Deep inelastic scattering as a probe of entanglement: confronting experimental data

Understand

Parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton.

• For very small $x$, the proton becomes a maximally entangled state.
• This approach leads to a simple relation $S = \ln N $ between the average number $N$ of color-singlet dipoles in the proton wave function and the entropy of the produced hadronic state $S$.
• At small $x$, the multiplicity of dipoles is given by the gluon structure function, $N = x G(x,Q^2)$.