Abstract
Charge symmetry breaking (CSB) is particularly strong in the A = 4 mirror hypernuclei . Recent four-body no-core shell model calculations that confront this CSB by introducing Λ-Σ0 mixing to leading-order chiral effective field theory hyperon-nucleon potentials are reviewed, and a shell-model approach to CSB in p-shell Λ hypernuclei is outlined.
Highlights
Charge symmetry of the strong interactions arises in QCD upon neglecting the few-MeV mass difference of up and down quarks
The lightest nuclei to exhibit charge symmetry breaking (CSB) are the A=3 mirror nuclei 3H–3He, where CSB contributes about 70 keV out of the 764 keV Coulomb-dominated binding-energy difference. This CSB contribution is of order 10−3 with respect to the strong interaction contribution in realistic A=3 binding energy calculations, and is consistent in both sign and size with the scattering-length difference app − ann ≈ 1.7 fm [1]. It can be explained by ρ0ω mixing in one-boson exchange models of the N N interaction, or by considering N Δ intermediate-state mass differences in models limited to pseudoscalar meson exchanges [2]
We review recent ab-initio no-core shell model (NCSM) calculaions of the A=4 Λ hypernuclei [14, 15] using a leading order (LO) χEFT Y N CS interaction model [11] in which CSB is generated by implementing Eq (1)
Summary
Charge symmetry of the strong interactions arises in QCD upon neglecting the few-MeV mass difference of up and down quarks. With ΛΣ matrix elements of order 10 MeV, the 3% CSB scale factor in Eq (1) suggests a CSB splitting ΔEx ∼ 300 keV, in good agreement with the observed splitting Ex(4ΛHe)−Ex(4ΛH)= 320 ± 20 keV [6], see Fig. 1 (right) which shows a relatively large splitting of the A=4 mirror hypernuclear g.s. levels, ΔBΛJ=0=233±92 keV [7, 8], with respect to the ≈70 keV CSB splitting in the mirror core nuclei 3H and 3He. Here we review recent ab-initio no-core shell model (NCSM) calculaions of the A=4 Λ hypernuclei [14, 15] using a LO χEFT Y N CS interaction model [11] in which CSB is generated by implementing Eq (1). We briefly review a shell model approach [9], confronting it with some available data in the p shell
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