Beam asymmetry $\Sigma$ for ${\pi }^{+}$ and ${\pi }^0$ photoproduction on the proton for photon energies from 1.102 to 1.862 GeV

Beam asymmetries for the reactions $\gamma p\to p{\pi }^0$ and $\gamma p\to n{\pi }^{+}$ have been measured with the CEBAF Large Acceptance Spectrometer (CLAS) and a tagged, linearly polarized photon beam with energies from 1.102–1.862 GeV. A Fourier moment technique for extracting beam asymmetries from experimental data is described. The results reported here possess greater precision and finer energy resolution than previous measurements. Our data for both pion reactions appear to favor the SAID and Bonn-Gatchina scattering analyses over the older Mainz MAID predictions. After incorporating the present set of beam asymmetries into the world database, exploratory fits made with the SAID analysis indicate that the largest changes from previous fits are for properties of the $\Delta \left(1700\right)3/2^{-}$ and $\Delta \left(1905\right)5/2^{+}$ states.

Figure 1

(a) Velocity $\beta$ versus momentum $p$ for all charged particles passing through CLAS in this experiment. (b) Mass of charged particles passing through CLAS in this experiment as determined by $\beta$ and $p$, with the pions and protons identified through GPID represented by the solid shaded and crosshatched regions, respectively.

Figure 2

(a) Spectrum of squared missing mass $M_X^2$ from the reaction $\gamma p\to pX$. (b) Missing mass $M_X$ from the reaction $\gamma p\to {\pi }^{+}X$. The ${\pi }^0$, $\eta$, and neutron peaks are indicated on the plots.

Figure 3

Yield extraction examples from previously published g1c ${\pi }^0$ differential cross sections [10]. Shown are data for the ${\pi }^0$ yield extraction for $E_{\gamma }=1.425$ GeV and $cos{\theta }_{\mathrm{c}.\mathrm{m}.}^p=-0.45$. (a) is the missing mass yield for this bin, with the accidental contribution displayed in shaded region. The accidental contribution is seen to be small and linear. (b) shows the missing mass distribution with the accidental contributions subtracted; the shaded region indicates the 2-$\pi$ contribution determined. (c) shows the extracted ${\pi }^0$ yield after contributions for accidentals and two-pion photoproduction have been subtracted from the missing mass distribution.

Figure 4

Extraction of the quantities $n$ and $d$ [defined in Appendix pp1 Eq. (A20)] for neutron (top two panels) and ${\pi }^0$ (bottom two panels) for the kinematic bin ${\theta }_{\mathrm{c}.\mathrm{m}.}^{\pi }={123}^{\circ }$ and $E_{\gamma }=1229$ MeV. (a) and (b) Reaction $\gamma p\to {\pi }^{+}n$. The $x$ axis is missing mass $M_X$ from the reaction $\gamma p\to {\pi }^{+}X$. (c) and (d) Reaction $\gamma p\to p{\pi }^0$. The $x$ axis is squared missing mass $M_X^2$ from the reaction $\gamma p\to pX$. The shaded region in each plot represents contributions from background.

Figure 5

Rough ${\pi }^0$ normalized yields for forward center-of-mass angles. (a) shows the normalized yields for runs with the PERP polarization orientation, while (b) shows the normalized yields for runs with the PARA orientation.

Figure 6

Rough ${\pi }^0$ beam asymmetries $\Sigma$ for forward (a), and backward (b) center-of-mass angles determined for polarized photons associated with the indicated photon tagger energy counter. Blue open circles represent values of $\Sigma$ determined by the Fourier moment method, while black points represent values of $\Sigma$ determined by the $\varphi$-bin method averaged over polarization orientations.

Figure 7

Frequency distribution for the rough ${\pi }^0$ data shown in Fig. 6 of the ratios of $\Sigma$ from the Fourier moment method divided by $\Sigma$ obtained from the $\varphi$-bin method for each photon tagger energy counter. (a) Forward center-of-mass angles. (b) Backward center-of-mass angles. A Gaussian fit to each of these distributions is also shown.

Figure 8

Beam asymmetry $\Sigma$ for $\vec{\gamma }p\to {\pi }^{0}p$ at $E_{\gamma }=1102–1444$ MeV versus pion center-of-mass production angle. Photon energy is indicated by $E$, while the center-of-mass total energy is indicated by $W$. Red solid (blue dash-dotted) lines correspond to the SAID DU13 (CM12 [27]) solution. Green dashed (black short-dashed) lines give the MAID07 [28] (BG2011-02 BnGa [29]) predictions. Experimental data are from the current (filled circles), Bonn [12, 13] (open circles), Yerevan [14, 15, 16, 17, 18, 19] (open triangle), GRAAL [20] (open square), CEA [21] (filled square), DNPL [22, 23] (cross), and LEPS [24] (asterisk). Plotted uncertainties are statistical. The plotted points from previously published experimental data [30] are those data points within 3 MeV of the photon energy indicated on each panel.

Figure 9

Beam asymmetry $\Sigma$ for $\vec{\gamma }p\to {\pi }^{0}p$ at $E_{\gamma }=1462–1862$ MeV versus pion center-of-mass production angle. The photon energy is shown as $E$. Notation as in Fig. 8.

Figure 10

Beam asymmetry $\Sigma$ for $\vec{\gamma }p\to {\pi }^{+}n$ at $E_{\gamma }=1112–1862$ MeV versus pion center-of-mass production angle. The photon energy is shown as $E$. Red solid (blue dash-dotted) lines correspond to the SAID DU13 (CM12 [27]) solution. Green dashed (black short-dashed) lines give the MAID07 [28] (BG2011-02 BnGa [29]) predictions. Experimental data are from the current (filled circles), GRAAL [25] (open square), Yerevan [26] (open triangle), CEA [21] (filled square), and DNPL [23] (cross). Plotted uncertainties are statistical. The plotted points from previously published experimental data [30] are those data points within 3 MeV of the photon energy indicated on each panel.

Figure 11

Fixed angle excitation functions of the beam asymmetry $\Sigma$ for $\vec{\gamma }p\to {\pi }^{0}p$. The pion center-of-mass production angle is shown. Notation as in Fig. 8.

Figure 12

Fixed angle excitation functions of the beam asymmetry $\Sigma$ for $\vec{\gamma }p\to {\pi }^{+}n$. The pion center-of-mass production angle is shown. Notation as in Fig. 10.

Figure 13

Moduli of the (a) $E_{0+}\left({\pi }^{0}p\right)$ and (b) $E_{0+}\left({\pi }^{+}n\right)$ amplitudes. Notation is the same as in Fig. 15.

Figure 14

Coefficients for associated Legendre functions of the second order for ${\pi }^{0}p$ (solid circles) and ${\pi }^{+}n$ (solid triangles). Solid lines are plotted to help guide the eye.

Figure 15

Isospin $I=3/2$ multipole amplitudes from threshold to $W=2.16$ GeV ($E_{\gamma }$ = 2.02 GeV) for $l=0,1$. Solid (dash-dotted) lines correspond to the SAID DU13 (CM12 [27]) solution. Dashed (short-dashed) lines give MAID07 [28], which terminates at $W=2$ GeV (BG2011-02 BnGa solution [29]). Vertical arrows indicate resonance energies $W_R$ and horizontal bars show full ($\Gamma$) and partial (${\Gamma }_{\pi N}$) widths associated with the SAID $\pi N$ solution SP06 [31].

Figure 16

Isospin $I=3/2$ multipole amplitudes from threshold to $W=2.16$ GeV ($E_{\gamma }$ = 2.02 GeV) for $l=2$. Notation as in Fig. 15.

Figure 17

Isospin $I=3/2$ multipole amplitudes from threshold to $W=2.16$ GeV ($E_{\gamma }$ = 2.02 GeV) for $l=3$. Notation as in Fig. 15.

Figure 18

Proton multipole $I=1/2$ amplitudes from threshold to $W=2.16$ GeV ($E_{\gamma }$ = 2.02 GeV) for $l=0,1$. Notation as in Fig. 15.

Figure 19

Proton multipole $I=1/2$ amplitudes from threshold to $W=2.16$ GeV ($E_{\gamma }$ = 2.02 GeV) for $l=2$. Notation as in Fig. 15.

Figure 20

Proton multipole $I=1/2$ amplitudes from threshold to $W=2.16$ GeV ($E_{\gamma }$ = 2.02 GeV) for $l=3$. Notation as in Fig. 15.