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

We investigate and compare quantum chromodynamics (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, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>S</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>ln</a:mi> <a:mo stretchy="false">⟨</a:mo> <a:mi>n</a:mi> <a:mo stretchy="false">⟩</a:mo> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> , 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.