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

In this work, we investigate the scaling behavior of the entropy associated with the charged hadron multiplicity distribution <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>P</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math> in proton-proton collisions at the LHC. We show that the growth of this entropic indicator as a function of the Bjorken-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>x</e:mi></e:math> variable exhibits universal behavior, consistent with observations from deep inelastic scattering. This universality suggests that the entropy scaling is a property of the initial state and reflects the diffusive nature of gluon dynamics at small <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>x</g:mi></g:math>. Furthermore, we demonstrate that high-multiplicity events are not accurately described by traditional Koba-Nielsen-Olesen 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 deeper insight into the dynamics of particle production in high-energy hadronic collisions.