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

The feasibility of observing true tauonium, the bound state of two tau leptons, <math display="inline"><msub><mi mathvariant="script">T</mi><mn>0</mn></msub><mo>≡</mo><mo stretchy="false">(</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>-</mo></msup><msub><mo stretchy="false">)</mo><mn>0</mn></msub></math>, via photon-photon collisions at <math display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></math> colliders and at the LHC, is studied. The production cross sections of the process <math display="inline"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msub><mi mathvariant="script">T</mi><mn>0</mn></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></math>—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 <math display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></math> collisions at BES III (<math display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>3.8</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>), Belle II (<math display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>10.6</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>), and FCC-ee (<math display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>91.2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>), as well as for ultraperipheral p-p, p-Pb, and Pb-Pb collisions at the LHC. Despite small <math display="inline"><msub><mi mathvariant="script">T</mi><mn>0</mn></msub></math> production cross sections and a final state swamped by decays from overlapping pseudoscalar and tensor charmonium states—the <math display="inline"><msub><mi>χ</mi><mrow><mi mathvariant="normal">c</mi><mn>2</mn></mrow></msub></math>, <math display="inline"><msub><mi>η</mi><mi mathvariant="normal">c</mi></msub><mo stretchy="false">(</mo><mn>2</mn><mi mathvariant="normal">S</mi><mo stretchy="false">)</mo></math>, and <math display="inline"><msub><mi>χ</mi><mrow><mi mathvariant="normal">c</mi><mn>0</mn></mrow></msub></math> states have masses only 2.5, 84, and 139 MeV away, respectively, from the <math display="inline"><msub><mi mathvariant="script">T</mi><mn>0</mn></msub></math> 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.