Probing Quantum Numbers and Decay Branching Ratios of Exotic States via Entanglement-Enabled Spin Interference

Abstract

Ultra-peripheral heavy-ion collisions (UPCs) coherently photo-produce vector mesons through two spatially separated and quantum-mechanically indistinguishable production sites, whose separation far exceeds the lifetime of the created resonance. The superposition of these amplitudes generates production-site entanglement, observed experimentally as entanglement-enabled spin-interference patterns in the angular distributions of the decay products. We show that these interference signatures provide a sensitive probe of spin-alignment transfer in hadronic decay chains, enabling intermediate-state quantum numbers and relative branching ratios to be measured from observed angular modulations. Using the decay $\rho(1450)\!\rightarrow\!\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ as example, we simulate the $a_{1}(1260)\pi$, $h_{1}(1170)\pi$, $\rho(\pi\pi)_{S}$, and $\pi(1300)\pi$ channels and demonstrate that each produces a distinct azimuthal $\cos 2\phi$ modulation. The $\pi(1300)\pi$ mode shows a uniquely separated response, allowing its branching fraction to be extracted directly. These results establish production-site entanglement in UPCs as a selective tool for hadron spectroscopy, particularly for broad or overlapping resonances that are otherwise difficult to disentangle.