Related papers: KNO scaling 30 years later
The normalised order-q moments of primarily charged-particle multiplicity distributions are studied for KNO scaling investigation in pp collisions as deduced from the results of the ATLAS at the LHC. The normalised moments for the LHC and…
A generalization of the Polyakov-Koba-Nielsen-Olesen scaling law of the multiplicity distributions P(n,s) is developed. It states that a suitable change in the normalization point of P(n,s) compensated by a rescaling can restore data…
It is shown that there is a second properly normalized KNO scaling function, $nP_n(n/\bar n)=\varphi(z)$, which has certain advantages in the analysis of KNO scaling. First, the $nP_n$ are not influenced by the statistical and systematic…
We analyze the charged particle multiplicity distributions in $p-p$ collisions and discuss the violation of the Koba--Nielsen--Olesen (KNO) scaling. We extract the deviations from the leading exponential behavior of the KNO scaled…
Multiplicity fluctuations at midrapidity in p+p collisions at high energies are described by a negative binomial distribution and exhibit approximate Koba-Nielsen-Olesen (KNO) scaling. We find that these KNO fluctuations are important also…
The single-particle inclusive fragmentation function and the particle multiplicity are observables of fundamental importance in studying properties of quantum chromodynamics at colliders. It is well-known that at high energies, the…
Multiplicity distributions and their scaling behaviour for various types of secondary charged particles produced in 28Si-nucleus collisions at 4.5A and 14.5A GeV are investigated. The validity of KNO scaling and its generalized form has…
What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…
We analyze various data of multiplicity distributions by means of the Modified Negative Binomial Distribution (MNBD) and its KNO scaling function, since this MNBD explains the oscillating behavior of the cumulant moment observed in e^+e^-…
We analyze the experimental data of $\mathtt{p}\mathtt{-}\mathtt{p}$ collisions by the ATLAS and confront it with the AGK model developed by two of the authors, the Kharzeev-Levin~(KL) model and the simple exponential behavior for the Koba,…
The Koba-Nielsen-Olesen (KNO) scaling of hadron multiplicity distributions, empirically confirmed to hold approximately in $e^+e^-$ collisions and Deep Inelastic Scattering, has been observed to be violated in hadron-hadron collisions. In…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
We investigate the KNO scaling function of the modified negative binomial distribution (MNBD), because this MNBD can explain the oscillating behaviors of the cumulant moment observed in $e^+e^-$ annihilations and in hadronic collisions. By…
In this work we study the multiplicity distributions (MDs) of charged particles within jets in proton-proton collisions, which were measured by the ATLAS collaboration in 2011, 2016 and 2019. The first data set refers to jets with lower…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
From a recently found family of analytic, finite and accelerating 1+1-dimensional solutions to perfect fluid relativistic hydrodynamics, we derive simple and powerful formulae to describe the rapidity and pseudorapidity density…
Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…
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 charged particles multiplicity distribution in the KNO form is discussed in processes of $e^+e^-$ annihilation at energies $\sqrt{s}$ 14 -- 206.2 GeV. The experimental data are compared to data, obtained with Monte Carlo simulation in…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…