Measurement of the differential cross sections of the ${\mathrm{\Sigma }}^{-}p$ elastic scattering in momentum range 470 to 850 $\mathrm{MeV}/c$

A high statistics $\mathrm{\Sigma }p$ scattering experiment is performed at the J-PARC Hadron Experimental Facility. Momentum-tagged ${\mathrm{\Sigma }}^{-}\mathrm{s}$ running in a liquid hydrogen target are accumulated by detecting the ${\pi }^{-}p\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction with a high intensity ${\pi }^{-}$ beam of 20 M/spill. The differential cross sections of the ${\mathrm{\Sigma }}^{-}p$ elastic scattering were derived with a drastically improved accuracy by identifying approximately 4500 events from $1.72\times {10}^7{\mathrm{\Sigma }}^{-}$. The derived differential cross section shows a clear forward-peaking angular distribution for a ${\mathrm{\Sigma }}^{-}$ momentum range from 470 to 850 $\mathrm{MeV}/c$. The accurate data will impose a strong constraint on the theoretical models of the baryon-baryon interactions.

Figure 1

Experimental concept of the $\mathrm{\Sigma }p$ scattering experiment and experimental setup with an enlarged figure around the ${\mathrm{LH}}_2$ target. Two successive two-body reactions of the ${\mathrm{\Sigma }}^{-}$ production (${\pi }^{-}p\to K^{+}{\mathrm{\Sigma }}^{-}$) and the ${\mathrm{\Sigma }}^{-}p$ scattering (${\mathrm{\Sigma }}^{-}p\to {\mathrm{\Sigma }}^{-}p$) are detected. The momentum of the produced $\mathrm{\Sigma }$ particles is obtained from the momenta of $\pi$ beam particles and scattered $K^{+}$ measured by the K1.8 beam line spectrometer and KURAMA spectrometer, respectively. The beam line spectrometer consists of two hodoscopes (BH1 and BH2) and three position detectors (BFT, BC3, and BC4). In the KURAMA spectrometer, five position detectors (SFT, SDC1, SCH, SDC2, and SDC3) and a TOF counter are used. The $\mathrm{\Sigma }p$ scattering events are detected by the CATCH system, which surrounds the ${\mathrm{LH}}_2$ target.

Figure 2

Reconstructed momentum for the ${\pi }^{-}$ beam.

Figure 3

Reconstructed mass squared distribution for all events (top), BFT single cluster events (middle), and BFT multicluster event (bottom).

Figure 4

Correlation between the momentum and energy deposit per unit length at the TOF, which was normalized as one for ${\pi }^{+}$. Left and right figures show the correlations of all events and the $K^{+}$ mass region for the BFT multicluster event, respectively. The region between two red lines was selected as the $K^{+}$ region for the BFT multicluster event.

Figure 5

Vertex distribution between the ${\pi }^{-}$ beam and outgoing $K^{+}$. The left figure shows the $z$ vertex distribution. The $z$ vertex region from $-150$ to 150 mm, which is shown by the red lines, was selected for the ${\mathrm{\Sigma }}^{-}$ production event at the ${\mathrm{LH}}_2$ target. The right figure shows the scatter plot between the $x$ and $y$ vertices. The dotted lines show the envelopes of the target container and vacuum window. The red-box region was selected to suppress the contamination of the reaction at the target container.

Figure 6

(a) Missing mass spectra of the ${\pi }^{-}p\to K^{+}X$ reaction for $K^{+}$ events (open histogram) and sideband events of $K^{+}$ (filled histogram) to estimate the effect of the contamination of the miscalculated event under the $K^{+}$ region in the mass square spectrum. The two lines show the selected area for the ${\mathrm{\Sigma }}^{-}$ particles. (b) ${\mathrm{\Sigma }}^{-}$ momentum reconstructed as the missing momentum of the ${\pi }^{-}p\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction.

Figure 7

Correlation between the scattering angle and kinetic energy measured by the CFT and BGO for the $pp$ scattering data with a 600-$\mathrm{MeV}/c$ proton beam. The locus corresponding to the elastic scattering can be identified.

Figure 8

Correlation between the total energy measured by the BGO and the energy deposit normalized to the unit length in CFT. The two curves show the selection region for the proton. Many of the $\pi \mathrm{s}$ were not stopped in the BGO and penetrated with only a part of the energy deposit.

Figure 9

Kinematical consistencies between the measured and calculated energies from the scattering angle assuming the four different scattering reactions: (a) $\mathrm{\Delta }E\left(np\right)$ distribution, (b) $\mathrm{\Delta }p\left({\pi }^{-}p\right)$ distribution, (c) $\mathrm{\Delta }E\left({\mathrm{\Sigma }}^{-}p\right)$ distribution, and (d) $\mathrm{\Delta }p({\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n)$ distribution. Peaks around $\mathrm{\Delta }E=0$ or $\mathrm{\Delta }p=0$ correspond to the assumed reaction events.

Figure 10

Top: Estimated ${\mathrm{\Sigma }}^{-}$ track length in the ${\mathrm{LH}}_2$ target for the four-momentum regions. Bottom: Contribution in the ${\mathrm{\Sigma }}^{-}$ track length of the miscalculated event in the $m^2$ distribution under the $K^{+}$ peak (filled histogram). Total track lengths ($L$) are also shown by summing up each track length.

Figure 11

Top: Momentum dependence of the CFT tracking for the proton obtained from the $pp$ scattering data and its simulation for a scattering angle of ${51}^{\circ }$ in the laboratory frame. Bottom: Estimated CFT tracking efficiency map as a function of the scattering angle and momentum of the proton.

Figure 12

Top: Momentum dependence of the BGO efficiency for the proton obtained from the $pp$ scattering data for a scattering angle of ${41}^{\circ }$ in the laboratory frame. The red and cross points show the estimated efficiencies from the $pp$ scattering data and geant4 simulation. Bottom: Estimated BGO efficiency map as a function of the scattering angle and momentum of the proton.

Figure 13

Detection efficiency for the ${\mathrm{\Sigma }}^{-}p$ elastic scattering events for the four ${\mathrm{\Sigma }}^{-}$ beam momentum regions. These efficiencies were the averaged values for all the vertex regions of $-150<vtz$ (mm) $<150$.

Figure 14

Kinematical consistency between the measured and calculated energies from the measured scattering angle assuming the four different scattering processes, (a) $\mathrm{\Delta }E\left(np\right)$, (b) $\mathrm{\Delta }p\left({\pi }^{-}p\right)$, (c) $\mathrm{\Delta }E\left({\mathrm{\Sigma }}^{-}p\right)$, and (d) $\mathrm{\Delta }p({\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n)$ distributions, for the angular region of $0\le cos\theta \le 0.1$ in the momentum range of 470 $<p$ ($\mathrm{MeV}/c$) $<$ 550. Data points with error bars and a green shaded histogram show the experimental data for the $K^{+}$ region and the sideband region of $K^{+}$ in the mass square spectrum, respectively. Simulated spectra for the assumed reactions are also shown and the histogram with a red line shows the sum of these spectra. The arrows in (a), (b), and (d) show the cut regions for the background suppression.

Figure 15

The same spectra in Fig. 14 after applying a cut to reject the background events by removing the background peak structures in the $\mathrm{\Delta }E\left(np\right),\mathrm{\Delta }p\left({\pi }^{-}p\right)$, and $\mathrm{\Delta }p({\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n)$.

Figure 16

Differential cross sections for four-momentum regions derived from different methods and background structures. The closed points and open points were obtained from BG1 obtained from the simultaneous fit for all four $\mathrm{\Delta }E,\mathrm{\Delta }p$ spectra and BG2 obtained from the single fit of the $\mathrm{\Delta }E\left({\mathrm{\Sigma }}^{-}p\right)$, respectively. The red and blue colors were obtained by the $z$ vertex dependent and $z$ vertex averaged methods, respectively.

Figure 17

Differential cross sections obtained in the present experiment (black points). The error bars and boxes show statistical and systematic uncertainties, respectively. The red points are averaged differential cross sections of 400 $<p$ ($\mathrm{MeV}/c$) $<$ 700 taken in KEK-PS E289 (the same points are plotted in all of the four-momentum regions). The dotted (magenta), dot-dashed (blue), and solid (yellow) lines represent the calculated cross sections by the Nijmegen ESC08c model based on the boson-exchange picture, the fss2 model including QCM, and the extended $\chi \mathrm{EFT}$ model, respectively.

Figure 18

$\mathrm{\Delta }E\left({\mathrm{\Sigma }}^{-}p\right)$ spectra for each scattering angle for $0.45<p(\mathrm{GeV}/c)<0.55$ (top) and $0.55<p(\mathrm{GeV}/c)<0.65$ (bottom). The data points and histograms are the same as those in Fig. 14.

Figure 19

$\mathrm{\Delta }E\left({\mathrm{\Sigma }}^{-}p\right)$ spectra for each scattering angle for $0.65<p(\mathrm{GeV}/c)<0.75$ (top) and $0.75<p(\mathrm{GeV}/c)<0.85$ (bottom). The data points and histograms are the same as those in Fig. 14.