Model-independent constraints on the shape parameters of dilepton angular distributions

TL;DR

This work derives model-independent, rotation-covariant constraints on the dilepton angular-distribution coefficients for vector J=1 states and introduces a frame-invariant polarization observable F that unifies the angular parameters across polarization frames. It shows that the Lam–Tung relation is a special case corresponding to F = 1/2 when all subprocesses yield transverse polarization, and that F can be measured from a one-dimensional cos alpha distribution. Applying the framework to Drell–Yan data, the authors argue that observed violations in pion-nucleus collisions cannot be explained by perturbative higher-order effects or axis misalignments, pointing instead to intrinsic production-dynamics. The formalism provides robust, testable constraints and a practical method for diagnosing the angular-momentum structure in dilepton decays across different processes and kinematics.

Abstract

The coefficients determining the dilepton decay angular distribution of vector particles obey certain positivity constraints and a rotation-invariant identity. These relations are a direct consequence of the covariance properties of angular momentum eigenstates and are independent of the production mechanism. The Lam-Tung relation can be derived as a particular case, simply recognizing that the Drell-Yan dilepton is always produced transversely polarized with respect to one or more quantization axes. The dilepton angular distribution continues to be characterized by a frame-independent identity also when the Lam-Tung relation is violated. Moreover, the violation can be easily characterized by measuring a one-dimensional distribution depending on one shape coefficient.

Figures (5)

• Figure 1: Sketch of the decay $V \rightarrow \ell^+ \ell^-$, showing the notations we use for axes, angles and angular momentum states. The $y$ and $z^\prime$ axes are oriented towards the reader.
• Figure 2: Allowed regions for the decay angular parameters (shaded areas). The upper plot also indicates the points corresponding to pure angular momentum configurations and to specific values of the rotation-invariant observable $\mathcal{F}$, introduced in Section \ref{['sec:invariant']}.
• Figure 3: $O(\alpha_s^0)$ and $O(\alpha_s^1)$ processes for Drell--Yan production, giving rise to transverse dilepton polarizations along different quantization axes: Collins--Soper (a), Gottfried--Jackson (b, c) and helicity (d).
• Figure 4: The E615 measurements of the Drell--Yan azimuthal anisotropy as a function of $p_{\rm T}$ (a) and of the polar anisotropy as a function of $x_1$ (b). The points are slightly displaced in the horizontal axis for improved visibility.
• Figure 5: The frame-invariant parameter $\mathcal{F}$ as a function of dilepton kinematic variables, derived from Drell--Yan measurements obtained with pion (a-c) and proton (d) beams. The E866 data points are slightly displaced in the horizontal axis for improved visibility.