Prospects for ditauonium discovery at colliders

The feasibility of observing ditauonium, the bound state of two tau leptons, at <math altimg="si1.svg"><msup><mrow><mi>e</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup></math> colliders (BES III at <math altimg="si2.svg"><msqrt><mrow><mi>s</mi></mrow></msqrt><mspace width="0.25em"/><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mspace width="0.25em"/><mn>3.78</mn></math> GeV, Belle II at <math altimg="si3.svg"><msqrt><mrow><mi>s</mi></mrow></msqrt><mspace width="0.25em"/><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mspace width="0.25em"/><mn>10.6</mn></math> GeV, a future super tau-charm factory (STCF) at <math altimg="si187.svg"><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>≈</mo><mn>2</mn><msub><mrow><mi>m</mi></mrow><mrow><mi>τ</mi></mrow></msub></math>, and the FCC-ee at <math altimg="si5.svg"><msqrt><mrow><mi>s</mi></mrow></msqrt><mspace width="0.25em"/><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mspace width="0.25em"/><mn>91.2</mn></math> GeV) as well as in hadronic and photon-photon collisions at the LHC, is studied. Cross sections and expected yields for spin-0 para- (<math altimg="si21.svg"><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mn>0</mn></mrow></msub></math>) and spin-1 ortho- (<math altimg="si7.svg"><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mn>1</mn></mrow></msub></math>) ditauonium are presented for nine different production and decay processes. Para-ditauonium can be observed at the FCC-ee via photon fusion in its diphoton decay (<math altimg="si8.svg"><mi>γ</mi><mi>γ</mi><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></math>). Ortho-ditauonium can be observed at STCF via <math altimg="si9.svg"><msup><mrow><mi>e</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup></math>, where a threshold scan with monochromatized beams can also provide a very precise extraction of the tau lepton mass with <math altimg="si10.svg"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>25</mn></math> keV) uncertainty. Observing pp <math altimg="si11.svg"><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mo stretchy="false">)</mo><mo linebreak="goodbreak" linebreakstyle="after">+</mo><mi>X</mi></math> at the LHC is possible by identifying its displaced vertex with a good control of the combinatorial dimuon background. In addition, we compute the rare decay branching fractions of ditauonium into quarkonium plus a photon.