The onset of ΛΛ hypernuclear binding

Abstract

Binding energies of light, A ≤ 6, ΛΛ hypernuclei are calculated using the stochastic variational method in a pionless effective field theory (/ πEFT) approach at leading order with the purpose of assessing critically the onset of binding in the strangeness S = −2 hadronic sector. The / πEFT input in this sector consists of (i) a ΛΛ contact term constrained by the ΛΛ scattering length aΛΛ, using a range of values compatible with ΛΛ correlations observed in relativistic heavy ion collisions, and (ii) a ΛΛN contact term constrained by the only available A ≤ 6 ΛΛ hypernucler binding energy datum of 6 ΛΛ He. The recently debated neutral three-body and four-body systems 3 ΛΛ n and 4 ΛΛ n are found unbound by a wide margin. A relatively large value of |aΛΛ| 1.5 fm is needed to bind 4 ΛΛ H, thereby questioning its particle stability. In contrast, the particle stability of the A = 5 ΛΛ hypernuclear isodoublet 5 ΛΛ H-5 ΛΛ He is robust, with Λ separation energy of order 1 MeV. PACS numbers: Introduction. Single-Λ and double-Λ (ΛΛ) hypernuclei provide a unique extension of nuclear physics into strange hadronic matter [1]. Whereas the behavior of a single Λ hyperon in atomic nuclei has been deduced quantitatively by studying Λ hypernuclei ( A Λ Z) from A=3 to 208 [2], only three ΛΛ hypernuclei ( A ΛΛ Z) are firmly established: the lightest known 6 ΛΛ He Nagara event [3] and two heavier ones, 10 ΛΛ Be and 13 ΛΛ B [4]. Remarkably, their binding energies come out consistently in shell-model calculations [5]. Few ambiguous emulsion events from KEK [6] and J- PARC [7] have also been reported. However, and perhaps more significant is the absence of any good data on the onset of ΛΛ hypernuclear binding for A < 6. In distinction from the heavier species, these very light s-shell species, if bound, could be more affected by microscopic strangeness S = −2 dynamics. An obvious issue is the effect of a possible ΞN dominated H dibaryon resonance some 20-30 MeV above the ΛΛ threshold [8,9] on ΛΛ hypernuclear binding in general.Several calculations of light A < 6 s-shell ΛΛ hypernuclei using ΛΛ interactions fitted to 6 ΛΛ He suggest a fairly weak ΛΛ interaction, with the onset of ΛΛ hypernuclear binding defered to A = 4. Indeed, a slightly bound I = 0

Jacobi no-core shell model for p-shell hypernuclei

“…(18) onto the basis Eq. (19), one obtains the flow equation in form of an integro-differential equation…”

“…For local interactions, configuration space methods, e.g. hyperspherical harmonics, Green's function Monte Carlo, expansion in Gaussians or stochastic variational method (SVM), have been successfully used to predict properties of light hypernuclei [16][17][18][19][20]. For very light systems, that goal can be likewise achieved by solving the Faddeevor Yakubovsky equations in momentum space [15,[21][22][23][24][25].…”

Possible Lightest Ξ Hypernucleus with Modern ΞN Interactions

“…Two bound states are found B Ξ = 13.5 MeV with (T, J π ) = (1/2, 3/2 + ) and B Ξ = 0.012 MeV with (T, J π ) = (1/2, 1/2 + ) with respect to the d + Ξ threshold. In addition, one bound state is found to be 1 33. MeV with (T, J π ) = (3/2, 1/2 + ) with respect to the D * + N threshold.…”

Neutral baryonic systems with strangeness

“…14, using local central Yukawatype Malfliet-Tjon interactions, concluded that the ΛΛnn system is unbound by a large margin. A recent calculation using the stochastic variational method in a pionless effective field theory approach 15 come to the identical conclusion. It is important to notice that in order to create a ΛΛnn bound state the four particles must coincide simultaneously since the system does not contain two-or three-body subsystem bound states, so that the probability of the event occurring is rather small.…”

“…Pionless effective field theory and the 3 ΛΛ n and 4 ΛΛ n systems Recently, Contessi et al 15 used a stochastic variational method to perform the first comprehensive pionless effective field theory study of ΛΛ hypernuclei with A ≤ 6. In addition to the interaction terms involved in the description of single-Λ hypernuclei, a two-body ΛΛ contact term constrained to the ΛΛ scattering length a ΛΛ was considered.…”