Measurement of the $K^{-}p\to {\Sigma }^0{\pi }^0$ reaction between 514 and 750 MeV/$c$

The reaction $K^{-}p\to {\Sigma }^0{\pi }^0\to$ neutrals was studied with the Crystal Ball detector at the BNL Alternating Gradient Synchrotron for beam momenta between 514 and 750 MeV/$c$. The photons from ${\Sigma }^0$ and ${\pi }^0$ decays were detected, as well as the neutron in a small fraction of the events. The differential cross section and the ${\Sigma }^0$ polarization are reported at eight momenta and nearly the full angular range. Total cross sections are derived from Legendre polynomial fits to the data. The measurements presented are of considerably higher precision than previous results.

Figure 1

Plan view of the experimental apparatus, including the Crystal Ball, beam counters ${\mathrm{S}}_2$ and ${\mathrm{S}}_{\mathrm{T}}$ and drift chambers ${\mathrm{D}}_2\text{−}{\mathrm{D}}_4$, various veto counters, the liquid-hydrogen target, and the lead collimator. Additional concrete shielding, another collimator farther upstream, and the hodoscope ${\mathrm{S}}_1$ and chamber ${\mathrm{D}}_1$ are not shown.

Figure 2

C6 beam line, including production target, dipole and quadrupole magnets, electrostatic separators, and the last two magnets in the primary-proton line before the target.

Figure 3

TDC spectra for one ${\mathrm{S}}_1$ hodoscope counter and one run at 514 and 750 MeV/$c$. The large peaks are from kaons, and the time per channel is 0.05 ns. The ${\mathrm{S}}_{\mathrm{T}}$ signal provided the stop timing, so pions would occur to the left of the kaon peak.

Figure 4

$\gamma \gamma$ invariant mass for two-cluster pion beam events at 714 MeV/$c$ after final energy calibrations. The peaks correspond to the ${\pi }^0$ and η masses, respectively.

Figure 5

Radial distance of the beam track from the nominal beam line ($r_I$) at the target center, $z_0=0$. The cut to reduce events with interactions in the target walls is also shown. The data were taken at 659 MeV/$c$.

Figure 6

Correlation of the time difference between the ${\mathrm{S}}_{\mathrm{TL}}$ and ${\mathrm{S}}_{\mathrm{TR}}$ signals with the horizontal projection of the beam track to ${\mathrm{S}}_{\mathrm{T}}$ at 750 MeV/$c$. A diagonal band is expected if there were no beam decays, scattering, or interactions, and no background or accidental events.

Figure 7

Typical TDC spectrum from a NaI crystal at 750 MeV/$c$. The time per channel is approximately 0.05 ns, and the Crystal Ball TDCs operated in the common-stop mode. The arrows show the timing cuts applied to the data.

Figure 8

Displays of single events showing the energy deposited in each crystal for (upper) a good $K^{-}p\to {\Sigma }^0{\pi }^0$ candidate, (middle) a $K^{-}$ decay to a ${\mu }^{-}$ or ${\pi }^{-}$ upstream of the CB, and (lower) an example of energy from outside the good timing window. Individual counters outlined in red are part of an identified γ cluster that passed the timing cut.

Figure 9

Comparison of the angular distribution for the $K^{-}p\to {\Sigma }^0{\pi }^0$ reaction with two different fiducial cuts at 659 MeV/$c$ laboratory momentum. The standard cut removed γ clusters centered in a guard crystal, while the restricted cut required the clusters to have ${39}^{°}⩽{\theta }_{\gamma }⩽{141}^{°}$.

Figure 10

Distribution of the minimum value of $\mathcal{F}$ from Eq. (3) for five-cluster events at 659 MeV/$c$ beam momentum, with the arrow indicating the cut to reduce backgrounds.

Figure 11

Distribution of the derived interaction vertex position $z_I$ from data at 659 MeV/$c$ beam momentum after subtraction of empty-target events. The cuts applied to the data are indicated. Monte Carlo simulations of the $z_I$ distribution including backgrounds and pileup, normalized to the same total number of events, are included for comparison as the open circles.

Figure 12

Distribution of the missing mass ${\mathrm{MM}}_{{\gamma }_1{\gamma }_2}$ is shown before the $\mathcal{F}$ cut, after the $\mathcal{F}$ cut but before mass cuts, and after all cuts. The data are for 659 MeV/$c$ beam momentum.

Figure 13

Distribution of the quantities (a) ${\mathrm{IM}}_{{\gamma }_1{\gamma }_2}$, (b) ${\mathrm{IM}}_{{\gamma }_4{\gamma }_5}$, (c) ${\mathrm{MM}}_{{\gamma }_1{\gamma }_2{\gamma }_3}$, and (d) ${\mathrm{MM}}_{{\gamma }_1{\gamma }_2}$ for data at 659 MeV/$c$ (solid circles). Simulation results (open circles), including backgrounds and pileup, are normalized to give the same number of events as the data.

Figure 14

Computed acceptance for the $K^{-}p\to {\Sigma }^0{\pi }^0\to (\gamma {\pi }^{0}n){\pi }^0$ reaction at 659 MeV/$c$ beam momentum after two iterations.

Figure 15

Measured distribution of cos ${\theta }_{\Lambda }$ at beam momenta of 714 and 659 MeV/$c$ with $-1.0⩽\cos ({\theta }_{\mathrm{c}.\mathrm{m}.})⩽+1.0$. The electromagnetic decay of the ${\Sigma }^0$ should have no angular dependence; the observed angular dependence is due to the gap in acceptance at the Crystal Ball exit tunnel. When these distributions were fit to a constant, the resulting chi-squared per degree of freedom exceeded 10 in both cases.

Figure 16

Measured angular distributions for the $K^{-}p\to {\Sigma }^0{\pi }^0$ reaction (solid circles) compared with data from Armenteros et al. [7] (open circles), Dombeck et al. [8] (crosses), and Baxter et al. [10] (open diamonds). The curves are the Legendre polynomial fits from Table . The uncertainties on each measurement shown are statistical only.

Figure 17

Measured total cross sections for the $K^{-}p\to {\Sigma }^0{\pi }^0$ reaction from this experiment (solid circles). Values from Refs. [6, 7, 8, 9, 10, 13] are shown for comparison. The momenta of several points were offset a few MeV/$c$ to be able to distinguish them. The uncertainties shown are statistical only; systematic uncertainties on the present measurements are approximately $\pm 10\%$.

Figure 18

Measured differential cross sections for the $K^{-}p\to {\Sigma }^0{\pi }^0$ reaction at cos$({\theta }_{\mathrm{c}.\mathrm{m}.})=-0.9$ from this experiment (solid circles). The uncertainties shown are statistical only. Values from Armenteros et al. [7] (open circles) and Baxter et al. [10] (open diamonds) are shown for comparison.

Figure 19

Polarization of the ${\Sigma }^0$ in the $K^{-}p\to {\Sigma }^0{\pi }^0$ reaction. The uncertainties shown are statistical only. Data from earlier measurements have not been included since their statistical uncertainties generally exceed ±1. The curves shown are from Legendre polynomial fits to the data; see Tables and .

Figure 20

Coefficients in Legendre polynomial fits to the data as ratios to $A_0$; see Tables and .