The polarized cross-section ratio ${\sigma }_{L{T}^{\prime }}/{\sigma }_0$ from hard exclusive ${\pi }^{-}{\mathrm{\Delta }}^{++}$ electroproduction off an unpolarized hydrogen target has been extracted based on beam-spin asymmetry measurements using a $10.2\mathrm{GeV}/10.6\mathrm{GeV}$ incident electron beam and the CLAS12 spectrometer at Jefferson Lab. The study, which provides the first observation of this channel in the deep-inelastic regime, focuses on very forward-pion kinematics in the valence regime, and photon virtualities ranging from $1.5{\mathrm{GeV}}^2$ up to $7{\mathrm{GeV}}^2$. The reaction provides a novel access to the $d$-quark content of the nucleon and to $p\to {\mathrm{\Delta }}^{++}$ transition generalized parton distributions. A comparison to existing results for hard exclusive ${\pi }^{+}n$ and ${\pi }^{0}p$ electroproduction is provided, which shows a clear impact of the excitation mechanism, encoded in transition generalized parton distributions, on the asymmetry.

• Received 21 March 2023
• Revised 22 May 2023
• Accepted 20 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.021901

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Published by the American Physical Society