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

H. Shao; K. Chao

Paper

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

Abstract

Based on a general form of the effective vertex functions for the decays of P-wave charmonia

, angular distribution formulas for the subsequent decays

and

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

and muon in the cascade decay

. The

polarization observables are expressed in terms of rational functions of the spin density matrix elements of

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

and

. To complement our previous direct-

polarization result, we also discuss the impact on the observable prompt-

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

and

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

, some of which disappear or are suppressed for vanishing higher-order multipole effects making the complete extraction difficult experimentally.