Cascades of gluons at high energies and their QI measures

TL;DR

The work develops a 1D dipole cascade framework with saturation and $2\to0$ annihilation to address entanglement and information flow in high-energy QCD. By computing von Neumann entropy $S(y)$, mean dipole number, variance, and purity from the evolving $p_n(y)$ distributions, it connects cascade dynamics to LHCb hadronic entropy measurements and makes testable purity predictions. It introduces two cascade variants, the $\beta$-cascade (recombination) and the $\gamma$-cascade (annihilation), and derives approximate Negative Binomial-distributed solutions for $p_n(y)$, providing a bridge between QCD evolution and quantum-information measures. This framework yields concrete, experimentally testable predictions for entropy and purity in hadronic collisions, enabling validation with current and future data.

Abstract

In this contribution we report on recent extension of one dimensional dipole cascade models to account for saturation and transition to vacuum \cite{Kutak:2025syp}. We analyze properties of the models using Quantum Information tools. Furthermore, we present a description of the hadronic entropy measured by LHCb and predictions for the purity measurement. %we provide description of hadronic entropy as measured by LHCb and provide predictions for measurement of purity.

Figures (4)

• Figure 1: Probabilities $p_n(y)$ ($n=1,\ldots ,10$) for the $\beta$ branching (\ref{['eq:EquationSat1']}) for $r=0.1$ (left) and $r=0.5$ (right), and $\alpha=0.5$. One can see that for small $r$ probabilities cross at $y_{\rm cross}\simeq 6.5$, whereas for larger $r$ they reach asymptotic values without crossing.
• Figure 2: Probabilities $p_n(y)$ ($n=0,\ldots ,10$) for the $\gamma$ branching (\ref{['eq:eqsat2']}) for $\alpha=0.5,~r=0.1$ and $s=0.5$ (left), and $s=1.5$ (right). Probability $p_0$ is shown as a blue dashed line. The corresponding $\beta$-cascade is shown in the left panel of Fig. \ref{['fig:pnyr']}.
• Figure 3: In the left panel: quantum measures as obtained from solutions of $\beta$-cascade Eq. (\ref{['eq:EquationSat1']}). In the right panel: quantum measures as obtained from solutions of $\gamma$-cascade Eq. (\ref{['eq:eqsat2']}).
• Figure 4: Entropy (left panel) and purity (right panel) obtained from the $\gamma$-cascade (solid lines) vs. data. Parameters of the $\gamma$-cascade were obtained by minimizing the $\chi^2$ for entropy (see text). Purity is therefore a prediction.