Observing true tauonium via two-photon fusion at $e^+e^-$ and hadron colliders

TL;DR

This paper explores the potential to observe true tauonium, a bound state of tau leptons, through photon-photon collisions at various colliders, analyzing production rates and background challenges to assess feasibility.

Contribution

It provides the first detailed calculations of tauonium production cross sections and background processes at multiple colliders, evaluating the experimental prospects for observing this elusive state.

Findings

Tauonium production cross sections are small but potentially detectable.

Backgrounds from charmonium states complicate detection but can be managed.

Observation of tauonium is feasible at Belle II and FCC-ee with high-precision measurements.

Abstract

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 ($\sqrt{s} = 3.8$ GeV), Belle II ($\sqrt{s} = 10.6$ GeV), and FCC-ee ($\sqrt{s} = 91.2$ 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 $\mathrm{\chi_{c2}}$, $\mathrm{\eta_{c}(2S)}$, and $\mathrm{\chi_{c0}}$ 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.