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 by longitudinally polarized virtual photons in deep-inelastic scattering. Upon tracing over the unresolved gluon, the reduced spin density matrix is block diagonal in the mirror parity of the production plane and is governed by two coefficients: a parity-odd normal-spin flip, which reduces the normal-axis correlation, and a parity-even stochastic rotation of the spin-correlation plane about its normal, which suppresses the in-plane spin coherences while leaving the normal-axis correlation unchanged. From the complete tree-level next-to-soft amplitude with the exact color-octet structure we derive both coefficients, together with the trace and antisymmetric in-plane terms, in closed form. The parity-odd coefficient is the larger one, by a factor of at least $3.5$, and grows as the inverse square of the heavy-quark transverse momentum. We estimate the resulting reduction of concurrence and Bell-CHSH violation, and propose an infrared-safe, radiation-binned EIC observable, formed at fixed Born kinematics after longitudinal-transverse separation, which isolates the two channels. We estimate its size, including multiple wide-angle emissions in an independent-emission model, the conditions under which detector and kinematic effects cancel, and the statistics required. The latter, however, exceed the yield of exclusive heavy-baryon pairs at nominal EIC luminosity by several orders of magnitude, makes the observable elusive for the measurement accessible in that channel.