1*S*) → \( p\overline{p} \),*Eur. Phys. J.***C 75**(2015) 311 [arXiv:1409.3612] [INSPIRE]. - [39]M. Butenschoen, Z.-G. He and B.A. Kniehl,
*η*_{c}*production at the LHC challenges nonrelativistic-QCD factorization*,*Phys. Rev. Lett.***114**(2015) 092004 [arXiv:1411.5287] [INSPIRE].ADSCrossRefGoogle Scholar - [40]H.-F. Zhang, Z. Sun, W.-L. Sang and R. Li,
*Impact of η*_{c}*hadroproduction data on charmonium production and polarization within NRQCD framework*,*Phys. Rev. Lett.***114**(2015) 092006 [arXiv:1412.0508] [INSPIRE].ADSCrossRefGoogle Scholar - [41]H. Han, Y.-Q. Ma, C. Meng, H.-S. Shao and K.-T. Chao,
*η*_{c}*production at LHC and indications on the understanding of J/ψ production*,*Phys. Rev. Lett.***114**(2015) 092005 [arXiv:1411.7350] [INSPIRE].ADSCrossRefGoogle Scholar - [42]P. Faccioli, V. Knünz, C. Lourenco, J. Seixas and H.K. Wöhri,
*Quarkonium production in the LHC era: a polarized perspective*,*Phys. Lett.***B 736**(2014) 98 [arXiv:1403.3970] [INSPIRE].ADSCrossRefGoogle Scholar - [43]G.T. Bodwin, H.S. Chung, U.-R. Kim and J. Lee,
*Fragmentation contributions to J/ψ production at the Tevatron and the LHC*,*Phys. Rev. Lett.***113**(2014) 022001 [arXiv:1403.3612] [INSPIRE].ADSCrossRefGoogle Scholar - [44]M. Butenschoen and B.A. Kniehl,
*World data of J/ψ production consolidate NRQCD factorization at NLO*,*Phys. Rev.***D 84**(2011) 051501 [arXiv:1105.0820] [INSPIRE].ADSGoogle Scholar - [45]Y. Feng, J.-P. Lansberg and J.-X. Wang,
*Energy dependence of direct-quarkonium production in pp collisions from fixed-target to LHC energies: complete one-loop analysis*,*Eur. Phys. J.***C 75**(2015) 313 [arXiv:1504.00317] [INSPIRE].ADSCrossRefGoogle Scholar - [46]G.T. Bodwin, E. Braaten and J. Lee,
*Comparison of the color-evaporation model and the NRQCD factorization approach in charmonium production*,*Phys. Rev.***D 72**(2005) 014004 [hep-ph/0504014] [INSPIRE].ADSGoogle Scholar - [47]A. Edin, G. Ingelman and J. Rathsman,
*Quarkonium production at the Tevatron through soft color interactions*,*Phys. Rev.***D 56**(1997) 7317 [hep-ph/9705311] [INSPIRE].ADSGoogle Scholar - [48]J. Damet, G. Ingelman and C. Brenner Mariotto,
*Prompt J/ψ production at the LHC*,*JHEP***09**(2002) 014 [hep-ph/0111463] [INSPIRE].ADSCrossRefGoogle Scholar - [49]C. Brenner Mariotto, M.B. Gay Ducati and G. Ingelman,
*Soft and hard QCD dynamics in hadroproduction of charmonium*,*Eur. Phys. J.***C 23**(2002) 527 [hep-ph/0111379] [INSPIRE].ADSCrossRefGoogle Scholar - [50]J.P. Lansberg,
*J/ψ, ψ*′*and*Y*production at hadron colliders: a review*,*Int. J. Mod. Phys.***A 21**(2006) 3857 [hep-ph/0602091] [INSPIRE].ADSCrossRefGoogle Scholar - [51]H. Fritzsch,
*Producing heavy quark flavors in hadronic collisions: a test of quantum chromodynamics*,*Phys. Lett.***B 67**(1977) 217 [INSPIRE].ADSCrossRefGoogle Scholar - [52]F. Halzen,
*CVC for gluons and hadroproduction of quark flavors*,*Phys. Lett.***B 69**(1977) 105 [INSPIRE].ADSCrossRefGoogle Scholar - [53]J.F. Amundson, O.J.P. Eboli, E.M. Gregores and F. Halzen,
*Colorless states in perturbative QCD: charmonium and rapidity gaps*,*Phys. Lett.***B 372**(1996) 127 [hep-ph/9512248] [INSPIRE].ADSCrossRefGoogle Scholar - [54]M. Bedjidian et al.,
*Hard probes in heavy ion collisions at the LHC: heavy flavor physics*, hep-ph/0311048 [INSPIRE]. - [55]N. Brambilla et al.,
*Heavy quarkonium: progress, puzzles and opportunities*,*Eur. Phys. J.***C 71**(2011) 1534 [arXiv:1010.5827] [INSPIRE].ADSCrossRefGoogle Scholar - [56]NNPDF collaboration, R.D. Ball et al.,
*Parton distributions for the LHC Run II*,*JHEP***04**(2015) 040 [arXiv:1410.8849] [INSPIRE]. - [57]R.D. Ball et al.,
*Parton distributions with LHC data*,*Nucl. Phys.***B 867**(2013) 244 [arXiv:1207.1303] [INSPIRE].ADSCrossRefGoogle Scholar - [58]H.-L. Lai et al.,
*New parton distributions for collider physics*,*Phys. Rev.***D 82**(2010) 074024 [arXiv:1007.2241] [INSPIRE].ADSGoogle Scholar - [59]R.E. Nelson, R. Vogt and A.D. Frawley,
*Narrowing the uncertainty on the total charm cross section and its effect on the J/ψ cross section*,*Phys. Rev.***C 87**(2013) 014908 [arXiv:1210.4610] [INSPIRE].ADSGoogle Scholar - [60]Quarkonium Working Group collaboration, N. Brambilla et al.,
*Heavy quarkonium physics*, hep-ph/0412158 [INSPIRE]. - [61]M.L. Mangano, P. Nason and G. Ridolfi,
*Heavy quark correlations in hadron collisions at next-to-leading order*,*Nucl. Phys.***B 373**(1992) 295 [INSPIRE].ADSCrossRefGoogle Scholar - [62]J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer et al.,
*The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations*,*JHEP***07**(2014) 079 [arXiv:1405.0301] [INSPIRE].ADSCrossRefGoogle Scholar - [63]P. Artoisenet, F. Maltoni and T. Stelzer,
*Automatic generation of quarkonium amplitudes in NRQCD*,*JHEP***02**(2008) 102 [arXiv:0712.2770] [INSPIRE].ADSCrossRefGoogle Scholar - [64]H.-S. Shao,
*HELAC-Onia: an automatic matrix element generator for heavy quarkonium physics*,*Comput. Phys. Commun.***184**(2013) 2562 [arXiv:1212.5293] [INSPIRE].ADSCrossRefGoogle Scholar - [65]H.-S. Shao,
*HELAC-Onia*2*.*0*: an upgraded matrix-element and event generator for heavy quarkonium physics*,*Comput. Phys. Commun.***198**(2016) 238 [arXiv:1507.03435] [INSPIRE].ADSCrossRefGoogle Scholar - [66]A. Buckley et al.,
*LHAPDF*6*: parton density access in the LHC precision era*,*Eur. Phys. J.***C 75**(2015) 132 [arXiv:1412.7420] [INSPIRE].ADSCrossRefGoogle Scholar - [67]ATLAS collaboration,
*Measurement of the differential cross-sections of prompt and non-prompt production of J/ψ and ψ*(2*S*)*in pp collisions at*\( \sqrt{s}=7 \)*and*8*TeV with the ATLAS detector*,*Eur. Phys. J.***C 76**(2016) 283 [arXiv:1512.03657] [INSPIRE]. - [68]F. Maltoni et al.,
*Analysis of charmonium production at fixed-target experiments in the NRQCD approach*,*Phys. Lett.***B 638**(2006) 202 [hep-ph/0601203] [INSPIRE].ADSCrossRefGoogle Scholar - [69]Y. Kubota and J. Turkewitz, private communication.Google Scholar
- [70]P. Artoisenet, R. Frederix, O. Mattelaer and R. Rietkerk,
*Automatic spin-entangled decays of heavy resonances in Monte Carlo simulations*,*JHEP***03**(2013) 015 [arXiv:1212.3460] [INSPIRE].ADSCrossRefGoogle Scholar - [71]T. Sjöstrand, S. Mrenna and P.Z. Skands,
*A brief introduction to PYTHIA*8*.*1,*Comput. Phys. Commun.***178**(2008) 852 [arXiv:0710.3820] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [72]S. Frixione and B.R. Webber,
*Matching NLO QCD computations and parton shower simulations*,*JHEP***06**(2002) 029 [hep-ph/0204244] [INSPIRE].ADSCrossRefGoogle Scholar - [73]CMS collaboration,
*Measurement of J/ψ and ψ*(2*S*)*prompt double-differential cross sections in pp collisions at*\( \sqrt{s}=7 \)*TeV*,*Phys. Rev. Lett.***114**(2015) 191802 [arXiv:1502.04155] [INSPIRE]. - [74]D. Price, private communication.Google Scholar
- [75]C.H. Kom, A. Kulesza and W.J. Stirling,
*Pair production of J/ψ as a probe of double parton scattering at LHCb*,*Phys. Rev. Lett.***107**(2011) 082002 [arXiv:1105.4186] [INSPIRE].ADSCrossRefGoogle Scholar - [76]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].ADSCrossRefGoogle Scholar - [77]T. Kasemets and M. Diehl,
*Angular correlations in the double Drell-Yan process*,*JHEP***01**(2013) 121 [arXiv:1210.5434] [INSPIRE].ADSCrossRefGoogle Scholar - [78]M. Diehl, T. Kasemets and S. Keane,
*Correlations in double parton distributions: effects of evolution*,*JHEP***05**(2014) 118 [arXiv:1401.1233] [INSPIRE].ADSCrossRefGoogle Scholar - [79]Axial Field Spectrometer collaboration, T. Akesson et al.,
*Double parton scattering in pp collisions at*\( \sqrt{s}=63 \)*GeV*,*Z. Phys.***C 34**(1987) 163 [INSPIRE]. - [80]UA2 collaboration, J. Alitti et al.,
*A study of multi-jet events at the CERN pp collider and a search for double parton scattering*,*Phys. Lett.***B 268**(1991) 145 [INSPIRE]. - [81]CDF collaboration, F. Abe et al.,
*Study of four jet events and evidence for double parton interactions in*\( p\overline{p} \)*collisions at*\( \sqrt{s}=1.8 \)*TeV*,*Phys. Rev.***D 47**(1993) 4857 [INSPIRE]. - [82]CDF collaboration, F. Abe et al.,
*Double parton scattering in*\( \overline{p}p \)*collisions at*\( \sqrt{s}=1.8 \)*TeV*,*Phys. Rev.***D 56**(1997) 3811 [INSPIRE]. - [83]D0 collaboration, V.M. Abazov et al.,
*Double parton interactions in γ*+ 3*jet events in*\( p\overline{p} \)*collisions*\( \sqrt{s}=1.96 \)*TeV.*,*Phys. Rev.***D 81**(2010) 052012 [arXiv:0912.5104] [INSPIRE]. - [84]CMS collaboration,
*Study of double parton scattering using W*+ 2*-jet events in proton-proton collisions at*\( \sqrt{s}=7 \)*TeV*,*JHEP***03**(2014) 032 [arXiv:1312.5729] [INSPIRE].