Soft-Radiation-Induced Decoherence of Heavy-Quark Spin Entanglement at the Electron-Ion Collider

Abstract

Using the soft-gluon theorem, we identify a soft-recoil mechanism by which unresolved gluon radiation induces decoherence in the spin correlations of heavy quark-antiquark pairs produced in deep-inelastic scattering. We show the eikonal soft contribution preserves the Born spin structure, whereas the subleading soft term generates stochastic recoil-induced rotations of the spin-correlation plane. Upon tracing over the unresolved gluon, these rotations produce an effective dephasing channel: the normal-axis correlation remains unchanged at this order, while the in-plane spin coherences are suppressed. We estimate the resulting reduction of concurrence and Bell-CHSH violation, and propose a radiation-binned EIC observable based on the ratio of in-plane to normal spin correlations. This observable isolates the characteristic anisotropic suppression predicted by the soft-recoil mechanism and provides a measurable handle on radiation-induced spin decoherence of an entangled quark-antiquark pair produced in a deep-inelastic scattering process.