Reciprocal symmetry and KNO scaling violation in proton-proton collisions

Abstract

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 probability and identify a reciprocal symmetry $z\leftrightarrow 1/z$ in the KNO violating corrections observed in the ATLAS and CMS data at $\sqrt{s}=7,\,8,\,13$~TeV. The symmetry imposes a local constraint on the multiplicity distribution at $n=\langle n\rangle$, namely $P'(\langle n\rangle)=-P(\langle n\rangle)/\langle n\rangle$, which we verify directly in the data. We use this constraint to extract the entanglement entropy from the well-measured region $n\simeq\langle n\rangle$, avoiding the large uncertainties associated with the distribution tail.