\begin{document}$ \Omega^{-} $\end{document} in the Cartesian coordinate system of baryon-antibaryon pairs produced in \begin{document}$ e^{+}e^{-} $\end{document} annihilation. Using the helicity formalism of Jacob and Wick, we derive the expression for the spin-3/2 density matrices. Our analysis is based on the angular distribution of the process \begin{document}$e^{+}e^{-}\rightarrow \psi(3686)\rightarrow $\end{document}\begin{document}$ \Omega^{-}\bar{\Omega}^{+}$\end{document} in the BESIII experiment. By decomposing the polarization state of \begin{document}$ \Omega^{-} $\end{document} particles along different coordinate axes, we examine the polarization dependence of the cross-section. Our results demonstrate that \begin{document}$ \Omega^{-} $\end{document} particles exhibit varying degrees of tensor polarization along the x-, y-, and z-axes, as well as weak vector polarization and rank-3 tensor polarization along the y-axis. To the best of our knowledge, this is the first study to calculate the polarization dependence of the cross-section distributions for the annihilation process \begin{document}$ e^+e^-\rightarrow \Omega^-\bar{\Omega}^+ $\end{document}. Our theoretical predictions are in good agreement with the experimental measurements."> Spin density matrix for <inline-formula><tex-math id="M1">\begin{document}${ \bf\Omega^{-}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/8ded9edf-70cb-45e5-9912-e541df03a39e/CPC-2023-0054_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/8ded9edf-70cb-45e5-9912-e541df03a39e/CPC-2023-0054_M1.png"/></alternatives></inline-formula> and its polarization alignment in <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol\psi\bf(3686)\rightarrow \Omega^{-}\bar{\Omega}^{+}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/8ded9edf-70cb-45e5-9912-e541df03a39e/CPC-2023-0054_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/8ded9edf-70cb-45e5-9912-e541df03a39e/CPC-2023-0054_M2.png"/></alternatives></inline-formula> -
  • [1]

    E. Rutherford, Phil. Mag. Ser.21(6), 669 (1911)

  • [2]

    A. N. Cooke, R. Horsley, Y. Nakamuraet al., PoS LATTICE2013, 278 (2014)

  • [3]

    V. E. Barnes, P. L. Connolly, D. J. Crennellet al., Phys. Rev. Lett.12, 204 (1964)

  • [4]

    M. Gell-Mann,Phys. Rev.125, 1067-1084 (1962); Y. Ne'eman, Nucl. Phys.26, 222 (1961)

  • [5]

    Gell-Mann,Phys. Lett.8, 214 (1964); G. Zweig, CERN-TH-401, 412 (1964)

  • [6]

    O. W. Greenberg, Phys. Rev. Lett.13, 598 (1964)

  • [7]

    B. W. Filippone and X. D. Ji, Adv. Nucl. Phys.26, 1 (2001)

  • [8]

    C. A. Aidala, S. D. Bass, D. Haschet al., Rev. Mod. Phys.85, 655 (2013)

  • [9]

    A. Deur, S. J. Brodsky, and G. F. De Téramond, Rept.Prog.Phys.82, 076201 (2019)

  • [10]

    R. Angeles-Martinez, A. Bacchetta, and I. I. Balitsky,et al.Acta Phys. Polon. B46(12), 2501 (2015)

  • [11]

    J. J. Ethier and E. R. Nocera, Ann. Rev. Nucl. Part. Sci.70, 43 (2020)

  • [12]

    A. Metz and A. Vossen, Prog. Part. Nucl. Phys.91, 136 (2016)

  • [13]

    Z. T. Liang and X. N. Wang,Phys. Rev. Lett.94, 102301 (2005)[Erratum:Phys. Rev. Lett.96, 039901 (2006)]

  • [14]

    G. Fäldt, Eur. Phys. J. A51(7), 74 (2015)

  • [15]

    G. Fäldt, Eur. Phys. J. A52(5), 141 (2016)

  • [16]

    G. Fäldt and A. Kupsc, Phys. Lett. B772, 16 (2017)

  • [17]

    M. Ablikimet al. [BESⅢ], Nature Phys.15, 631 (2019)

  • [18]

    M. Ablikimet al. [BESⅢ], Nature606(7912), 64 (2022)

  • [19]

    K. H. Sun and H. B. Li, Physics51(7), 491 (2022)

  • [20]

    A. Bacchetta and P. J. Mulders, Phys. Rev. D62, 114004 (2000)

  • [21]

    M. G. Doncel, L. Michel, and P. Minnaert, Nucl. Phys. B38, 477 (1972)

  • [22]

    A. Z. Dubnickova, S. Dubnicka, and M. P. Rekalo, Nuovo Cim. A109, 241 (1996)

  • [23]

    S. y. Wei, Y. k. Song, and Z. t. Liang, Phys. Rev. D89(1), 014024 (2014)

  • [24]

    K. b. Chen, Z. t. Liang, Y. k. Songet al., Phys. Rev. D102(3), 034001 (2020)

  • [25]

    S. Kumano and Q. T. Song, Phys. Rev. D103(1), 014025 (2021)

  • [26]

    S. Acharyaet al. [ALICE], Phys. Rev. Lett.125(1), 012301 (2020)

  • [27]

    M. S. Abdallahet al. [STAR], Nature614(7947), 244 (2023)

  • [28]

    H. S. Song, Phys. Rev.162, 1615 (1967)

  • [29]

    J. Kim and H. S. Song, Annals Phys.108, 99 (1977)

  • [30]

    M. Ablikimet al. [BESⅢ], Phys. Rev. Lett.126(9), 092002 (2021)

  • [31]

    M. Jacob and G. C. Wick, Annals Phys.7, 404 (1959)

  • [32]

    E. Perotti, G. Fäldt, A. Kupscet al., Phys. Rev. D99(5), 056008 (2019)

  • [33]

    W. Yang, Nucl. Phys. A997, 121729 (2020)

  • [34]

    J. Zhao, Z. Zhang, Z. t. Lianget al., Phys. Rev. D106(9), 094006 (2022)

  • [35]

    E. Perotti, J. Phys. Conf. Ser.1024(1), 012019 (2018)

  • [36]

    E. Leader,Spin in Particle Physics, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Series Vol. 15 (Cambridge University Press, Cambridge, England, 2011)

  • [37]

    Paul A. M. Dirac, Proc. Roy. Soc. Lond. A117, 610 (1928)

  • [38]

    Alexandru Proca, J. Phys. Radium7, 347 (1936)

  • [39]

    William Rarita and Julian Schwinger, Phys. Rev.60, 61 (1941)

Baidu
map