Evaluation of the $E2/M1$ ratio in the $N\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1232)$ transition from the $\stackrel{P\vec}{\ensuremath{\gamma}}\stackrel{P\vec}{p}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{0}$ reaction

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Evaluation of the $E 2 / M 1$ ratio in the $N \to Δ (1232)$ transition from the $\vec{γ} \vec{p} \to p π^{0}$ reaction

E. Mornacchi et al. (A2 Collaboration at MAMI)

Phys. Rev. C 109, 055201 – Published 6 May 2024

Abstract

A new data set for the helicity-dependent differential cross section of the single-meson photoproduction reaction $γ p \to p π^{0}$ was obtained for the photon energy interval 150–400 MeV. The experiment was performed at the A2 tagged photon facility of the Mainz Microtron MAMI using a circularly polarized photon beam and a longitudinally polarized proton target. The reaction products were detected with the large-acceptance Crystal Ball and TAPS calorimeters covering 97% of the full solid angle. These new results, obtained with a fine energy and polar angle binning, greatly increase both the existing quantity and quality of the data available for this observable. A moment analysis, based on a finite expansion in Legendre polynomials, was applied to these data by using a bootstrap-based fitting method to correctly account for their systematic uncertainties. From the resulting decomposition of the differential cross sections, the $E 2 / M 1$ ratio for the $N \to Δ (1232)$ transition was determined to be $[- 2.38 \pm 0.16 (stat . + sys .) \pm 0.10 (model)] %$ . Combining this value with previous results also allowed us to evaluate the most precise available estimate of the $E 2 / M 1$ ratio to be used for all further reference and model comparisons.