Abstract
The large charge symmetry breaking (CSB) implied by the Λ binding energy difference ΔBΛ4(0g.s.+)≡BΛ(HeΛ4)−BΛ(HΛ4)=0.35±0.06 MeV of the A=4 mirror hypernuclei ground states, determined from emulsion studies, has defied theoretical attempts to reproduce it in terms of CSB in hyperon masses and in hyperon–nucleon interactions, including one pion exchange arising from Λ–Σ0 mixing. Using a schematic strong-interaction ΛN↔ΣN coupling model developed by Akaishi and collaborators for s-shell Λ hypernuclei, we revisit the evaluation of CSB in the A=4 Λ hypernuclei and extend it to p-shell mirror Λ hypernuclei. The model yields values of ΔBΛ4(0g.s.+)∼0.25 MeV. Smaller size and mostly negative p-shell binding energy differences are calculated for the A=7–10 mirror hypernuclei, in rough agreement with the few available data. CSB is found to reduce by almost 30 keV the 110 keV BΛ10 g.s. doublet splitting anticipated from the hyperon–nucleon strong-interaction spin dependence, thereby explaining the persistent experimental failure to observe the 2exc−→1g.s.−γ-ray transition.
Highlights
Charge symmetry breaking (CSB) in nuclear physics is primarily identified by considering the difference between nn and pp scattering lengths, or the binding-energy difference between the mirror nuclei 3H and 3He [1]
About 70 keV out of the Coulomb-dominated 764 keV bindingenergy difference is commonly attributed to CSB which can be explained either by ρ0ω mixing in one-boson exchange models of the NN interaction, Preprint submitted to Physics Letters B
Which is less than 0.05 for 8ΛLi and less than 0.025 for 1Λ0 B in our (ΛΣ)e coupling model, see Table 3. It was shown in this work how a relatively large CSB contribution of order 250 keV arises in (ΛΣ) coupling models based on Akaishi’s centralinteraction G-matrix calculations in s-shell hypernuclei [16, 17], coming close to the binding energy difference BΛ(4ΛHe)−BΛ(4ΛH) = 350 ± 60 keV deduced from emulsion studies [3]
Summary
Charge symmetry breaking (CSB) in nuclear physics is primarily identified by considering the difference between nn and pp scattering lengths, or the binding-energy difference between the mirror nuclei 3H and 3He [1]. The large ∆BΛ4 values reported for both 0+g.s. and 1+exc states have defied theoretical attempts to explain these differences in terms of hadronic or quark CSB mechanisms within four-body calculations [8, 9, 10, 11, 12]. Accommodating ∆BΛ values in the p shell with ∆BΛ4 by using reasonable phenomenological CSB interactions is impossible, as demonstrated in recent four-body clustermodel calculations of p-shell Λ hypernuclei [15] This difficulty may be connected to the absence of explicit ΛN ↔ ΣN coupling in these cluster-model calculations, given that such explicit coupling was shown to generate nonnegligible CSB contributions to ∆BΛ4 (0+g.s.) [12].
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