New determination of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>η</mml:mi></mml:math>transition form factor in the Dalitz decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>η</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:mrow></mml:math>with the Crystal Ball/TAPS detectors at the Mainz Microtron

The Dalitz decay $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ has been measured in the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\eta}p$ reaction with the Crystal Ball and TAPS multiphoton spectrometers, together with the photon-tagging facility at the Mainz Microtron MAMI. The experimental statistic used in this work is one order of magnitude greater than in any previous measurement of $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$. The value obtained for the slope parameter ${\ensuremath{\Lambda}}^{\ensuremath{-}2}$ of the $\ensuremath{\eta}$ transition form factor, ${\ensuremath{\Lambda}}^{\ensuremath{-}2}=(1.95\ifmmode\pm\else\textpm\fi{}0.{15}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.{10}_{\mathrm{syst}})$ GeV${}^{\ensuremath{-}2}$, is in good agreement with recent measurements conducted in $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\gamma}$ decays, as well as with recent form-factor calculations. The uncertainty obtained in the value of ${\ensuremath{\Lambda}}^{\ensuremath{-}2}$ is lower compared to results from previous measurements of the $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ decay.