Predictions for charmed nuclei based on $$Y_c N$$ forces inferred from lattice QCD simulations

Abstract

Charmed nuclei are investigated utilizing $$\varLambda _c N$$ Λ c N and $$\varSigma _c N$$ Σ c N interactions that have been extrapolated from lattice QCD simulations at unphysical masses of $$m_\pi = 410$$ m π = 410 –570 MeV to the physical point using chiral effective field theory as guideline. Calculations of the energies of $$\varLambda _c$$ Λ c single-particle bound states for various charmed nuclei from $$^{\ 5}_{\varLambda _c}$$ Λ c 5 Li to $$^{209}_{\varLambda _c}$$ Λ c 209 Bi are performed using a perturbative many-body approach. This approach allows one to determine the finite nuclei $$\varLambda _c$$ Λ c self-energy from which the energies of the different bound states can be obtained. Though the $$\varLambda _c N$$ Λ c N interaction inferred from the lattice results is only moderately attractive, it supports the existence of charmed nuclei. Already the lightest nucleus considered is found to be bound. The spin-orbit splitting of the p- and d-wave states turns out to be small, as in the case of single $$\varLambda $$ Λ hypernuclei. Additional calculations based on the Faddeev-Yakubovsky equations suggest that also $$A=4$$ A = 4 systems involving a $$\varLambda _c$$ Λ c baryon are likely to be bound, but exclude a bound $$^{\, 3}_{\varLambda _c}\hbox {He}$$ Λ c 3 He state.

Ground State Properties of Charmed Hypernuclei with Mean Field Approach

“…This is also in contrast with the work of Vidaña et al and Haidenbauer et al (see Refs. [26,29] for details) where stronger N-Λ c attraction were found, as in our case.…”

“…The Λ c bound states of QMC calculations are inside the gap defined between model A and Model C of Vidaña et al for the A≤ 50 region. However, the interactions calculated from the HAL QCD with the chiral effective field theory [29] results in a less attractive NΛ c potential compared to the interactions derived from hyperon-nucleon potential of the Jülich group [26], where the binding energy differences are 7.2 ± 1.5 MeV for Model C and 49 ± 1.5 MeV for Model A for 209 Λc Bi charmed hypernucleus. Another recent calculation was done by Wu et al, with QMC model, where coupling constants are obtained from both the naive quark counting rules and the HAL QCD predictions [25].…”

“…Vidaña et al also calculated charmed hypernuclei, using SU(4) extension of the meson-exchange hyperon-nucleon potential of the Jülich group, where phase shifts of Model B and Model C are compatible with the low energy region of extrapolation from Haidenbauer and Krein [26]. Recently, charmed hypernuclei from 5 Λc Li to 209 Λc Bi have been calculated with the same approach developed by Haidenbauer et al [29]. On the contrary to HAL QCD results [27] [26,29] for details) predicted bound Λ c hypernuclei for the A≥ 50 region, where Λ c binding energies are compatible with previous QMC calculations [22][23][24].…”

“…Recently, charmed hypernuclei from 5 Λc Li to 209 Λc Bi have been calculated with the same approach developed by Haidenbauer et al [29]. On the contrary to HAL QCD results [27] [26,29] for details) predicted bound Λ c hypernuclei for the A≥ 50 region, where Λ c binding energies are compatible with previous QMC calculations [22][23][24]. The Λ c bound states of QMC calculations are inside the gap defined between model A and Model C of Vidaña et al for the A≤ 50 region.…”

Comment on "$Λ_c N$ interaction in leading order covariant chiral effective field theory"

“…Such an extrapolation was performed by us in Ref. [4], for Λ c N and in [5] for Σ c N . We used as guideline conventional (non-relativistic) chiral effective field theory (χEFT) [6] up to next-to-leading order (NLO).…”