Measurement of the $\mathrm{\Sigma }$ beam asymmetry for the $\omega$ photoproduction off the proton and the neutron at the GRAAL experiment

We report on new measurements of the beam asymmetry for $\omega$ photoproduction on protons and neutrons in hydrogen and deuterium targets from the GRAAL Collaboration. The beam asymmetry values are extracted from the reaction threshold ($E_{\gamma }=1.1$ GeV in the free nucleon kinematics) up to 1.5 GeV of incoming photon energy. For the first time both the radiative and the three-pion decay channels are simultaneously investigated on the free proton. Results from the two decay channels are in agreement, leading to the world's most precise measurements of the beam asymmetry for $\omega$ photoproduction off free protons. First experimental results on the deuteron allow the extraction of the $\mathrm{\Sigma }$ beam asymmetry on quasifree nucleons. The beam asymmetry angular distributions obtained for the free and the quasifree kinematics show the same behavior, similar to the findings in pseudoscalar meson photoproduction reactions. First results of the beam asymmetry on the quasifree neutrons are presented, showing different strengths and angular distributions from the results on the proton target.

Figure 1

Experimental distribution of the difference between the calculated and the measured energy of the $\omega$ meson. The two vertical lines indicate the range of the selected energy region (first selection cut). Simulation studies show that the background events mainly populate the bump structure corresponding to the largest difference between calculated and measured energy.

Figure 2

Transverse momentum distribution of final-state particles: $x \text{vs} y$ distribution in a three-dimensional (3D) image (left panel) and corresponding level curves (right panel). First row, panels (a) and (b): experimental distribution on the free proton target (Sec. 3a). Second row, panels (c) and (d): experimental distribution on the quasifree proton (Sec. 3c). Third row, panel (e) and (f): experimental distribution on the quasifree neutron (Sec. 3c).

Figure 3

Effects of the selection criteria on the $\omega$ mass distribution for simulated data. Empty black circles: all events; full black squares: distribution after the cut on the number of residual signals in the forward detector; full black upward triangles: distribution after the cut on the energy deposited by residual signals in the BGO calorimeter (required to be smaller than 5 MeV); full black downward triangles: distribution after the kinematical cut on the difference between the calculated and the measured energy of the $\omega$ meson (cut number 1) and the transverse momentum conservation (cut number 2); full red circles: distribution after the cut on the proton missing mass (cut number 3). The black vertical line corresponds to the condition applied on the three final-state photons invariant mass (cut number 4). The distribution of the remaining background events is shown by the empty blue squares. Background contamination is estimated to be smaller than 6% of all selected events from simulation studies.

Figure 4

Examples of the fit on the proton missing mass distribution. Dashed line: signal contribution. Dotted line: back-ground contribution. Solid line: global fit. Panel (a) shows the experimental distribution and the fit for the events corresponding to $E_{\gamma }=1.39$ GeV, ${\theta }_{\omega }^{*}={126}^{\circ }, {\varphi }_{\omega }=213.{75}^{\circ }$ for the vertical polarization. The $\omega$ event distribution is described by a Breit-Wiegner function while the background event distribution, mainly due to the nonresonant three-pion production, is described by a third-order polynomial function. Panel (b) shows the observed distribution and corresponding fit for the highest energy bin $E_{\gamma }=1.48$ GeV, ${\theta }_{\omega }^{*}={162}^{\circ }, {\varphi }_{\omega }=303.{75}^{\circ }$ for the horizontal polarization. The $\omega$ event distribution is described by a Gaussian function while the background event distribution is described by a first-order polynomial function. In the fourth energy bin, the fitting procedure is considered not reliable due to the limited statistics and the beam asymmetry is not extracted.

Figure 5

Effects of events selection criteria on the Fermi momentum distribution for the quasifree proton [panel (a)] and the quasifree neutron [panel (b)]. Fermi momentum is evaluated as described in the text. Full black triangles: Fermi momentum distributions after the cut on the transverse momentum; full black squares: distributions after the cut on the difference between the measured and the calculated energy of the $\omega$ meson, bidimensional selection on the three final-state photons invariant mass, and recoil nucleon missing mass; full red circles: Fermi momentum distributions of selected events.

Figure 6

An example of the azimuthal distribution used for the extraction of the $\mathrm{\Sigma }$ beam asymmetry at fixed values of $E_{\gamma }$ and ${\theta }_{\omega }^{*}$ (in this example, $E_{\gamma }=1.39$ GeV and ${\theta }_{\omega }^{*}={126}^{\circ }$). The vertical error bars correspond to the statistical errors. The horizontal ones correspond to the $\phi$-bin width.

Figure 7

$\mathrm{\Sigma }$ beam asymmetry for the reaction $\vec{\gamma }p\to \omega p$: both the radiative decay (full circles) and the three-pion decay (full squares) of the $\omega$ meson are investigated. Statistical errors are within the marker size. Systematical errors are not shown. Data are compared with previously published results on the three-pion decay channel [15] (open squares) and radiative decay [25] (open circles). Theoretical curves are from the model by Zhao [17, 18]: solid lines correspond to the full model, dot-dashed lines do not include contributions from the ${\text{P}}_{13}$(1720) resonance, dashed lines correspond to the expected beam asymmetry when $s$- and $u$-channel contributions are not taken into account.

Figure 8

$\mathrm{\Sigma }$ beam asymmetry for the reaction $\vec{\gamma }p\to \omega p$. Full circles are the results of the present analysis for the radiative decay channel; full squares are the results of the present analysis for the three-pion decay channel. Blue stars are the results obtained by the weighted mean of the beam asymmetry values extracted independently for the two decay modes. Statistical errors are within the marker size. Systematical errors are not shown. Thin lines are from Bonn-Gatchina partial wave analysis [22]; dot-dashed lines are the predictions from [20] at threshold; dashed lines are the results from [24]; dotted curves are predictions from Giessen model [21]; solid curves are from [17, 18].

Figure 9

Comparison of the results obtained for the $\omega$ photoproduction on the free proton (full circles) and on the quasifree proton (full triangles) in a ${\text{D}}_2$ target. The error bars correspond to statistical errors. Systematical errors are not shown. A generally good agreement between free proton and quasifree proton results is observed, hinting at results for the quasifree neutron as reliable to extract information about the $\omega$ photoproduction reaction off the free neutron. Solid curves are from [17, 18].

Figure 10

Absolute first results of the $\mathrm{\Sigma }$ beam asymmetry for the $\omega$ photoproduction on the neutron (open triangles) from the ${\text{D}}_2$ target. The error bars correspond to statistical errors. Systematical errors are not shown. They are compared with the results on the quasifree proton (full triangles). Very different angular distributions are observed, indicating that different contributions are involved in the two reactions. Data are compared with the theoretical prediction from [41] (solid line) for the $\omega$ photoproduction on a free neutron target.