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

Abstract

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.

Figures (3)

• Figure 1: (a) Schematic illustration of the coordinate system used in this paper. The definition of the $x$, $y$, and $z$ axes is described in the text. $\epsilon$ is the polarization vector. $\Phi$ is the azimuthal angle between the polarization vector and the impact parameter. (b) Feynman diagrams for the Drell-S${\rm\ddot{o}ding}$ mechanism. The incident photon fluctuates into a virtual $\pi^+\pi^-$ pair, which subsequently undergoes elastic scattering off the nuclear target. The photon momentum is denoted by $k$, and the $\pi^\pm$ momenta by $q^\pm$. The proton momentum before (after) scattering is $p$ ($p'$).
• Figure 2: Comparison between the calculated $\pi^+\pi^-$ invariant mass spectrum and experimental data. The left panel is the result for Pb+Pb collisions at 2.76 TeV and the right panel is the result for Au+Au collisions at 200 GeV. The blue solid curve represents the calculated Drell-S${\rm\ddot{o}ding}$ contribution, while the green dashed line indicates the resonant $\rho^0$ contribution. The red curve shows the total contribution, which provides excellent agreement with experimental data (black points).
• Figure 3: The second-order azimuthal modulation $2\langle \cos 2\phi \rangle$ of DS $\pi^+\pi^-$ pairs as a function of transverse momentum in ultra-peripheral heavy-ion collisions, arising from the interference of linearly polarized photoproduction amplitudes.