Coherent photoproduction of $\pi {}^{+}$ from ${}^3\mathrm{He}$

We have measured the differential cross section for the $\gamma$${}^3\mathrm{He}$$\to \pi {}^{+}t$ reaction. This reaction was studied using the Continuous Electron Beam Accelerator Facility (CEBAF) Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Real photons produced with the Hall-B bremsstrahlung tagging system in the energy range from 0.50 to 1.55 GeV were incident on a cryogenic liquid ${}^3\mathrm{He}$ target. The differential cross sections for the $\gamma$${}^3\mathrm{He}$$\to \pi {}^{+}t$ reaction were measured as a function of photon-beam energy and pion-scattering angle. Theoretical predictions to date cannot explain the large cross sections except at backward angles, showing that additional components must be added to the model.

Figure 1

Diagrams for the dispersive and pion rescattering terms in nuclear pion photoproduction. The two-body diagrams are shown in (c) and (d). Figure is from Ref. [10].

Figure 2

Differential cross section at ${\theta }_{\pi }^{\mathrm{c}.\mathrm{m}.}={137}^{°}$ as a function of nuclear momentum transfer $Q^2$ from Ref. [3]. The dotted (dashed) curves show the PWIA (DWIA) results. The dash-dotted curve includes the corrections due to coupling with the breakup channels, and the solid line shows the complete calculation with the additional two-body mechanisms. Figure is from Ref. [10].

Figure 3

Difference between the Tagger time and the start-counter (ST) time (solid histogram). The tagger and ST coincidence time for selected events is required to be within 1 ns (shaded histogram). The secondary peaks, corresponding to the nearby beam buckets, are also visible.

Figure 4

Hadron mass calculated from the time-of-flight information. The histogram in the top panel shows the mass distribution for all positively charged hadrons. The solid histogram in the lower panel is the selected sample of pions and tritons that are detected in coincidence. The shaded histogram shows the same distribution after applying all the kinematical cuts to remove the background (see Sec. 3c for details).

Figure 5

Distributions of the missing mass squared of the detected triton (left) and pion (right) before (top) and after (bottom) the energy-loss corrections. Gaussian fits shown in solid blue are performed to determine the mean value and the width of each distribution. The accepted values for the pion and triton mass squared are 0.0195 and 7.890 (GeV/$c$${}^2$)${}^2$, respectively.

Figure 6

The $\pi {}^{+}t$ two-body final-state kinematics require the missing energy (upper left), missing mass squared (upper right), and missing momentum (lower left) to be zero, and the $\pi {}^{+}t$ opening angle (lower right) to be ${180}^{°}$. The peaks correspond to the real coherent $\pi {}^{+}t$ events from the ${}^3\mathrm{He}$ target. The shaded areas correspond to the nearly background-free sample of $\pi {}^{+}t$ events after the five kinematical cuts described in the text were applied.

Figure 7

Cuts were applied on various kinematical variables to remove the background. Upper left: The difference between the measured and calculated pion-scattering angles. Upper right: The difference between the magnitude of pion and triton momenta. Lower left: The difference between the pion and triton azimuthal angles. Lower right: The sum of the cosines of the pion and triton scattering angles. All quantities are shown in the center-of-mass frame.

Figure 8

The calculated values for the missing mass squared for the detected pion (top) and the detected triton (bottom), before (solid histogram) and after (shaded histogram) applying the kinematic cuts. The background is removed by the kinematic cuts.

Figure 9

Simulated TOF masses for Monte Carlo generated events, plotted for both logarithmic (top) and linear (bottom) scales, before (solid histogram) and after (shaded areas) applying all of the cuts.

Figure 10

Measured differential cross sections as a function of $E_{\gamma }$ for ${\theta }_{\pi }{}^{\mathrm{c}.\mathrm{m}.}$ $=$ 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, and 140 deg. The error bars indicate statistical uncertainties only.

Figure 11

Measured differential cross sections as a function of ${\theta }_{\pi }{}^{\mathrm{c}.\mathrm{m}.}$ for $E_{\gamma }=$ 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, and 1.2 GeV. CLAS acceptance limits the detection of the small angle pions. The error bars indicate statistical uncertainties only.

Figure 12

Momentum-transfer dependence of the differential cross section for a fixed pion angle of 137 deg in the c.m. frame. The curves show the calculations by Tiator and Kamalov for three different assumptions: plane-wave impulse approximation PWIA (dotted lines); distorted-wave impulse approximation DWIA (dashed lines); and DWIA $+$ two-body mechanism [10] (solid lines). Our data from CLAS are shown as open circles and from Ref. [3] as filled circles.

Figure 13

Momentum-transfer dependence of the differential cross section for a fixed pion angle of 90 deg in the c.m. frame. The curves are described in Fig. 12. Our data from CLAS are shown as open circles and from Ref. [9] as a filled circle.

Figure 14

Momentum-transfer dependence of the differential cross section for a fixed pion angle of 60 deg in the c.m. frame. The curves are described in Fig. 12. Our data from CLAS are shown as open circles. Note that in the forward direction, the DWIA and the DWI $+$ two-body calculations coincide, as expected, so the two-body mechanism included in the model does not contribute.

Figure 15

Comparison of the model calculations from Tiator and Kamalov with the differential cross section as a function of pion scattering angle in the c.m. frame for various photon-energy bins. The model includes DWIA $+$ two-body mechanism (see text).