Factorisation, Parton Entanglement and the Drell-Yan Process

TL;DR

This work addresses the observed violation of the Lam-Tung relation in Drell-Yan lepton-pair angular distributions by examining the spin structure of the annihilating quark–antiquark pair. It compares two theoretical pictures: a general, possibly entangled $\rho^{(q,\bar{q})}$ and a factorised form akin to Boer99 that relies on transverse-momentum dependent distributions such as $h_1^{\perp}$, showing how the observable $\kappa$ encodes spin correlations. A Gaussian TMD toy model illustrates how $h_1^{\perp}$ can produce the required $\kappa$, while a more general framework allows nonzero $F_3$, $G_3$, and $H_{33}$, leading to potential discriminants via $k_T$ and $Q^2$ dependencies and flavour studies. The authors also outline an instanton-based mechanism that induces helicity flips and generates nontrivial spin correlations, yielding a calculable expression for $\kappa$ and suggesting that instantons could contribute to the observed effects. Overall, the paper motivates experimental reconstruction of the full $q\bar{q}$ density matrix and cross-process tests to determine whether parton-level entanglement plays a role in hadronic reactions.

Abstract

We discuss the angular distribution of the lepton pair in the Drell-Yan process, hadron+hadron -> γ^* X -> l^+ l^- X. This process gives information on the spin-density matrix ρ^{(q,\bar{q})} of the annihilating quark-antiquark pair in q+\bar{q} -> l^+ l^-. There is strong experimental evidence that even for unpolarised initial hadrons ρ^{(q,\bar{q})} is nontrivial, and therefore the quark-antiquark system is polarised. We discuss the possibilities of a general ρ^{(q,\bar{q})} -which could be entangled- and a factorising ρ^{(q,\bar{q})}. We argue that instantons may lead to a nontrivial ρ^{(q,\bar{q})} of the type indicated by experiments.

Figures (2)

• Figure 1: The generic Drell-Yan process.
• Figure 2: The instanton-induced process $q_\text{\tiny$L$}+\overline{q}_\text{\tiny$L$}\to\gamma^\ast+\hbox{$(n_f-1)\,\left[q_\text{\tiny$R$}+\overline{q}_\text{\tiny$R$}\right]$}+n_g\,g\,.$