The feasibility of observing true tauonium, the bound state of two tau leptons, ${\mathcal{T}}_0\equiv ({\tau }^{+}{\tau }^{-}{)}_0$, via photon-photon collisions at $e^{+}{e}^{-}$ colliders and at the LHC, is studied. The production cross sections of the process $\gamma \gamma \to {\mathcal{T}}_0\to \gamma \gamma$—as well as those of all relevant backgrounds: spin-0 and 2 charmonium resonances decaying to diphotons, and light-by-light scattering—are computed in the equivalent photon approximation for $e^{+}{e}^{-}$ collisions at BES III ($\sqrt{s}=3.8\mathrm{GeV}$), Belle II ($\sqrt{s}=10.6\mathrm{GeV}$), and FCC-ee ($\sqrt{s}=91.2\mathrm{GeV}$), as well as for ultraperipheral p-p, p-Pb, and Pb-Pb collisions at the LHC. Despite small ${\mathcal{T}}_0$ production cross sections and a final state swamped by decays from overlapping pseudoscalar and tensor charmonium states—the ${\chi }_{\mathrm{c}2}$, ${\eta }_{\mathrm{c}}(2\mathrm{S})$, and ${\chi }_{\mathrm{c}0}$ states have masses only 2.5, 84, and 139 MeV away, respectively, from the ${\mathcal{T}}_0$ peak—evidence and observation of the ground state of the heaviest leptonium appears feasible at Belle II and FCC-ee, respectively, with in-situ high-precision measurements of the irreducible backgrounds.

• Received 18 March 2022
• Accepted 22 April 2022
• Corrected 31 May 2022

DOI:https://doi.org/10.1103/PhysRevD.105.093008

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Published by the American Physical Society