Page Entropy of Proton System in Deep-Inelastic-Scattering at Small-$x$

TL;DR

This paper applies Page's black hole entropy theory to proton systems in deep-inelastic scattering, revealing a novel entanglement entropy relation that aligns with experimental data at small Bjorken x.

Contribution

It introduces a new approach by using black hole entropy concepts to analyze proton entanglement entropy in deep-inelastic scattering.

Findings

Proton entanglement entropy approximates to S = ln m - 1/2.

Calculated entropy agrees with recent H1 collaboration measurements.

Entropy depends on parton density at small Bjorken x.

Abstract

The partons model reveals the dynamical structure of nucleons (protons and neutrons). Studies related to thermodynamic quantities of nucleons are interesting and topical questions. In this work, for the first time we apply Page's theory of the studies of black hole to investigate the entropy of proton system. Inspired by the quantum entanglement entropy in black hole information theories, we establish the proton entanglement with the similar way. Based our calculations, the proton entanglement entropy has the approximate form $S = \ln m -1/2$, where $m$ represents the partons density of proton (mainly gluon and sea quark contributions) at small Bjorken $x$. Our calculations using Page's theory are well in agreement with the recent DIS measurements from H1 collaboration.