\begin{document}$ Z\to VV $\end{document} and \begin{document}$ Z\to VP $\end{document}, with V and P denoting vector and pseudoscalar quarkonia, respectively. It is assumed that the leading-order QCD diagrams would give the dominant contributions to these processes, and the corresponding branching fractions, for instance, \begin{document}$ {\cal B}(Z\to J/\Psi J/\Psi) $\end{document}, have been estimated to be approximately\begin{document}$ 10^{-13} $\end{document} in literature. However, these decays could also happen through electromagnetic transitions \begin{document}$ Z\to V\gamma^* $\end{document} and \begin{document}$ Z\to P\gamma^* $\end{document}, with the virtual photon transforming into V. Interestingly, the smallness of the vector quarkonium mass can give rise to a large factor \begin{document}$ m_Z^2/m_V^2 $\end{document} relative to the QCD contributions, which thus counteracts the suppression from the electromagnetic coupling. We systematically include these two types of contributions in our calculation to predict branching fractions for these decays. Particularly, owing to the virtual photon effects, it is found that \begin{document}$ {\cal B}(Z\to J/\Psi J/\Psi) $\end{document} will be significantly enhanced, up to \begin{document}$ 10^{-10} $\end{document}."> Note on rare <i>Z</i>-boson decays to double heavy quarkonia -
  • [1]

    A.M. Sirunyanet al. (CMS Collaboration), Phys. Lett. B797, 134811 (2019), arXiv:1905.10408[hep-ex

  • [2]

    (CMS Collaboration), arXiv:2206.03525 [hep-ex]

  • [3]

    L. Bergström and R.W. Robinett, Phys. Rev. D41, 3513 (1990)

  • [4]

    A.K. Likhoded and A.V. Luchinsky, Mod. Phys. Lett. A33, 1850078 (2018), arXiv:1712.03108[hep-ph

  • [5]

    T. Appelquist and H. D. Politzer, Phys. Rev. Lett.34, 43 (1975)

  • [6]

    A. De Rujula and S.L. Glashow, Phys. Rev. Lett.34, 46 (1975)

  • [7]

    J. H. Kühn, J. Kaplan, and E. Safiani, Nucl. Phys. B157, 125 (1979)

  • [8]

    C. H. Chang, Nucl. Phys. B172, 425 (1980)

  • [9]

    W.Y. Keung, Phys. Rev. D23, 2072 (1981)

  • [10]

    E. L. Berger and D. Jones, Phys. Rev. D23, 1521 (1981)

  • [11]

    L. Clavelli, Phys. Rev. D26, 1610 (1982)

  • [12]

    L. Clavelli, T. Gajdosik, and I. Perevalova, Phys. Lett. B523, 249 (2001), arXiv:hep-ph/0110076

  • [13]

    L. Clavelli, P. Coulter, and T. Gaidosik, Phys. Lett. B526, 360 (2002)

  • [14]

    V. Barger and R. Phillips,Collider Physics(updated edition), (Westview Press, 1996)

  • [15]

    G. Hao, C.F. Qiao, P. Sun, and Y. Jia, J. High Energy Phys.02, 057 (2007)

  • [16]

    L.D. Landau, Dokl. Akad. Nauk SSSR60, 207 (1948)

  • [17]

    C. N. Yang, Phys. Rev.77, 242 (1950)

  • [18]

    G.T. Bodwin, H.S. Chung, D. Kang, J. Lee, and C. Yu, Phys. Rev. D77, 094017 (2008), arXiv:0710.0994[hep-ph

  • [19]

    H.S. Chung, J. Lee, and C. Yu, Phys. Lett. B697, 48 (2011), arXiv:1011.1554[hep-ph

  • [20]

    G. Bodwin, F. Petriello, S. Stoynev, and M. Velasco, Phys. Rev. D88, 053003 (2013), arXiv:1306.5770[hep-ph

  • [21]

    D.N. Gao, Phys. Lett. B737, 366 (2014), arXiv:1406.7102[hep-ph

  • [22]

    D.N. Gao and X. Gong, Phys. Lett. B832, 137243 (2022), arXiv:2203.00514[hep-ph

  • [23]

    L. Bergström and R.W. Robinett, Phys. Lett. B245, 249 (1990)

  • [24]

    S. Fleming, Phys. Rev. D48, R1914 (1993), arXiv:hep-ph/9304270

  • [25]

    S. Fleming, Phys. Rev. D50, 5808 (1994), arXiv:hep-ph/9403396

  • [26]

    A. M. Sirunyanet al. (CMS Collaboration), Phys. Rev. Lett.121, 141801 (2018), arXiv:1806.04213[hep-ex

  • [27]

    G. Guberina, J. H. Kühn, R. D. Pecceiet al., Nucl. Phys. B174, 317 (1980)

  • [28]

    G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D51, 1125 (1995)

  • [29]

    G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D55, 5853 (1997)

  • [30]

    X. Luo, H.B. Fu, H.J. Tian, and C. Li, arXiv:2209.08802[hep-ph]

  • [31]

    X.G. He and G. Valencia, Phys. Rev. D66, 013004 (2002)

  • [32]

    S. Gori, J. Gu, and L.-T. Wang, J. High Energy Phys.04, 062 (2016), arXiv:1508.07010[hep-ph

  • [33]

    H. Dong, P. Sun, B. Yan, and C.-P. Yuan, Phys. Lett. B829, 137076 (2022), arXiv:2201.11635[hep-ph

  • [34]

    Y. Grossman, M. König, and M. Neubert, J. High Energy Phys.04, 101 (2015), arXiv:1501.06569[hep-ph

  • [35]

    M. Cepedaet al., CERN Yellow Rep. Monogr.7, 221 (2019), arXiv:1902.00134[hep-ph

  • [36]

    FCC Collaboration, A. Abada,et al., Eur. Phys. J. C79, 474 (2019)

  • [37]

    CEPC Study Group, J. B. Guimarães da Costaet al., arXiv:1811.10545[hep-ex]

Baidu
map