Precise Measurement of Differential Cross Sections of the ${\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n$ Reaction in Momentum Range $470–650\mathrm{MeV}/c$

The differential cross sections of the ${\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n$ reaction were measured accurately for the ${\mathrm{\Sigma }}^{-}$ momentum ($p_{\mathrm{\Sigma }}$) ranging from 470 to $650\mathrm{MeV}/c$ at the J-PARC Hadron Experimental Facility. Precise angular information about the ${\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n$ reaction was obtained for the first time by detecting approximately 100 reaction events at each angular step of $\mathrm{\Delta }\cos \theta =0.1$. The obtained differential cross sections show a slightly forward-peaking structure in the measured momentum regions. The cross sections integrated for $-0.7\le \cos \theta \le 1.0$ were obtained as $22.5\pm 0.68$ [statistical error(stat.)] $\pm 0.65$ [systematic error(syst.)] mb and $15.8\pm 0.83(\mathrm{stat})\pm 0.52(\mathrm{syst})\mathrm{mb}$ for $470<p_{\mathrm{\Sigma }}(\mathrm{MeV}/c)<550$ and $550<p_{\mathrm{\Sigma }}(\mathrm{MeV}/c)<650$, respectively. These results show a drastic improvement compared with past measurements of the hyperon-proton scattering experiments. They will play essential roles in updating the theoretical models of the baryon-baryon interactions.

Figure 1

Kinematical consistency between the measured energy (momentum) and the calculated one from the measured scattering angle assuming the four different scattering processes, (a) $\mathrm{\Delta }{E}_p(np)$, (b) $\mathrm{\Delta }{p}_p({\pi }^{-}p)$, (c) $\mathrm{\Delta }{E}_p({\mathrm{\Sigma }}^{-}p)$, and (d) $\mathrm{\Delta }{p}_{\mathrm{\Lambda }}({\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n)$ distributions, for the angular region of $0.3\le \cos \theta \le 0.4$ for the ${\mathrm{\Sigma }}^{-}$ momentum between 470 and $550\mathrm{MeV}/c$. Data points with error bars and green-hatched histograms show the experimental data for the $K^{+}$ region and the sideband region of $K^{+}$ in the mass-squared spectrum, respectively. Simulated spectra for the assumed reactions are also shown, and the histogram of the red line shows the sum of these spectra.

Figure 2

(a),(b) Number of $\mathrm{\Sigma }p\to \mathrm{\Lambda }n$ reaction events detected for each scattering angle for two ${\mathrm{\Sigma }}^{-}$ beam momentum regions. The error bars and boxes show the statistical and systematic errors, respectively. (c),(d) Detection efficiency for the ${\mathrm{\Sigma }}^{-}p\to \mathrm{\Lambda }n$ scattering events for two ${\mathrm{\Sigma }}^{-}$ beam momentum regions. These efficiencies are the averaged values for all vertex regions of $-150<vtz$ (mm) $<150$. The red boxes show the systematic uncertainties originating from the tracking efficiency of CFT.

Figure 3

(a),(b) Differential cross sections obtained in the present experiment (black points) for two momentum regions. The error bars and boxes show the statistical and systematic uncertainties, respectively. The dotted magenta and green lines represent the calculations by the Nijmegen ESC08c [25] and ESC16 [26] interactions based on the boson-exchange model. The dot-dashed (blue) line shows the calculation using the fss2 model, including QCM [29]. The solid orange and red lines show the calculations using two versions of the extended $\chi$ EFT model, NLO13 [36] and NLO19 [37], respectively. In both cases, the cutoff value of 600 MeV is used. (c) Integrated cross section for $-0.7\le \cos \theta \le 1$ measured in the present experiment (black points). Past data measured with a bubble chamber [7] are also shown as blue squares.