Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models

Krzysztof Kutak, Sándor Lökös

TL;DR

The paper investigates the entropy of hadronic final states in the high-energy limit using QCD dipole cascade models. It introduces the observable $S(\ln \langle n \rangle)$ and compares two models—the 1D Mueller dipole model and a generalized conformal-dipole model—by extracting $S_h(\ln \langle n \rangle)$ from measured multiplicity distributions in $p+p$ collisions and fitting model parameters. The main finding is that the generalized model with conformal weight $h \approx 0.92$ describes the data significantly better than the 1D model, predicting larger mean multiplicities and entropies, consistent with initial-state entropy considerations and suggesting beyond-BFKL/DGLAP dynamics and vacuum contributions. This supports the maximal entropy/initial-state entanglement conjecture and motivates including recombination/saturation effects and pursuing higher-precision, wide-rapidity measurements in future experiments such as an Electron-Ion Collider.

Abstract

We investigate and compare QCD dipole cascade models, the 1D Mueller dipole model, its high energy limit and its generalization that follows from studies of 1D systems with conformal symmetry. To address the ambiguity stemming from different definitions of the rapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, $S(\ln\langle n \rangle)$, as a universal observable. From the solutions of the models, we calculate both the entropy and the average charged particle multiplicity and compare to data measured in proton-proton collisions. We obtained these quantities directly from the measured multiplicity distributions and determine the model parameters via fits. We find that the generalized dipole model provides a significantly better description of the data than the 1D Mueller model.

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models

TL;DR

The paper investigates the entropy of hadronic final states in the high-energy limit using QCD dipole cascade models. It introduces the observable and compares two models—the 1D Mueller dipole model and a generalized conformal-dipole model—by extracting from measured multiplicity distributions in collisions and fitting model parameters. The main finding is that the generalized model with conformal weight describes the data significantly better than the 1D model, predicting larger mean multiplicities and entropies, consistent with initial-state entropy considerations and suggesting beyond-BFKL/DGLAP dynamics and vacuum contributions. This supports the maximal entropy/initial-state entanglement conjecture and motivates including recombination/saturation effects and pursuing higher-precision, wide-rapidity measurements in future experiments such as an Electron-Ion Collider.

Abstract

We investigate and compare QCD dipole cascade models, the 1D Mueller dipole model, its high energy limit and its generalization that follows from studies of 1D systems with conformal symmetry. To address the ambiguity stemming from different definitions of the rapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, , as a universal observable. From the solutions of the models, we calculate both the entropy and the average charged particle multiplicity and compare to data measured in proton-proton collisions. We obtained these quantities directly from the measured multiplicity distributions and determine the model parameters via fits. We find that the generalized dipole model provides a significantly better description of the data than the 1D Mueller model.

Paper Structure

This paper contains 10 sections, 19 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Dipole cascade models
  3. 1D Mueller dipole model
  4. Generalized Mueller dipole model
  5. Comparisons of the models
  6. Data and fit description
  7. Data comparison
  8. Conclusions and discussion
  9. Rescaling the general solution
  10. Entropy scaling in proton-proton collisions

Figures (4)

  • Figure 1: The $P_n$ distributions of the 1D Mueller model and the generalized model for different rapidities. The parameters were set to the fitted values given in Tab. \ref{['tab:CK_data_comparison']}.
  • Figure 2: The log of mean multiplicity as the function of rapidity calculated from the 1D Mueller model and he generalized model. The parameters were set to the fitted values given in Tab. \ref{['tab:CK_data_comparison']}.
  • Figure 3: The entropy as the function of rapidity calculated from the 1D Mueller model and he generalized model. The parameters were set to the fitted values given in Tab. \ref{['tab:CK_data_comparison']}.
  • Figure 4: The 1D Mueller model underestimates the entropy in the low average multiplicity region, asymptotically approaches the universal limit discussed around Eq. \ref{['eq:universal']}. The generalized model have similar asymptotics, but is able to describe the data in the low $\ln\langle n \rangle$ region. The fit parameters are given in Tab. \ref{['tab:CK_data_comparison']}.