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Register a new userFurther Theoretical Analysis on the $K^{-} {}^{3} text{He} to Lambda p n$ Reaction for the $bar{K} N N$ Bound-State Search in the J-PARC E15 Experiment
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Based on the scenario that a $bar{K} N N$ bound state is generated and it eventually decays into $Lambda p$, we calculate the cross section of the $K^{-} {}^{3} text{He} to Lambda p n$ reaction, which was recently measured in the J-PARC E15 experiment. We find that the behavior of the calculated differential cross section $d ^{2} sigma / d M_{Lambda p} d q_{Lambda p}$, where $M_{Lambda p}$ and $q_{Lambda p}$ are the $Lambda p$ invariant mass and momentum transfer in the $(K^{-} , , n)$ reaction in the laboratory frame, respectively, is consistent with the experiment. Furthermore, we can reproduce almost quantitatively the experimental data of the $Lambda p$ invariant mass spectrum in the momentum transfer window $350 text{ MeV} /c < q_{Lambda p} < 650 text{ MeV} /c$. These facts strongly suggest that the $bar{K} N N$ bound state was indeed generated in the J-PARC E15 experiment.
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We theoretically analyze the $K^{-} {}^{3} text{He} to Lambda p n$ reaction for the $bar{K} N N$ bound-state search in the J-PARC E15 experiment. We find that, by detecting a fast and forward neutron in the final state, an almost on-shell $bar{K}$ is guaranteed, which is essential to make a bound state with two nucleons from ${}^{3} text{He}$. Then, this almost on-shell $bar{K}$ can bring a signal of the $bar{K} N N$ bound state in the $Lambda p$ invariant-mass spectrum, although it inevitably brings a kinematic peak above the $bar{K} N N$ threshold as well. As a consequence, we predict two peaks across the $bar{K} N N$ threshold in the spectrum: the lower peak coming from the $bar{K} N N$ bound state, and the higher one originating from the kinematics.
We have performed an exclusive measurement of the $K^{-}+! ~^{3}{rm He} to Lambda pn$ reaction at an incident kaon momentum of $1 {rm GeV}/c$.In the $Lambda p$ invariant mass spectrum, a clear peak was observed below the mass threshold of $bar{K}!+!N!+!N$, as a signal of the kaonic nuclear bound state, $bar{K}NN$.The binding energy, decay width, and $S$-wave Gaussian reaction form-factor of this state were observed to be $B_{K} = 42pm3({rm stat.})^{+3}_{-4}({rm syst.}) {rm MeV}$, $Gamma_{K} = 100pm7({rm stat.})^{+19}_{-9}({rm syst.}) {rm MeV}$, and $Q_{K} = 383pm11({rm stat.})^{+4}_{-1}({rm syst.}) {rm MeV}/c$, respectively. The total production cross-section of $bar{K}NN$, determined by its $Lambda p$ decay mode, was $sigma^{tot}_{K} cdot BR_{Lambda p} = 9.3pm0.8({rm stat.})^{+1.4}_{-1.0}({rm syst.}) mu{rm b}$.We estimated the branching ratio of the $bar{K}NN$ state to the $Lambda p$ and $Sigma^{0}p$ decay modes as $BR_{Lambda p}/BR_{Sigma^{0}p} sim 1.7$, by assuming that the physical processes leading to the $Sigma N!N$ final states are analogous to those of $Lambda pn$.
The formation of a deeply-bound $K^-pp$ state by the $^3$He(in-flight $K^-$,$n$) reaction is investigated theoretically in the distorted-wave impulse approximation using the Greens function method. The expected inclusive and semi-exclusive spectra at $p_{K^-}$ = 1.0 GeV/c and $theta_n = 0^{circ}$ are calculated for the forthcoming J-PARC E15 experiment. We employ optical potentials between the $K^-$ and ``$pp$ core-nucleus, and demonstrate systematically the dependence of the spectral shape on $V_0$ and $W_0$, which are the real and imaginary parts of the strength for the optical potential, respectively. The necessary condition to observe a distinct peak of the $K^-pp$ bound state with $I=1/2$, $J^pi=0^-$ in the spectrum turns out to be that the value of $V_0$ is deeper than $sim-100$ MeV and $W_0$ shallower than $sim-100$ MeV, of which the strength parameters come up to recent theoretical predictions.
To search for an S= -1 di-baryonic state which decays to $Lambda p$, the $ {rm{}^3He}(K^-,Lambda p)n_{missing}$ reaction was studied at 1.0 GeV/$c$. Unobserved neutrons were kinematically identified from the missing mass $M_X$ of the $ {rm{}^3He}(K^-,Lambda p)X$ reaction in order to have a large acceptance for the $Lambda pn$ final state. The observed $Lambda p n$ events, distributed widely over the kinematically allowed region of the Dalitz plot, establish that the major component comes from a three nucleon absorption process. A concentration of events at a specific neutron kinetic energy was observed in a region of low momentum transfer to the $Lambda p$. To account for the observed peak structure, the simplest S-wave pole was assumed to exist in the reaction channel, having Breit-Wigner form in energy and with a Gaussian form-factor. A minimum $chi^2$ method was applied to deduce its mass $M_X =$ 2355 $ ^{+ 6}_{ - 8}$ (stat.) $ pm 12$ (syst.) MeV/c$^2$, and decay-width $Gamma_X = $ 110 $ ^{+ 19}_{ - 17}$ (stat.) $ pm 27$ (syst.) MeV/c$^2$, respectively. The form factor parameter $Q_X sim$ 400 MeV/$c$ implies that the range of interaction is about 0.5
The $bar{K} + N to K + Xi$ reaction is studied for center-of-momentum energies ranging from threshold to 3 GeV in an effective Lagrangian approach that includes the hyperon $s$- and $u$-channel contributions as well as a phenomenological contact amplitude. The latter accounts for the rescattering term in the scattering equation and possible short-range dynamics not included explicitly in the model. Existing data are well reproduced and three above-the-threshold resonances were found to be required to describe the data, namely, the $Lambda(1890)$, $Sigma(2030)$, and $Sigma(2250)$. For the latter resonance we have assumed the spin-parity of $J^P=5/2^-$ and a mass of 2265 MeV. The $Sigma(2030)$ resonance is crucial in achieving a good reproduction of not only the measured total and differential cross sections, but also the recoil polarization asymmetry. More precise data are required before a more definitive statement can be made about the other two resonances, in particular, about the $Sigma(2250)$ resonance that is introduced to describe a small bump structure observed in the total cross section of $K^- + p to K^+ + Xi^-$. The present analysis also reveals a peculiar behavior of the total cross section data in the threshold energy region in $K^- + p to K^+ + Xi^-$, where the $P$- and $D$-waves dominate instead of the usual $S$-wave. Predictions for the target-recoil asymmetries of the $bar{K} + N to K + Xi$ reaction are also presented.
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