Abstract
In this paper, we present a detailed next-to-leading-order (NLO) study of J/ψ angular distributions in e+e− → J/ψ + ηc, χcJ (J = 0, 1, 2) within the nonrelativistic QCD factorization (NRQCD). The numerical NLO expressions for total and differential cross sections, i.e., \( \frac{d\sigma}{d\cos \theta } \) = A + B cos2 θ, are both derived. With the inclusion of the newly-calculated QCD corrections to A and B, the αθ (= B/A) parameters in J/ψ + χc0 and J/ψ + χc1 are moderately enhanced, while the magnitude of αθJ/ψ+χc2 is significantly reduced; regarding the production of J/ψ + ηc, the αθ value remains unchanged. By comparing with experiment, we find the predicted αθJ/ψ+ηc is in good agreement with the Belle measurement; however, αθJ/ψ+χc0 is still totally incompatible with the experimental result, and this discrepancy seems to hardly be cured by proper choices of the charm-quark mass, the renormalization scale, and the NRQCD matrix elements.
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References
Belle collaboration, Observation of double c\( \overline{c} \) production in e+e− annihilation at \( \sqrt{s} \) ≈ 10.6 GeV, Phys. Rev. Lett. 89 (2002) 142001 [hep-ex/0205104] [INSPIRE].
Belle collaboration, Study of double charmonium production in e+e− annihilation at \( \sqrt{s} \) ≈ 10.6 GeV, Phys. Rev. D 70 (2004) 071102 [hep-ex/0407009] [INSPIRE].
BaBar collaboration, Measurement of double charmonium production in e+e− annihilations at \( \sqrt{s} \) = 10.6 GeV, Phys. Rev. D 72 (2005) 031101 [hep-ex/0506062] [INSPIRE].
E. Braaten and J. Lee, Exclusive Double Charmonium Production from e+e− Annihilation into a Virtual Photon, Phys. Rev. D 67 (2003) 054007 [Erratum ibid. 72 (2005) 099901] [hep-ph/0211085] [INSPIRE].
K.-Y. Liu, Z.-G. He and K.-T. Chao, Problems of double charm production in e+e− annihilation at \( \sqrt{s} \) = 10.6 GeV, Phys. Lett. B 557 (2003) 45 [hep-ph/0211181] [INSPIRE].
K.-Y. Liu, Z.-G. He and K.-T. Chao, Search for excited charmonium states in e+e− annihilation at \( \sqrt{s} \) = 10.6 GeV, Phys. Rev. D 77 (2008) 014002 [hep-ph/0408141] [INSPIRE].
K. Hagiwara, E. Kou and C.-F. Qiao, Exclusive J/ψ productions at e+e− colliders, Phys. Lett. B 570 (2003) 39 [hep-ph/0305102] [INSPIRE].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
J.P. Ma and Z.G. Si, Predictions for e+e− → J/ψηc with light-cone wave-functions, Phys. Rev. D 70 (2004) 074007 [hep-ph/0405111] [INSPIRE].
A.E. Bondar and V.L. Chernyak, Is the BELLE result for the cross section σ(e+e− → J/ψηc) a real difficulty for QCD?, Phys. Lett. B 612 (2005) 215 [hep-ph/0412335] [INSPIRE].
V.V. Braguta, A.K. Likhoded and A.V. Luchinsky, Excited charmonium mesons production in e+e− annihilation at \( \sqrt{s} \) = 10.6 GeV, Phys. Rev. D 72 (2005) 074019 [hep-ph/0507275] [INSPIRE].
G.T. Bodwin, D. Kang and J. Lee, Reconciling the light-cone and NRQCD approaches to calculating e+e− → J/ψηc, Phys. Rev. D 74 (2006) 114028 [hep-ph/0603185] [INSPIRE].
Y.-J. Zhang, Y.-j. Gao and K.-T. Chao, Next-to-leading order QCD correction to e+e− → J/ψηc at \( \sqrt{s} \) = 10.6 GeV, Phys. Rev. Lett. 96 (2006) 092001 [hep-ph/0506076] [INSPIRE].
H.-M. Choi and C.-R. Ji, Perturbative QCD analysis of exclusive J/ψηc production in e+e− annihilation, Phys. Rev. D 76 (2007) 094010 [arXiv:0707.1173] [INSPIRE].
G.T. Bodwin, J. Lee and C. Yu, Resummation of Relativistic Corrections to e+e− → J/ψηc, Phys. Rev. D 77 (2008) 094018 [arXiv:0710.0995] [INSPIRE].
B. Gong and J.-X. Wang, QCD corrections to J/ψ plus ηc production in e+e− annihilation at \( \sqrt{s} \) = 10.6 GeV, Phys. Rev. D 77 (2008) 054028 [arXiv:0712.4220] [INSPIRE].
Y.-J. Zhang, Y.-Q. Ma and K.-T. Chao, Factorization and NLO QCD correction in e+e− → J/ψ(ψ(2S)) + χc0 at B Factories, Phys. Rev. D 78 (2008) 054006 [arXiv:0802.3655] [INSPIRE].
V.V. Braguta, Double charmonium production at B-factories within light cone formalism, Phys. Rev. D 79 (2009) 074018 [arXiv:0811.2640] [INSPIRE].
Y.-J. Sun, X.-G. Wu, F. Zuo and T. Huang, The Cross section of the process e+e− → J/ψηc within the QCD light-cone sum rules, Eur. Phys. J. C 67 (2010) 117 [arXiv:0911.0963] [INSPIRE].
N. Brambilla et al., Heavy Quarkonium: Progress, Puzzles, and Opportunities, Eur. Phys. J. C 71 (2011) 1534 [arXiv:1010.5827] [INSPIRE].
K. Wang, Y.-Q. Ma and K.-T. Chao, QCD corrections to e+e− → J/ψ(ψ(2S)) + χcj(J = 0, 1, 2) at B Factories, Phys. Rev. D 84 (2011) 034022 [arXiv:1107.2646] [INSPIRE].
H.-R. Dong, F. Feng and Y. Jia, O(αs) corrections to J/ψ + χcJ production at B factories, JHEP 10 (2011) 141 [Erratum ibid. 02 (2013) 089] [arXiv:1107.4351] [INSPIRE].
H.-R. Dong, F. Feng and Y. Jia, O(αsv2) correction to e+e− → J/ψ + ηc at B factories, Phys. Rev. D 85 (2012) 114018 [arXiv:1204.4128] [INSPIRE].
S.-Q. Wang, X.-G. Wu, X.-C. Zheng, J.-M. Shen and Q.-L. Zhang, J/ψ + χcJ Production at the B Factories under the Principle of Maximum Conformality, Nucl. Phys. B 876 (2013) 731 [arXiv:1301.2992] [INSPIRE].
X.-H. Li and J.-X. Wang, O(αsυ2) correction to J/ψ plus ηc production in e+e− annihilation at \( \sqrt{s} \) = 10.6 GeV, Chin. Phys. C 38 (2014) 043101 [arXiv:1301.0376] [INSPIRE].
N. Brambilla et al., QCD and Strongly Coupled Gauge Theories: Challenges and Perspectives, Eur. Phys. J. C 74 (2014) 2981 [arXiv:1404.3723] [INSPIRE].
G.T. Bodwin, H.S. Chung and J. Lee, Double logarithms in e+e− → J/ψ + ηc, Phys. Rev. D 90 (2014) 074028 [arXiv:1406.1926] [INSPIRE].
Z. Sun, X.-G. Wu, Y. Ma and S.J. Brodsky, Exclusive production of J/ψ + ηc at the B factories Belle and Babar using the principle of maximum conformality, Phys. Rev. D 98 (2018) 094001 [arXiv:1807.04503] [INSPIRE].
Y. Jiang and Z. Sun, Further studies on the exclusive productions of J/ψ + χcJ (J = 0, 1, 2) via e+e− annihilation at the B factories, Eur. Phys. J. C 78 (2018) 892 [arXiv:1809.09071] [INSPIRE].
H.-J. Tao, Y.-J. Sun, S.-P. Guo, W. Hong and Q. Huang, The Excited Charmonium Production in e+ e− Annihilation, arXiv:1901.09142 [INSPIRE].
J.-P. Lansberg, New Observables in Inclusive Production of Quarkonia, Phys. Rept. 889 (2020) 1 [arXiv:1903.09185] [INSPIRE].
L. Zeng, H.-B. Fu, D.-D. Hu, L.-L. Chen, W. Cheng and X.-G. Wu, Revisiting the production of J/ψ + ηc via the e+e− annihilation within the QCD light-cone sum rules, Phys. Rev. D 103 (2021) 056012 [arXiv:2102.01842] [INSPIRE].
A.V. Berezhnoy, I.N. Belov, S.V. Poslavsky and A.K. Likhoded, One-loop corrections to the processes e+e− → γ, Z → J/ψ ηc and e+e− → Z → J/ψ J/ψ, Phys. Rev. D 104 (2021) 034029 [arXiv:2101.01477] [INSPIRE].
B. Gong and J.-X. Wang, Next-to-leading-order QCD corrections to e+e− → J/ψcc at the B factories, Phys. Rev. D 80 (2009) 054015 [arXiv:0904.1103] [INSPIRE].
H.-F. Zhang and Z. Sun, Leptonic current structure and azimuthal asymmetry in deeply inelastic scattering, Phys. Rev. D 96 (2017) 034002 [arXiv:1701.08728] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
R. Mertig, M. Bohm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 345.
F. Feng, Apart: A Generalized Mathematica Apart Function, Comput. Phys. Commun. 183 (2012) 2158 [arXiv:1204.2314] [INSPIRE].
A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].
J.-X. Wang, Progress in FDC project, Nucl. Instrum. Meth. A 534 (2004) 241 [hep-ph/0407058] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
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Sun, Z. Next-to-leading-order study of J/ψ angular distributions in e+e− → J/ψ + ηc, χcJ at \( \sqrt{s} \) ≈ 10.6 GeV. J. High Energ. Phys. 2021, 73 (2021). https://doi.org/10.1007/JHEP09(2021)073
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DOI: https://doi.org/10.1007/JHEP09(2021)073