Abstract
Quarkonium production offers good possibilities to study gluon TMDs. In this proceedings contribution this topic is explored for the linearly polarized gluons inside unpolarized hadrons and unpolarized gluons inside transversely polarized hadrons. It is argued that \(\chi _{b0/2}\) and \(\eta _b\) production at LHC are best to study the effects of linearly polarized gluons in hadronic collisions, by means of angular independent ratios of ratios of cross sections. This can be directly compared to \(\cos 2\phi \) asymmetries in heavy quark pair and dijet production in DIS at a future high-energy Electron-Ion Collider (EIC), which probe the same TMDs. In the small-x limit this corresponds to the Weizsäcker–Williams (WW) gluon distributions, which should show a change in behavior for transverse momenta around the saturation scale. Together with investigations of the dipole (DP) gluon distributions, this can provide valuable information about the polarization of the Color Glass Condensate if sufficiently small x-values are reached. Quarkonia can also be useful in the study of single transverse spin asymmetries. For transversely polarized hadrons the gluon distribution can be asymmetric, which is referred to as the Sivers effect. It leads to single spin asymmetries in for instance \(J{/}\psi \) (pair) production at AFTER@LHC, which probe the WW or f-type gluon Sivers TMD. It allows for a test of a sign-change relation w.r.t. the gluon Sivers TMD probed at an EIC in open heavy quark pair production. Single spin asymmetries in backward inclusive C-odd quarkonium production, such as \(J{/}\psi \) production, may offer probes of the DP or d-type gluon Sivers TMD at small x-values in the polarized proton, which in that limit corresponds to a correlator of a single Wilson loop, describing the spin-dependent odderon.
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References
D.W. Sivers, Single spin production asymmetries from the hard scattering of point-like constituents. Phys. Rev. D 41, 83–90 (1990)
P.J. Mulders, J. Rodrigues, Transverse momentum dependence in gluon distribution and fragmentation functions. Phys. Rev. D 63, 094021 (2001)
W.J. den Dunnen, J.P. Lansberg, C. Pisano, M. Schlegel, Accessing the transverse dynamics and polarization of gluons inside the proton at the LHC. Phys. Rev. Lett. 112, 212001 (2014)
P. Sun, B.-W. Xiao, F. Yuan, Gluon distribution functions and Higgs boson production at moderate transverse momentum. Phys. Rev. D 84, 094005 (2011)
D. Boer, W.J. den Dunnen, C. Pisano, M. Schlegel, W. Vogelsang, Linearly polarized gluons and the Higgs transverse momentum distribution. Phys. Rev. Lett. 108, 032002 (2012)
D. Boer, W.J. den Dunnen, TMD evolution and the Higgs transverse momentum distribution. Nucl. Phys. B 886, 421 (2014)
M.G. Echevarría, T. Kasemets, P.J. Mulders, C. Pisano, QCD evolution of (un)polarized gluon TMDPDFs and the Higgs \(q_T\)-distribution. JHEP 1507, 158 (2015)
A. Signori, Gluon TMDs in quarkonium production. Few Body Syst. 57, 651 (2016)
D. Boer, Linearly polarized gluon effects in unpolarized collisions. PoS QCDEV 2015, 023 (2015)
V.A. Novikov et al., Charmonium and gluons: basic experimental facts and theoretical introduction. Phys. Rept. 41, 1 (1978)
W. Beenakker, R. Kleiss, G. Lustermans, No Landau-Yang in QCD. arXiv:1508.07115 [hep-ph] (2015)
P. Hägler et al., Towards a solution of the charmonium production controversy: \(k^-\) perpendicular factorization versus color octet mechanism. Phys. Rev. Lett. 86, 1446 (2001)
G.T. Bodwin, E. Braaten, J. Lee, Comparison of the color-evaporation model and the NRQCD factorization approach in charmonium production. Phys. Rev. D 72, 014004 (2005)
F. Maltoni, A.D. Polosa, Observation potential for eta(b) at the Tevatron. Phys. Rev. D 70, 054014 (2004)
J.P. Lansberg, S.J. Brodsky, F. Fleuret, C. Hadjidakis, Quarkonium physics at a fixed-target experiment using the LHC Beams. Few Body Syst. 53, 11 (2012)
R. Baier, R. Rückl, Hadronic collisions: a quarkonium factory. Z. Phys. C 19, 251 (1983)
G.T. Bodwin, E. Braaten, G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium. Phys. Rev. D 51, 1125 (1995)
D. Boer, C. Pisano, Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER. Phys. Rev. D 86, 094007 (2012)
J.P. Ma, J.X. Wang, S. Zhao, Breakdown of QCD factorization for p-wave quarkonium production at low transverse momentum. Phys. Lett. B 737, 103 (2014)
D. Boer, C. Lorcé, C. Pisano, J. Zhou, The gluon Sivers distribution: status and future prospects. Adv. High Energy Phys. 2015, 371396 (2015). [arXiv:1504.04332 [hep-ph]]
I. Schmidt, J. Soffer, J.J. Yang, Transverse single spin asymmetries in photon production. Phys. Lett. B 612, 258 (2005)
A. Bacchetta et al., The Sivers single-spin asymmetry in photon-jet production. Phys. Rev. Lett. 99, 212002 (2007)
J.P. Lansberg et al., Spin physics and TMD studies at A Fixed-Target ExpeRiment at the LHC (AFTER@LHC). EPJ Web Conf. 85, 02038 (2015)
D. Boer et al., Gluons and the quark sea at high energies: distributions, polarization, tomography. arXiv:1108.1713 (2011)
R. Zhu, P. Sun, F. Yuan, Low transverse momentum heavy quark pair production to probe gluon tomography. Phys. Lett. B 727, 474 (2013)
S.J. Brodsky, D.S. Hwang, I. Schmidt, Final state interactions and single spin asymmetries in semi-inclusive deep inelastic scattering. Phys. Lett. B 530, 99–107 (2002)
J.C. Collins, Leading twist single transverse-spin asymmetries: Drell–Yan and deep inelastic scattering. Phys. Lett. B 536, 43–48 (2002)
A.V. Belitsky, X. Ji, F. Yuan, Final state interactions and gauge invariant parton distributions. Nucl. Phys. B 656, 165–198 (2003)
A.V. Efremov, A.V. Radyushkin, Field theoretic treatment of high momentum transfer processes. 3. gauge theories. Theor. Math. Phys. 44, 774–784 (1981) [Teor. Mat. Fiz. 44, 327–341 (1980)]
J.C. Collins, D.E. Soper, G. Sterman, Relation of parton distribution functions in the Drell–Yan process to deeply inelastic scattering. Phys. Lett. B 126, 275–278 (1983)
D. Boer, P.J. Mulders, Color gauge invariance in the Drell–Yan process. Nucl. Phys. B 569, 505–526 (2000)
S.J. Brodsky, D.S. Hwang, I. Schmidt, Initial state interactions and single spin asymmetries in Drell–Yan processes. Nucl. Phys. B 642, 344–356 (2002)
D. Boer, P.J. Mulders, F. Pijlman, Universality of T-odd effects in single spin and azimuthal asymmetries. Nucl. Phys. B 667, 201–241 (2003)
D. Boer, P.J. Mulders, C. Pisano, J. Zhou, Asymmetries in heavy quark pair and dijet production at an EIC. JHEP 1608, 001 (2016)
J.W. Qiu, M. Schlegel, W. Vogelsang, Probing gluonic spin-orbit correlations in photon pair production. Phys. Rev. Lett. 107, 062001 (2011)
J.P. Lansberg, H.S. Shao, Double-quarkonium production at a fixed-target experiment at the LHC (AFTER@LHC). Nucl. Phys. B 900, 273 (2015)
M.G.A. Buffing, A. Mukherjee, P.J. Mulders, Generalized universality of definite rank gluon transverse momentum dependent correlators. Phys. Rev. D 88, 054027 (2013)
J. Collins, J.-W. Qiu, \(k_{T}\) factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions. Phys. Rev. D 75, 114014 (2007)
T.C. Rogers, P.J. Mulders, No generalized TMD-factorization in hadro-production of high transverse momentum hadrons. Phys. Rev. D 81, 094006 (2010)
C.J. Bomhof, P.J. Mulders, F. Pijlman, Gauge link structure in quark-quark correlators in hard processes. Phys. Lett. B 596, 277–286 (2004)
M.G.A. Buffing, A. Mukherjee, P.J. Mulders, Generalized universality of higher transverse moments of quark TMD correlators. Phys. Rev. D 86, 074030 (2012)
M.G.A. Buffing, P.J. Mulders, Color entanglement for azimuthal asymmetries in the Drell–Yan process. Phys. Rev. Lett. 112, 092002 (2014)
T.C. Rogers, Extra spin asymmetries from the breakdown of transverse-momentum-dependent factorization in hadron-hadron collisions. Phys. Rev. D 88, 014002 (2013)
F. Dominguez, C. Marquet, B.W. Xiao, F. Yuan, Universality of unintegrated gluon distributions at small x. Phys. Rev. D 83, 105005 (2011)
D. Boer, M.G.A. Buffing, P.J. Mulders, Operator analysis of p\(_{T}\) -widths of TMDs. JHEP 1508, 053 (2015)
G.A. Chirilli, B.W. Xiao, F. Yuan, One-loop factorization for inclusive hadron production in \(pA\) collisions in the saturation formalism. Phys. Rev. Lett. 108, 122301 (2012)
P. Kotko et al., Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions. JHEP 1509, 106 (2015)
D. Kharzeev, Y.V. Kovchegov, K. Tuchin, Cronin effect and high p(T) suppression in pA collisions. Phys. Rev. D 68, 094013 (2003)
F. Gelis, A. Peshier, Probing colored glass via q anti-q photoproduction. Nucl. Phys. A 697, 879 (2002)
A. Metz, J. Zhou, Distribution of linearly polarized gluons inside a large nucleus. Phys. Rev. D 84, 051503 (2011)
A. Dumitru, T. Lappi, V. Skokov, The distribution of linearly polarized gluons and elliptic azimuthal anisotropy in DIS dijet production at high energy. Phys. Rev. Lett. 115, 252301 (2015)
S. Catani, M. Ciafaloni, F. Hautmann, High-energy factorization and small x heavy flavor production. Nucl. Phys. B 366, 135 (1991)
D. Boer, P.J. Mulders, C. Pisano, Dijet imbalance in hadronic collisions. Phys. Rev. D 80, 094017 (2009)
C. Pisano et al., Linear polarization of gluons and photons in unpolarized collider experiments. JHEP 1310, 024 (2013)
A. Mukherjee, S. Rajesh, Probing transverse momentum dependent parton distributions in charmonium and bottomonium production. Phys. Rev. D 93, 054018 (2016)
D. Boer, M.G. Echevarría, P. Mulders, J. Zhou, Single spin asymmetries from a single Wilson loop. Phys. Rev. Lett. 116, 122001 (2016)
D. Boer et al., Gluon and Wilson loop TMDs for hadrons of spin \(\le \) 1. JHEP 1610, 013 (2016)
R.M. Godbole, A. Misra, A. Mukherjee, V.S. Rawoot, Transverse single spin asymmetry in \(e+p^\uparrow \rightarrow e+J/\psi +X \) and transverse momentum dependent evolution of the Sivers function. Phys. Rev. D 88, 014029 (2013)
A. Mukherjee, S. Rajesh, \(J/\psi \) production in \(ep^{\uparrow }\) collision in color octet model and Sivers asymmetry. arXiv:1609.05596 [hep-ph] (2016)
A. Schäfer, J. Zhou, Transverse single spin asymmetry in hadronic \(\eta _{c, b}\) production. Phys. Rev. D 88, 014008 (2013)
R.M. Godbole, A. Kaushik, A. Misra, Transverse single spin asymmetry in \(p+p^\uparrow \rightarrow D +X \). arXiv:1606.01818 [hep-ph] (2016)
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Boer, D. Gluon TMDs in Quarkonium Production. Few-Body Syst 58, 32 (2017). https://doi.org/10.1007/s00601-016-1198-6
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DOI: https://doi.org/10.1007/s00601-016-1198-6