Friday, September 21, 2012

1209.4610 (Hua-Sheng Shao et al.)

Spin correlations in polarizations of P-wave charmonia $χ_{cJ}$ and
impact on $J/ψ$ polarization
   [PDF]

Hua-Sheng Shao, Kuang-Ta Chao
Based on a general form of the effective vertex functions for the decays of P-wave charmonia $\chicj$, compact formulas for the angular distributions of the $\jpsi$ in the $\chicj\rightarrow \jpsi \gamma$ decay and the muon in the subsequently cascade decay $\chicj\rightarrow \jpsi \gamma\rightarrow \mu^+\mu^-\gamma$ are derived. While the former are the same as those obtained in a different approach by using the angular momentum relation, the latter ones are new. Similar to the $J/\psi$ case, the $\chicj$ polarization observables can be expressed in terms of rational functions of the yields spin density matrix elements of $\chicj$. A reweighting method is proposed to determine the production spin density matrix elements of the $\chi_{c2}$. Some generalized rotation-invariant relations for arbitrary integer-spin particles are also derived. Special cases are applied to the polarizations of $\chi_{c1}$ and $\chi_{c2}$. In particular, we discuss the possible impact of $\chicj$ and $\psi'$ feed-down on the prompt $\jpsi$ polarization. As a phenomenological illustration, we present the angular distributions in terms of the spin density matrix elements of $\chi_{c1}$ and $\chi_{c2}$ production in four different frames at the Large Hadron Collider.
View original: http://arxiv.org/abs/1209.4610

No comments:

Post a Comment