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Normalized radial flight distance distributions for the $\TM \to e^+ e^-$ signal (blue solid) with dissociation, (blue dotted) without dissociation, and (red dashed) the $e^+ e^-$ background from $B$-hadron decays.

The required integrated luminosity for a $5\,\sig$ discovery of \TM as function of the final reconstruction efficiency, $\varepsilon_f$ for the proposed (blue) $e^+ e^-$ and (red) $e^+ e^- \gamma$ searches.

The differential cross sections with respect to the $e^+e^-$ invariant mass for the expected \TM signal and combinatorial background at LHCb, assuming the normalization in Tab.~\ref{tab:eeN} for case (i) and (ii). Global efficiencies of 20\% and 6\% are assumed to reconstruct the \TM and \TM plus photon candidates, respectively. In these conditions, a $5\,\sigma$ observation would be possible with an integrated luminosity of 15\,fb$^{-1}$ in case (i) and of 30\,fb$^{-1}$ in case (ii). The invariant mass resolution of the signal is described in the text. The shift observed in the central position of the signal peak, due to the lack of reconstructed bremsstrahlung from the electrons, is compatible with that of Ref.~\cite{MarinBenito:2193358}. For the combinatorial background, the resulting invariant mass distribution is obtained from simulation.

The differential cross sections with respect to the $e^+e^-$ invariant mass for the expected \TM signal and combinatorial background at LHCb, assuming the normalization in Tab.~\ref{tab:eeN} for case (i) and (ii). Global efficiencies of 20\% and 6\% are assumed to reconstruct the \TM and \TM plus photon candidates, respectively. In these conditions, a $5\,\sigma$ observation would be possible with an integrated luminosity of 15\,fb$^{-1}$ in case (i) and of 30\,fb$^{-1}$ in case (ii). The invariant mass resolution of the signal is described in the text. The shift observed in the central position of the signal peak, due to the lack of reconstructed bremsstrahlung from the electrons, is compatible with that of Ref.~\cite{MarinBenito:2193358}. For the combinatorial background, the resulting invariant mass distribution is obtained from simulation.

\TM branching ratio to BSM final states in Eqs.~\eqref{eq:BRgammaS}--\eqref{eq:BRgammaA} which are allowed by $(g-2)_\mu$ at the $5\,\sigma$.

Dark photon parameter space in dark photon mass and kinetic mixing with (gray) previous limits and future reach from (magenta) Belle II, (purple) FASER, (cyan) HPS, and (green/yellow) LHCb. \TM corresponds to the marked point, using Eqs.~\eqref{eq:mTM} and \eqref{eq:epsTM}.