Polarization observables in double neutral pion photoproduction

Abstract

Measurements of target asymmetries and double-polarization observables for the reaction are reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility (Bonn University) using the Bonn frozen-spin butanol ( ${\text{C}}_4{\text{H}}_9$ OH) target, which provided transversely polarized protons. Linearly polarized photons were produced via bremsstrahlung off a diamond crystal. The data cover the photon energy range from to and nearly the complete angular range. The results have been included in the BnGa partial wave analysis. Experimental results and the fit agree very well. Observed systematic differences in the branching ratios for decays of and ${\Delta }^{\ast }$ resonances are attributed to the internal structure of these excited nucleon states. Resonances which can be assigned to SU(6) $\times$ O(3) two-oscillator configurations show larger branching ratios to intermediate states with non-zero intrinsic orbital angular momenta than resonances assigned to one-oscillator configurations.

Fig. 1

Setup of the CBELSA/TAPS experiment

Fig. 2

Distributions of the variables used for the kinematic cuts are shown for on a logarithmic scale. For each of the four cuts (coplanarity, polar angle of the proton, missing mass, and -invariant mass) the spectrum is shown in red after just the time cut (including the side-band subtraction) and in green after all cuts except the one on the variable shown. The invariant -mass contains all combinations and therefore also combinatorial background

Fig. 3

Definition of kinematic variables in the CMS. Details see text

Fig. 4

Confidence level distribution of hydrogen data (blue), butanol data (black) and butanol with carbon data subtracted (red) for the hypothesis . In this plot, only very broad data selection cuts were applied to the data

Fig. 5

Example of the mass distribution of the nearest neighbors. The signal (red) is described by the sum of two Gaussian functions (the narrower one with negative amplitude), the background function (dashed blue) is a second order polynomial. The dip on the pion peak is due to the fact that the fit uses the best combination for the fitted pion. The data is binned here for presentational purposes only. The horizontal bars indicate the (variable) bin width

Fig. 6

Fractional background contribution (in %) depending on beam energy and (left), (center), or (right)

Fig. 7

Fractional background contribution (in %) depending on beam energy and (left), (center), or (right)

Fig. 8

Definition of the relevant angles in the laboratory frame and the reaction frame. Details see text

Fig. 9

Coplanarity spectrum from data taken with the butanol target (black) and with the carbon target (red). The latter already scaled. Events with are shown. The insert shows the same spectrum on a linear axis

Fig. 10

Value of the dilution factor depending on and .

Fig. 11

Example of the predicted target asymmetry $\mathrm{T}$ for two beam energies as a function of or determined from generated Monte Carlo events (red band). The blue band results from taking the acceptance into account. The widths of the bands are given by the statistical uncertainties of the MC event sample

Fig. 12

The target asymmetry $\mathrm{T}$ as a function of beam energy and . The colored lines represent PWA solutions: $2\pi$-MAID in black, BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 13

The target asymmetry $\mathrm{T}$ as a function of beam energy and . The colored lines represent PWA solutions: -MAID in black, BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 14

The target asymmetry ${\mathrm{P}}_y$ as a function of beam energy and . The open symbols make use of the symmetry properties. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 15

The target asymmetry ${\mathrm{P}}_x$ as a function of beam energy and . The open symbols make use of the symmetry properties. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 16

The target asymmetry $\text{T}$ as a function of beam energy and . The colored lines represent PWA solutions: $2\pi$-MAID in black, BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 17

The target asymmetry $\mathrm{T}$ as a function of beam energy and . The colored lines represent PWA solutions: $2\pi$-MAID in black, BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 18

The target asymmetry ${\mathrm{P}}_y$ as a function of beam energy and . The open symbols make use of the symmetry properties. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 19

The target asymmetry ${\mathrm{P}}_x$ as a function of beam energy and . The open symbols make use of the symmetry properties. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 20

The double polarization observables $\tilde{\text{P}}$ and H as a function of beam energy and (left), or and (right). The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 21

The double polarization observables $\tilde{\text{P}}$ and $\mathrm{H}$ as a function of beam energy and (left), or and (right). The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 22

Four-dimensional determination of the target asymmetry ${\mathrm{P}}_y$ as a function of . The is varied within a row, the invariant mass within a column. Only a single energy bin is shown here. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 23

Four-dimensional determination of the target asymmetry ${\mathrm{P}}_x$ as a function of . The is varied within a row, the invariant mass within a column. Only a single energy bin is shown here. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 24

Four-dimensional determination of the target asymmetry ${\mathrm{P}}_y$ as a function of . The is varied within a row, the invariant mass within a column. Only a single energy bin is shown here. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 25

Four-dimensional determination of the target asymmetry ${\mathrm{P}}_x$ as a function of . The is varied within a row, the invariant mass within a column. Only a single energy bin is shown here. The colored lines represent PWA solutions: BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 26

Partially integrated target asymmetry for the same energy bin as shown in Fig. 22 as a function of (left), (center), and (right). The colored lines represent PWA solutions: $2\pi$-MAID in black, BnGa 2014-02 in red, new BnGa 2022-02 in blue. The systematic uncertainty is shown as a gray band

Fig. 27

The sums of branching ratios into , are compared to the sums of branching ratios into , , and of the resonances listed in Table 2. The branching ratios (BR) of one-oscillator excitations decaying into the ground states or are depicted as black dots, when decaying into the excited states , , or as red squares. Mixed-oscillator states decaying into the ground states mentioned above are shown as blue dots, when decaying into the excited states mentioned above as green squares. Additionally the mean branching ratios are shown on the right as well as colored lines