Deep inelastic scattering as a probe of entanglement: the complete QCD dipole cascade

Abstract:We study entanglement entropy in Deep Inelastic Scattering (DIS) using the dipole formulation of the high-energy limit of QCD. We argue that a reduced density matrix arises in low $x$ DIS due to a trace over unobserved color degrees of freedom and we obtain entanglement entropy in terms of dipole multiplicities, directly from the von Neumann entropy. %In the present study we explicitly construct a density matrix representing the entangled state of the photon and proton and perform a trace over unobserved degrees of freedom. Dipole multiplicities are obtained from a solution to low $x$ evolution equations, which we solve numerically. Unlike previous studies, we take into account both transverse-size and azimuthal-angle dependence in the dipole evolution kernel. We study both the exact solution of the equation as well as its double leading-logarithmic approximation (DLLA). We find that for the same initial dipole size, the DLLA solution generates a larger entropy. %We interpret this as information loss due to erasing data on daughter dipole sizes. Finally, we calculate the dipole multiplicities and entanglement entropy and compare our results to the Shannon entropy of hadron multiplicities, as measured by the H1 collaboration.

arXiv:2607.18464 [hep-ph]

(or arXiv:2607.18464v1 [hep-ph] for this version)

https://doi.org/10.48550/arXiv.2607.18464 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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