Measurement of the charge symmetry breaking $d+d\to {}^4\mathrm{He}+{\pi }^0$ reaction near threshold

We describe the observation of the isospin violating and charge symmetry breaking reaction $dd\to \alpha {\pi }^0$ just above threshold. Measurements using a magnetic channel (gated by two photons) of the ${}^4\mathrm{He}$ scattering angle and momentum (from time of flight) permitted reconstruction of the ${\pi }^0$ “missing mass,” the quantity used to separate distributions of ${}^4\mathrm{He}+{\pi }^0$ events from a continuum containing ${}^4\mathrm{He}+\gamma +\gamma$ and ${}^4\mathrm{He}+{\pi }^0+\gamma$ events. A review has been completed of the apparatus, relevant geant simulations, various corrections, and the $d+p$ scattering cross section used as a luminosity calibration. The new values of the total cross section for neutral pion production are $14.3\pm 2.2\left(\mathrm{stat}\right)\pm 1.6\left(\mathrm{sys}\right)$ pb at 228.5 MeV and $17.3\pm 3.4\left(\mathrm{stat}\right)\pm 2.4\left(\mathrm{sys}\right)$ pb at 231.8 MeV. The uncertainty remains dominated by statistical errors. These cross sections arise from the down-up quark mass difference and quark electromagnetic effects.

Figure 1

Layout of the experimental setup showing the target, approximate locations of the Pb-glass arrays, and the magnetic channel in relation to a segment of the electron-cooled storage ring. Quadrupole magnets (Q1, Q2, and Q3), wire chambers (WC1, WC2, and WC3), scintillation trigger $(\mathrm{\Delta }\mathrm{E}1,\mathrm{\Delta }\mathrm{E}2$, and E), and veto (V1 and V2) detectors are shown. The luminosity monitor detectors are small and consequently are omitted here.

Figure 2

Cross-sectional view through the midplane of the target box, showing two pumping stages with holes for the beam entrance and exit, the target box walls, left and right monitor scintillators, and left and right deuteron recoil detectors for the luminosity calibration. The two circles in the center are below beam height and represent the outer size of the gas jet nozzle and the cold head. Just behind the calibration stopping detectors are the two walls of steel used as field clamps for the $6^{\circ }$ separation magnet. The ${44}^{\circ }$ detectors observed $d+d$ elastic scattering coincidences. Each also operated in coincidence with an opposite side ${25}^{\circ }$ system to observe $d+p$ elastic scattering (using an HD target). The left and right $\mathrm{\Delta }\mathrm{E}$-E telescopes were removed whenever the Pb-glass arrays were rolled into place.

Figure 3

A view of the entrance to the septum magnet. The large channel that curves to the left is for recoil ${}^4\mathrm{He}$. The field windings are located inside the red form around this channel. The insulated windings appear as tan in the picture. The smaller square channel to the right is for the circulating deuteron beam in the Cooler ring. Note that the windings dip and travel in between the ${}^4\mathrm{He}$ channel and the beam pipe, thus keeping the stray field low in the vicinity of the beam.

Figure 4

${}^3\mathrm{He}$ recoil distribution in wire chamber WC1 for the $pd\to h{\pi }^0$ reaction at 200.2 MeV. (Top) The 2-D plot shows the locus of events produced by a $1.{45}^{\circ }$ opening cone of ${}^3\mathrm{He}$ recoils. (Bottom) The projection onto the $X$ axis shows a distribution with sharp edges.

Figure 5

Two views of the reconstruction of the $pd\to h\mathrm{X}$ reaction ${}^3\mathrm{He}$ recoil missing mass with a linear plot on top and a logarithmic plot on bottom. The data were obtained using the magnetic channel elements set for the $0.{95}^{\circ }{}^3\mathrm{He}$ recoil cone from the $pd\to h{\pi }^0$ reaction at a proton beam energy of 199.4 MeV. The ${\pi }^0$ peak at $135\mathrm{MeV}/{\mathrm{c}}^2$ has a FWHM of 240 keV.

Figure 6

Cluster summed pulse height spectra for the left (top) and the right (bottom) Pb-glass arrays obtained for events from the $pd\to h{\pi }^0$ reaction at a proton beam energy of 199.4 MeV. The points are the data, and the histograms are from the simulation of the experiment. The peak in the top panel corresponds to an intrinsic $\gamma$-ray energy of 68.5 MeV, and the peak in the bottom panel corresponds to an intrinsic $\gamma$-ray energy of 70.2 MeV. The majority of the width in each spectrum originates from the resolution of the Pb-glass modules.

Figure 7

The distributions of recoil deuterons from $d+d$ elastic scattering as a function of distance along the beam line in centimeters. The top panel is for production running and the lower panel is for the reduced pushing pressure used during the cross-section calibration. The curves represent the background Gaussian and the sum of the foreground and background Gaussian shapes. The drop on the edges of the lower panel distribution mark the limits of the aperture in front of the position-sensitive silicon detector.

Figure 8

Data for $d+p$ elastic scattering from the KVI experiment [51] at 108 (down triangles with green connecting line) and 120 MeV (up triangles with blue connecting line). The blue and red curves represent the best fit at 114.3 and 116.0 MeV, respectively.

Figure 9

Measurements of the center-of-mass cross section for $p+d$ elastic scattering in a narrow angle range and as a function of proton beam energy. The top panel shows data near ${91}^{\circ }$ while the bottom panel shows data near ${109}^{\circ }$. The open circle data were measured at 65 [49], 70 [50], 90 [56, 57], 95 [46], 98 [58], 135 [50, 52], 146 [47], 155 [48], 198 [53], and 250 [59] MeV. The Ermisch data, represented by the solid squares, were measured at 108, 120, 135, 150, 170, and 190 MeV [51]. The dashed blue line represents a straight line on these graphs through the Ermisch data. The solid line intersects the Sekiguchi measurements at 135 MeV and has the same slope. The two red circles are located at 114.3 and 116.0 MeV along this line.

Figure 10

Scatterplot of the energy deposited in the $\mathrm{\Delta }\mathrm{E}2$ detector vs one quadrant of the $\mathrm{\Delta }\mathrm{E}1$ detector. The scales represent ADC channel numbers. The zero is suppressed in order to avoid a large peak in the lower left corner from protons. The He band appears above and to the right of the proton pileup events. The window is drawn around the ${}^4\mathrm{He}$ portion so that losses may be avoided. A clean separation from ${}^3\mathrm{He}$ is not possible in this spectrum alone.

Figure 11

Scatter plot of energy deposited in the E detector versus the $\mathrm{\Delta }\mathrm{E}2$ detector. The window is drawn around the ${}^4\mathrm{He}$ group. This feature contains a continuum of ${}^4\mathrm{He}$ generated from $\left(d,{}^4\mathrm{He}\right)$ reactions on residual gas and pumping baffles in the main scattering chamber. Events from $dd\to \alpha {\pi }^0$ reactions are found in the upper part of this band.

Figure 12

Scatterplots of the beam right and left Pb-glass array showing the time of the largest Pb-glass event relative to the trigger timing of ${}^4\mathrm{He}$ events in the magnetic channel. All such pairings are shown for beam right. In that spectrum, a rectangular window selects events that are in coincidence with the magnetic channel and above roughly 15 MeV (similar to the window for beam left). A similar display is shown for beam left, but for only those events that fall within the window for beam right. This eliminates much of the random background at low pulse height. The gate on good ${\pi }^0$ decays is very clean.

Figure 13

(Top) The locus of ${}^3\mathrm{He}$ recoils observed in WC2 for the $pd\to h{\pi }^0$ calibration run made at a proton beam energy of 200.2 MeV. (Bottom) The locus of events obtained for the simulation.

Figure 14

Candidate $dd\to \alpha {\pi }^0$ events at 228.5 (top) and 231.8 MeV (bottom) as a function of missing mass. The solid black spectrum shows both a narrow peak at the ${\pi }^0$ energy and a more broadly distributed background of mostly double radiative capture. The $dd\to \alpha \gamma \gamma$ contribution to the background is shown by the blue curve in the top panel and the purple curve in the bottom panel [73]. In addition, another contribution due to $dd\to \alpha {\pi }^0\gamma$, shown by a blue curve, has been included in the bottom panel. See text for further details.