Determination of chi_c and chi_b polarizations from dilepton angular distributions in radiative decays

TL;DR

The paper addresses how χ_c and χ_b polarizations are transmitted to J/ψ and Υ in radiative decays and how to extract them without being hamstrung by photon multipole uncertainties or production mechanisms. It develops a production-frame–independent multipole-expansion formalism for χ_j → V γ decays and demonstrates that the dilepton angular distributions from V → ℓℓ− can directly reveal χ polarization, especially at high momentum where frame definitions align and photon multipoles have minimal impact. The authors provide explicit angular distributions for both photon and dilepton channels, define polarization frames, and show how to avoid relying on photon reconstruction while clarifying inconsistencies in prior calculations. These results enable cleaner, more robust measurements of χ polarization in high-energy experiments and improve interpretation of feed-down effects in quarkonium polarization studies.

Abstract

The angular distributions of the decay products in the successive decays chi_c (chi_b) to J/psi (Upsilon) gamma and J/psi (Upsilon) to l+l- are calculated as a function of the angular momentum composition of the decaying chi meson and of the multipole structure of the photon radiation, using a formalism independent of production mechanisms and polarization frames. The polarizations of the chi states produced in high energy collisions can be derived from the dilepton decay distributions of the daughter J/psi or Upsilon mesons, with a reduced dependence on the details of the photon reconstruction or simulation. Moreover, this method eliminates the dependence of the polarization measurement on the actual details of the multipole structure of the radiative transition. Problematic points in previous calculations of the chi_c decay angular distributions are identified and clarified.

Figures (3)

• Figure 1: Definition of axes and decay angles for $\chi \rightarrow V \gamma$ (a) and for $V \rightarrow \ell^+ \ell^-$ in two options, with the dilepton polarization axis being the $V$ direction in the $\chi$ rest frame (b) or parallel to the $\chi$ polarization axis (c).
• Figure 2: Dependence of the parameters $\lambda_\Theta$ (a) and $\lambda_\vartheta$ (b) of the $\chi_{1}$ photon and dilepton distributions and of the parameters $\lambda_\Theta^{(1)}$ (c) and $\lambda_\vartheta$ (d) of the $\chi_{2}$ photon and dilepton distributions on the relative contribution of the magnetic quadrupole transition amplitude.
• Figure 3: Allowed regions for the angular parameters of the dilepton distributions produced by the decay of vector states of any origin (light-shaded bib:LTviolation), of $\chi_{2}$ daughters (darker) and of $\chi_{1}$ daughters (darkest).