Probing Yoctosecond Quantum Dynamics in Toponium Formation at Colliders

The formation of toponium, a bound state of top and anti-top quarks, provides an unprecedented system for investigating quantum state dynamics at ultrashort timescales. We explore two distinct phenomenological descriptions of this process: a 'wavelike' scenario emphasizing the role of quantum superposition at creation, and a 'particlelike' scenario where a finite formation time is governed by relativistic causality. Both descriptions are compatible with the principles of relativistic quantum field theory. We propose to distinguish these scenarios by exploiting the top quark's intrinsic lifetime ($\tau_t \sim 5.02 \times 10^{-25}$\,s) as a quantum chronometer. We simulate the cross-section ratio $R_b = \sigma(e^+e^- \to b\bar{b})/\sum_q \sigma(e^+e^- \to q\bar{q})$ ($q = u,d,s,c,b$) near $\sqrt{s} = 343$\,GeV at future lepton colliders (CEPC/FCC-ee). These distinct scenarios yield observable $R_b$ profiles, enabling $>5\sigma$ discrimination with 1500\,fb$^{-1}$ of data. Preliminary LHC data provide independent $2$--$3\sigma$ support. This framework establishes a collider-based method to explore time-dependent quantum phenomena in particle production with yoctosecond ($10^{-24}$\,s) resolution.