Universality of scaling entropy in charged hadron multiplicity distributions at the LHC

TL;DR

The paper addresses how charged-hadron multiplicity distributions in $pp$ collisions exhibit entropy growth that mirrors small-$x$ gluon dynamics, suggesting a universal scaling law. It constructs a theoretical link between initial-state parton entropy $S^{\text{parton}}(x)=C+\lambda\log(1/x)$ and the hadron-multiplicity entropy $S^{\text{mult}}=-\sum_N P(N)\log P(N)$, using a diffusion-type scaling for $P(N)$ and a Tsallis-based framework; it then tests this against CMS, ATLAS, and ALICE data, removing the soft component to isolate the semi-hard regime. The results show a universal $\lambda$ consistent with DIS measurements ($\lambda_{\text{DIS}}=0.322\pm0.007$) across LHC datasets, along with diffusion scaling in high-multiplicity events and systematic KNO scaling violations in the tails. This supports a picture where initial-state, small-$x$ dynamics govern both entropy growth and multiplicity fluctuations, with implications for $pA$, heavy-ion, and future Electron–Ion Collider studies.

Abstract

In this work, we investigate the scaling behavior of the entropy associated with the charged hadron multiplicity distribution P(N) in proton-proton collisions at the LHC. We show that the growth of this entropic indicator as a function of the Bjorken x variable exhibits a universal behavior, consistent with observations from deep inelastic scattering (DIS). This universality suggests that the entropy scaling is a property of the initial state and reflects the diffusive nature of gluon dynamics at small x. Furthermore, we demonstrate that high-multiplicity events are not accurately described by traditional KNO scaling and require a more precise description based on a diffusion scaling framework. This new scaling emerges naturally from the universal growth of partonic entropy and offers a deeper insight into the dynamics of particle production in high-energy hadronic collisions.

Figures (7)

• Figure 1: Multiplicity data (full box) and interpolated values (unfilled) at some $N$ bins. The vertical line shows the cut imposed of $N_{min} = 10$.
• Figure 2: Left side: Experimental entropy (color bars) compared with scaling entropy line as a function of $\log(1/x)$ in each rapidity bin when available. The full lines correspond to DIS entropy determined from H1 data. Right: resulting $\lambda$ compared with blue interval corresponding from H1 fit uncertainty.
• Figure 3: The same as Fig. \ref{['fig:entropy1']} for the Sets 3 and 4.
• Figure 4: Entropy as a function of the dispersion to each data set. The full line is a linear global fit.
• Figure 5: Each data set scaling line at different rapidities.