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Register a new userDeeply-bound $K^- pp$ state in the $^3$He(in-flight $K^-$, $n$) spectrum and its moving pole near the $pi Sigma N$ threshold
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The formation of a deeply-bound $K^- pp$ state with $I=1/2$, $J^pi=0^-$ by the $^3$He(in-flight $K^-$, $n$) reaction is theoretically investigated in a distorted-wave impulse approximation using the Greens function method. The expected inclusive and semi-exclusive spectra at $p_{K^-} = 1.0$ GeV/c and $theta_{rm lab} = 0^{circ}$ are calculated for the forthcoming J-PARC E15 experiment. We demonstrate these spectra with several types of phenomenological $K^-$-``$pp$ optical potentials $U^{rm opt}(E)$ which have an energy-dependent imaginary part multiplied by a phase space suppression factor, fitting to recent theoretical predictions or experimental candidates of the $K^-pp$ bound state. The results show that a cusp-like peak at the $pi Sigma N$ threshold is an unique signal for the $K^-pp$ bound state in the spectrum including the [$K^-pp$] $to$ $Y + N$ decay process from the two-nucleon $K^-$ absorption, as well as a distinct peak of the $K^-pp$ bound state. The shape of the spectrum is explained by a trajectory of a moving pole of the $K^-pp$ bound state in the complex energy plane. The importance of the spectrum with [$K^-pp$] $to$ $Y + N$ from the two-nucleon $K^-$ absorption is emphasized in order to extract clear evidence of the $K^-pp$ bound state.
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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
An experiment to search for the $K^-pp$ bound state was performed via the in-flight $^3$He($K^-,n)$ reaction using 5.3 $times$ $10^9$ kaons at 1 GeV/$c$ at the J-PARC hadron experimental facility. In the semi-inclusive neutron missing-mass spectrum at $theta_{n}^{lab}=0^circ$, no significant peak was observed in the region corresponding to $K^-pp$ binding energy larger than 80 MeV, where a bump structure has been reported in the $Lambda p$ final state in different reactions. Assuming the state to be isotropically decaying into $Lambda p$, mass-dependent upper limits on the production cross section were determined to be 30--180, 70--250, and 100--270 $mu$b/sr, for the natural widths of 20, 60, and 100 MeV, respectively, at 95% confidence level.
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.
The cross sections for the reactions pp -> p Lambda^0K^+ and pn -> n Lambda^0K^+ are calculated near threshold of the final states. The theoretical ratio of the cross sections R = sigma(pn -> n Lambda^0K^+)/ sigma(pp ->pLambda^0K^+) = 3 shows the enhancement of the pn interaction with respect to the pp interaction near threshold of the strangeness production N Lambda^0K^+. Such an enhancement is caused by the contribution of the np interaction in the isospin-singlet state, which is stronger than the $pn$ interaction in the isospin-triplet state. For the confirmation of this result we calculate the cross sections for the reactions pp -> pp pi^0, pi^0 p -> Lambda^0 K^+ and pi^-p -> Lambda^0 K^0 near threshold of the final states. The theoretical cross sections agree well with the experimental data.
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