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Based on a general form of the effective vertex functions for the decays of P-wave charmonia $chicj$, angular distribution formulas for the subsequent decays $chicjrightarrow jpsi gamma$ and $jpsi to mu^+mu^-$ are derived. The formulas are the same as those obtained in a different approach in the literature. Our formulas are expressed in a more general form, including parity violation effects and the full angular dependence of $jpsi$ and muon in the cascade decay $chicjtojpsigammatomu^+mu^-gamma$. The $chicj$ polarization observables are expressed in terms of rational functions of the spin density matrix elements of $chicj$ production. Generalized rotation-invariant relations for arbitrary integer-spin particles are also derived and their expressions in terms of observable angular distribution parameters are given in the $chi_{c1}$ and $chi_{c2}$. To complement our previous direct-$jpsi$ polarization result, we also discuss the impact on the observable prompt-$jpsi$ polarization. As an illustrative application of our angular distribution formulas, we present the angular distributions in terms of the tree-level spin density matrix elements of $chi_{c1}$ and $chi_{c2}$ production in several different frames at the Large Hadron Collider. Moreover, a reweighting method is also proposed to determine the entire set of the production spin density matrix elements of the $chi_{c2}$, some of which disappear or are suppressed for vanishing higher-order multipole effects making the complete extraction difficult experimentally.
Using $4.479 times 10^{8}$ $psi(3686)$ events collected with the BESIII detector, we search for the decays $psi(3686) rightarrow e^{+}e^{-}chi_{c0,1,2}$ and $chi_{c0,1,2} rightarrow e^{+}e^{-}J/psi$. The decays $psi(3686) rightarrow e^{+}e^{-}chi_{c0
We compute fragmentation corrections to hadroproduction of the quarkonium states $J/psi$, $chi_{cJ}$, and $psi(2S)$ at leading power in $m_c^2/p_T^2$, where $m_c$ is the charm-quark mass and $p_T$ is the quarkonium transverse momentum. The computatio
Using $4.48 times 10^{8}$ $psi(3686)$ events collected with the BESIII detector, we search for the decays $chi_{cJ} rightarrow mu^{+}mu^{-}J/psi$ through the radiative decays $psi(3686) rightarrow gammachi_{cJ}$, where $J=0,1,2$. The decays $chi_{c1,
Using a sample of 106 million $psi(3686)$ decays, $psi(3686) to gamma chi_{cJ} (J = 0, 1, 2)$ and $psi(3686) to gamma chi_{cJ}, chi_{cJ} to gamma J/psi$ $(J = 1, 2)$ events are utilized to study inclusive $chi_{cJ} to$ anything, $chi_{cJ} to$ hadrons
By including the interference effect between the QCD and the QED diagrams, we carry out a complete analysis on the exclusive productions of $e^+e^- to J/psi+chi_{cJ}$ ($J=0,1,2$) at the $B$ factories with $sqrt{s}=10.6$ GeV at the next-to-leading-ord