Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ω</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><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:mrow></mml:math> and <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> Dalitz decays with the A2 setup at the Mainz Microtron

Abstract

The Dalitz decays $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ and $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{e}^{\ensuremath{-}}$ have been measured in the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\eta}p$ and $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\omega}p$ reactions, respectively, with the A2 tagged-photon facility at the Mainz Microtron. The value obtained for the slope parameter of the electromagnetic transition form factor of $\ensuremath{\eta}, {\mathrm{\ensuremath{\Lambda}}}_{\ensuremath{\eta}}^{\ensuremath{-}2}=(1.97\ifmmode\pm\else\textpm\fi{}0.{11}_{\mathrm{tot}})\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{\ensuremath{-}2}$, is in good agreement with previous measurements of the $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\gamma}$ decays. The uncertainty obtained in the value of ${\mathrm{\ensuremath{\Lambda}}}_{\ensuremath{\eta}}^{\ensuremath{-}2}$ is lower than in previous results based on the $\ensuremath{\eta}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ decay. The value obtained for the $\ensuremath{\omega}$ slope parameter, ${\mathrm{\ensuremath{\Lambda}}}_{\ensuremath{\omega}{\ensuremath{\pi}}^{0}}^{\ensuremath{-}2}=(1.99\ifmmode\pm\else\textpm\fi{}0.{21}_{\mathrm{tot}})\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{\ensuremath{-}2}$, is somewhat lower than previous measurements based on $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, but the results for the $\ensuremath{\omega}$ transition form factor are in better agreement with theoretical calculations, compared to earlier experiments.