On the Inversion of High Energy Proton

TL;DR

This paper introduces a novel inverse algorithm combining entropy minimization, Fourier transforms, and bootstrap methods to invert a nonlinear integral equation, providing new insights into high energy QCD phenomena from LHC data.

Contribution

The paper presents a new inverse algorithm for the K-fold stochastic autoconvolution integral equation, enabling analysis of high energy proton data with finite statistics.

Findings

Revealed a strong double peak structure in proton multiplicity data

Applied the algorithm to LHC data at various energies and pseudorapidities

Demonstrated the algorithm's ability to uncover features barely visible without inversion

Abstract

Inversion of the K-fold stochastic autoconvolution integral equation is an elementary nonlinear problem, yet there are no de facto methods to solve it with finite statistics. To fix this problem, we introduce a novel inverse algorithm based on a combination of minimization of relative entropy, the Fast Fourier Transform and a recursive version of Efron's bootstrap. This gives us power to obtain new perspectives on non-perturbative high energy QCD, such as probing the ab initio principles underlying the approximately negative binomial distributions of observed charged particle final state multiplicities, related to multiparton interactions, the fluctuating structure and profile of proton and diffraction. As a proof-of-concept, we apply the algorithm to ALICE proton-proton charged particle multiplicity measurements done at different center-of-mass energies and fiducial pseudorapidity intervals at the LHC, available on HEPData. A strong double peak structure emerges from the inversion, barely visible without it.