The production of a pair of $\tau$ leptons via photon-photon fusion, $\gamma\gamma\to\tau\tau$, is observed for the first time in proton-proton collisions, with a significance of 5.3 standard deviations. This observation is based on a data set recorded with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with a pair of $\tau$ leptons produced via photon-photon fusion are selected by requiring them to be back-to-back in the azimuthal direction and to have a minimum number of charged hadrons associated with their production vertex. The $\tau$ leptons are reconstructed in their leptonic and hadronic decay modes. The measured fiducial cross section of $\gamma\gamma\to\tau\tau$ is $\sigma^\text{fid}_\text{obs}$ = 12.4$^{+3.8}_{-3.1}$ fb. Constraints are set on the contributions to the anomalous magnetic moment ($a_\tau$) and electric dipole moments ($d_\tau$) of the $\tau$ lepton originating from potential effects of new physics on the $\gamma\tau\tau$ vertex: $a_\tau$ = 0.0009$_{-0.0031}^{+0.0032}$ and $\lvert d_\tau \rvert$$\lt$ 2.9 $\times$ 10$^{-17}$$e\,$cm (95% confidence level), consistent with the standard model.
Normalized distributions of $N_\mathrm{tracks}^\mathrm{PU}$ in windows of 0.1 cm width along the $z$ axis using a sample of $\mu\mu$ events with $|m_{\mu\mu}-m_\mathrm{Z}|<15\,\mathrm{GeV}$ from the 2017 data set. The windows included here are located at the beamspot center, and one or two beamspot widths ($\sigma \approx 3.5\,\mathrm{cm}$) away from the center. The ratio of beamspot-corrected simulation to data is taken as a residual correction to the simulations. The last bin includes the overflow, and the number of events in each bin are divided by the respective bin width. The distributions are normalized to 1, and the uncertainties in the number of simulated events are statistical only. Similar distributions and corrections are derived independently for the other data-taking periods, and the corrections derived as an event weight can be found in the Supplementary Figures 1-4 for each data-taking period.
Normalized distributions of of the number of reconstructed tracks ($N_\mathrm{tracks}$) in a 0.1 cm wide window in the $z$ direction, centered on the dimuon reconstructed vertex ($|z_\mathrm{tracks}-z_\mathrm{\mu\mu}|<0.05\,\mathrm{cm}$). A sample of $\mu\mu$ events with $|m_{\mu\mu}-m_\mathrm{Z}|<15\,\mathrm{GeV}$ and acoplanarity $A<0.015$ from the 2017 data set are used. The Drell-Yan is split into bins of number of hard-scattering (HS) tracks ($N_\mathrm{tracks}^\mathrm{HS}$).
Distributions of $m_{\mu\mu}$ in the $\mu\mu$ channel of the $N_\mathrm{tracks}=0$ and 1 categories with acoplanarity $A<0.015$, and for the combined 2016-2018 data set. The shape of the inclusive background distribution is estimated from the observed data in the $3\leq N_\mathrm{tracks} \leq7$ sideband, and is rescaled to fit the observed data in $75<N_\mathrm{tracks}<105\,\mathrm{GeV}$.
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