Interference-induced entanglement in an effectively zero-lifetime particle pair

Quantum entanglement in high-energy collisions is often obscured by finite lifetimes, dynamical evolution, and final-state interactions, complicating the identification of genuinely quantum correlations. Ultra-peripheral heavy-ion collisions provide a clean benchmark via the Drell-S${\rm\ddot{o}ding}$ production of nonresonant pion pair, realizing an effectively zero-lifetime particle pair whose quantum correlations are fixed at production and remain robust against subsequent elastic scattering. The coherent superposition of photoproduction amplitudes from two indistinguishable nuclei encodes the linear polarization of quasi-real photons in the orbital motion of the pair, generating a nonfactorizable two-particle quantum state. This entanglement leaves a direct experimental imprint: a characteristic second-harmonic azimuthal modulation in momentum space arising from spin-dependent interference between the two sources. In this paper, we establish a quantitative framework for Drell-S${\rm\ddot{o}ding}$ pion-pair production in relativistic heavy-ion collisions and predict the magnitude and transverse-momentum dependence of the entanglement-induced azimuthal asymmetry. Our results provide experimentally accessible signatures of interference-induced entanglement and a controlled test of quantum coherence in relativistic environments.