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Register a new user$Xi^- t$ quasibound state instead of $LambdaLambda nn$ bound state
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We study the coupled $LambdaLambda nn-Xi^- pnn$ system to check whether the inclusion of channel coupling is able to bind the $LambdaLambda nn$ system. We use a separable potential three-body model of the coupled $LambdaLambda nn - Xi^- pnn$ system as well as a variational four-body calculation with realistic interactions. Our results exclude the possibility of a $LambdaLambda nn$ bound state by a large margin. However, we have found a $Xi^- t$ quasibound state above the $LambdaLambda nn$ threshold.
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We use an existing model of the $LambdaLambda N - Xi NN$ three-body system based in two-body separable interactions to study the $(I,J^P)=(1/2,1/2^+)$ three-body channel. For the $LambdaLambda$, $Xi N$, and $LambdaLambda - Xi N$ amplitudes we have constructed separable potentials based on the most recent results of the HAL QCD Collaboration. They are characterized by the existence of a resonance just below or above the $Xi N$ threshold in the so-called $H$-dibaryon channel, $(i,j^p)=(0,0^+)$. A three-body resonance appears {2.3} MeV above the $Xi d$ threshold. We show that if the $LambdaLambda - Xi N$ $H$-dibaryon channel is not considered, the $LambdaLambda N - Xi NN$ $S$ wave resonance disappears. Thus, the possible existence of a $LambdaLambda N - Xi NN$ resonance would be sensitive to the $LambdaLambda - Xi N$ interaction. The existence or nonexistence of this resonance could be evidenced by measuring, for example, the $Xi d$ cross section.
The Faddeev equations for the $Xi NN$ bound-state problem are solved where the three $S$=$-2$ baryon-baryon interactions of Julich-Bonn-Munchen chiral EFT, HAL QCD and Nijmegen ESC08c are used. The $T$-matrix $T_{Xi N, Xi N}$ obtained within the original $LambdaLambda$-$Xi N$-$SigmaSigma$ $/$ $Xi N$-$Lambda Sigma$-$SigmaSigma$ coupled-channel framework is employed as an input to the equations. We found no bound state for Julich-Bonn-Munchen chiral EFT and HAL QCD but ESC08c generates a bound state with the total isospin and spin-parity $(T,J^{pi})=(1/2, 3/2^+)$ where the decays into $LambdaLambda N$ are suppressed.
Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches this procedure does not involve the use of delta-function constraints on the relative four-momentum. In the absence of negative-energy states, the kernels of the three-dimensional equations derived by this technique may be represented as sums of time-ordered perturbation theory diagrams. Consequently, such equations have two major advantages over quasi-potential equations: they may easily be written down in any Lorentz frame, and they include the meson-retardation effects present in the original four-dimensional equation. Secondly, a simple four-dimensional equation with the correct one-body limit is obtained by a reorganization of the generalized ladder Bethe-Salpeter kernel. Thirdly, our approach to deriving three-dimensional equations is applied to this four-dimensional equation, thus yielding a retarded interaction for use in the three-dimensional bound-state equation of Wallace and Mandelzweig. The resulting three-dimensional equation has the correct one-body limit and may be systematically improved upon. The quality of the three-dimensional equation, and our general technique for deriving such equations, is then tested by calculating bound-state properties in a scalar field theory using six different bound-state equations. It is found that equations obtained using the method espoused here approximate the wave functions obtained from their parent four-dimensional equations significantly better than the corresponding quasi-potential equations do.
In an emulsion-counter hybrid experiment performed at J-PARC, a $Xi^-$ absorption event was observed which decayed into twin single-$Lambda$ hypernuclei. Kinematic calculations enabled a unique identification of the reaction process as $Xi^{-} + ^{14}$N$ rightarrow ^{10}_Lambda$Be + $^5_Lambda$He. For the binding energy of the $Xi^{-}$ hyperon in the $Xi^-$-$^{14}$N system a value of $1.27 pm 0.21$ MeV was deduced. The energy level of $Xi^-$ is likely a nuclear $1p$ state which indicates a weak ${Xi}N$-$LambdaLambda$ coupling.
We highlight Hermiticity issues in bound-state equations whose kernels are subject to a highly asymmetric mass and momentum distribution and whose eigenvalue spectrum becomes complex for radially excited states. We trace back the presence of imaginary components in the eigenvalues and wave functions to truncation artifacts and suggest how they can be eliminated in the case of charmed mesons. The solutions of the gap equation in the complex plane, which play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are discussed for several interaction models and qualitatively and quantitatively compared to analytic continuations by means of complex-conjugate pole models fitted to real solutions.
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