pith:CZKNPGFP

We extract the deviations from the leading exponential behavior of the KNO scaled probability and identify a reciprocal symmetry z↔1/z in the KNO violating corrections observed in the ATLAS and CMS data at √s=7,8,13 TeV. The symmetry imposes a local constraint on the multiplicity distribution at n=⟨n⟩, namely P'(⟨n⟩)=−P(⟨n⟩)/⟨n⟩, which we verify directly in the data. We use this constraint to extract the entanglement entropy from the well-measured region n≃⟨n⟩, avoiding the large uncertainties associated with the distribution tail.

That the observed z↔1/z symmetry in the KNO-violating corrections is a genuine physical feature of the multiplicity distribution rather than an artifact of the specific data sets, binning choices, or analysis procedure, and that the resulting local constraint at n=⟨n⟩ is sufficient by itself to determine the entanglement entropy without further model assumptions about the global shape of P(n).

A z ↔ 1/z reciprocal symmetry is found in KNO scaling violations in pp collisions, imposing the constraint P'(⟨n⟩) = −P(⟨n⟩)/⟨n⟩ that enables entanglement entropy extraction from the well-measured multiplicity region.