Missing-mass spectroscopy with the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction to search for ${}_{\mathrm{\Lambda }}{}^6\mathrm{H}$

We searched for the bound state of the neutron-rich $\mathrm{\Lambda }$-hypernucleus ${}_{\mathrm{\Lambda }}{}^6\mathrm{H}$, using the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ double charge-exchange reaction at a ${\pi }^{-}$ beam momentum of $1.2\mathrm{GeV}/c$ at J-PARC. A total of $1.4\times {10}^{12}{\pi }^{-}$ was driven onto a ${}^6\mathrm{Li}$ target of 3.5-$\mathrm{g}/{\mathrm{cm}}^2$ thickness. No event was observed below the bound threshold, i.e., the mass of ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}+2n$, in the missing-mass spectrum of the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction in the $2^{\circ }<{\theta }_{\pi K}<{20}^{\circ }$ angular range. Furthermore, no event was found up to $2.8\mathrm{MeV}/c^2$ above the bound threshold. We obtained the double-differential cross section spectra of the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction in the angular range of $2^{\circ }<{\theta }_{\pi K}<{14}^{\circ }$. An upper limit of 0.56 nb/sr (90% C.L.) was obtained for the production cross section of the ${}_{\mathrm{\Lambda }}{}^6\mathrm{H}$ hypernucleus bound state. In addition, not only the bound state region, but also the $\mathrm{\Lambda }$ continuum region and part of the ${\mathrm{\Sigma }}^{-}$ quasifree production region of the ${}^6\mathrm{Li}({\pi }^{-},K^{+}$) reaction were obtained with high statistics. The present missing-mass spectrum will facilitate the investigation of the ${\mathrm{\Sigma }}^{-}$-nucleus optical potential for ${\mathrm{\Sigma }}^{-}-{}^5\mathrm{He}$ through spectrum shape analysis.

Figure 1

Schematic view of the experimental setup.

Figure 2

$M_{\mathrm{scat}}^2$ distributions of the scattered particles for the momentum ranges of (a) $750<p_{\mathrm{SKS}}<800\mathrm{MeV}/c$ and (b) $900<p_{\mathrm{SKS}}<950\mathrm{MeV}/c$ in the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction. The nonhatched and hatched histograms indicate data obtained before and after the TOF $dE/dx$ gating, respectively. The solid lines around the $K^{+}$ peak in (a) represent the $M_{\mathrm{scat}}^2$ selection range, which is $2\sigma$ of the Gaussian function, at $p_{\mathrm{SKS}}=775\mathrm{MeV}/c$. The dashed lines in (b) are the $M_{\mathrm{scat}}^2$ selection range at $925\mathrm{MeV}/c$ extrapolated from the momentum region in which the $K^{+}$ peak is observed.

Figure 3

(a)–(c) Correlation plots between $dE/dx$ in the TOF wall segments and momenta of the scattered particles for particles selected using $M_{\mathrm{scat}}^2$ for data set D. (d)–(f) The analogous plots for data set A. The $dE/dx$ gating region for $K^{+}$ is indicated by the black lines. The gating bandwidth is constant below $960\mathrm{MeV}/c$, but narrows when the momentum is increased above $960\mathrm{MeV}/c$.

Figure 4

Reaction vertex distributions along the beam axis for data sets (a) A (${}^6\mathrm{Li}$ target) and (b) D (${\mathrm{CH}}_2$ target). The detector positions around the target are indicated by the dashed lines. The hatched region was selected as the target cut region.

Figure 5

Mean value of $dP$ as a function of the beam momentum. The data points were obtained from data set E, the ${\pi }^{+}$ beam through run. The vertical and horizontal axes indicate the mean value of $dP$ and the beam momentum, respectively. The solid line is the quadratic fitting function $h\left(p\right)$.

Figure 6

Missing-mass spectrum of the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction in the angular range of $2^{\circ }<{\theta }_{\pi K}<{14}^{\circ }$. Two mass thresholds, ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}+2n$ and ${}^5\mathrm{He}+{\mathrm{\Sigma }}^{-}$, are indicated by the dashed lines. The horizontal axis bin width is $2\mathrm{MeV}/c^2$.

Figure 7

Excitation energy spectrum of the ${}_{\mathrm{\Lambda }}{}^{12}\mathrm{C}$ hypernucleus obtained by the $\mathrm{C}({\pi }^{+},K^{+})X$ reaction. The peak position of the first Gaussian function was set to 0 MeV. The low-lying states were fitted with three Gaussian functions. The peak separation and their relative amplitude were fixed. The dot-dashed lines represent each Gaussian function and the solid line is their sum. The missing-mass resolution was found to be $2.9\mathrm{MeV}/c^2$ (FWHM).

Figure 8

Horizontal position dependence of SFT-SDC2 local tracking efficiency. The origin of the horizontal axis corresponds to the detector center. Decreased efficiency is observed near the center, because of the beam focus.

Figure 9

Vertex selection efficiency as a function of the reaction angle ${\theta }_{\pi K}$.

Figure 10

Double-differential cross sections of the ${\pi }^{-}p\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction at $1.39-\mathrm{GeV}/c$ beam momentum in $4^{\circ }<{\theta }_{\pi K}<6^{\circ }$ angular range in (a) laboratory system and (b) after subtracting background. The arrows indicate the integration range used to estimate the cross section.

Figure 11

Double-differential cross sections of the ${\pi }^{+}p\to K^{+}{\mathrm{\Sigma }}^{+}$ reaction at $1.39-\mathrm{GeV}/c$ beam momentum in $4^{\circ }<{\theta }_{\pi K}<6^{\circ }$ angular range in (a) laboratory system and (b) after subtracting background. The arrows indicate the integration range used to estimate the cross section.

Figure 12

Differential cross section of the ${\mathrm{\Sigma }}^{-}$ production via the ${\pi }^{-}p\to K^{+}{\mathrm{\Sigma }}^{-}$ reaction in c.m. system and those from the past experiments. Our data are indicated by filled squares. The data points indicated by open and filled triangles are from Ref. [34] and the open circles correspond to data from Ref. [35].

Figure 13

Differential cross section of the ${\mathrm{\Sigma }}^{+}$ production via the ${\pi }^{+}p\to K^{+}{\mathrm{\Sigma }}^{+}$ reaction in c.m. system and that from the past experiment [36]. Our data and those from Ref. [36] are indicated by filled squares and open circles, respectively.

Figure 14

Missing-mass spectrum of the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction in $2^{\circ }<{\theta }_{\pi K}<{14}^{\circ }$ angular range at $1.2-\mathrm{GeV}/c$ beam momentum. The vertical axis is the double-differential cross section averaged over the ${\theta }_{\pi K}$ region. A magnified view in the vicinity of the ${}_{\mathrm{\Lambda }}{}^6\mathrm{H}$ bound state region is given in the inset plot. The error bars show the statistical errors. The systematic errors in each bin are represented by the bar graph at the bottom. The two vertical dashed lines represent the mass thresholds, ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}+2n$ and ${}^5\mathrm{He}+{\mathrm{\Sigma }}^{-}$.

Figure 15

Raw missing-mass spectrum in angular range of (a) $2^{\circ }<{\theta }_{\pi K}<{14}^{\circ }$ and (b) ${14}^{\circ }<{\theta }_{\pi K}<{20}^{\circ }$.

Figure 16

Missing-mass spectra of the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction in every $2^{\circ }$ bin width. The missing-mass spectra are shown in the same manner as in Fig. 14.

Figure 17

Angular distribution of the integrated cross sections of the ${}^6\mathrm{Li}({\pi }^{-},K^{+})X$ reaction. The closed squares represent the ${\mathrm{\Sigma }}^{-}$ quasifree production cross section integrated between the missing-mass range of 5865 and $5920\mathrm{MeV}/c^2$. The open squares indicate the cross section of the $\mathrm{\Lambda }$ continuum integrated between the missing-mass range of 5800 to $5865\mathrm{MeV}/c^2$, multiplied by a factor of 10. The error bars are statistical only.