Charmed nuclei within a microscopic many-body approach

Single-particle energies of the $\Lambda_c$ chamed baryon are obtained in several nuclei from the relevant self-energy constructed within the framework of a perturbative many-body approach. Results are presented for a charmed baryon-nucleon ($Y_cN$) potential based on a SU(4) extension of the meson-exchange hyperon-nucleon potential $\tilde A$ of the J\"{u}lich group. Three different models (A, B and C) of this interaction, that differ only on the values of the couplings of the scalar $\sigma$ meson with the charmed baryons, are considered. Phase shifts, scattering lengths and effective ranges are computed for the three models and compared with those predicted by the $Y_cN$ interaction derived in Eur. Phys. A {\bf 54}, 199 (2018) from the extrapolation to the physical pion mass of recent results of the HAL QCD Collaboration. Qualitative agreement is found for two of the models (B and C) considered. Our results for $\Lambda_c$-nuclei are compatible with those obtained by other authors based on different models and methods. We find a small spin-orbit splitting of the $p-, d-$ and $f-$wave states as in the case of single $\Lambda$-hypernuclei. The level spacing of $\Lambda_c$ single-particle energies is found to be smaller than that of the corresponding one for hypernuclei. The role of the Coulomb potential and the effect of the coupling of the $\Lambda_cN$ and $\Sigma_cN$ channels on the single-particle properties of $\Lambda_c-$nuclei are also analyzed. Our results show that, despite the Coulomb repulsion between the $\Lambda_c$ and the protons, even the less attractive one of our $Y_cN$ models (model C) is able to bind the $\Lambda_c$ in all the nuclei considered. The effect of the $\Lambda_cN-\Sigma_cN$ coupling is found to be almost negligible due to the large mass difference of the $\Lambda_c$ and $\Sigma_c$ baryons.

[1]  I. Vidaña.  Single-particle spectral function of the Λ hyperon in finite nuclei , 2016, CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST).

[2]  E. Tomasi-Gustafsson.  The P¯ANDA$\mathrm {\overline {P}ANDA}$ experiment at FAIR , 2018, Hyperfine Interactions.

[3]  G. Krein,et al.  Scattering of charmed baryons on nucleons , 2017, The European Physical Journal A.

[4]  Takumi Iritani,et al.  Λ c N interaction from lattice QCD and its application to Λ c hypernuclei , 2017, 1710.05545.

[5]  G. Krein,et al.  Nuclear-bound quarkonia and heavy-flavor hadrons , 2017, 1706.02688.

[6]  K. Tsushima,et al.  Production of Λc+ hypernuclei in antiproton–nucleus collisions , 2016, 1701.02225.

[7]  Advanced Science Research Center,et al.  A model of charmed baryon–nucleon potential and two- and three-body bound states with charmed baryon , 2015, 1509.02445.

[8]  Yan-Rui Liu,et al.  $\Lambda_c N$ bound states revisited , 2011, 1103.4624.

[9]  A. Schäfer,et al.  Prospects of open charm production at GSI-FAIR and J-PARC , 2007, 0708.3010.

[10]  F. Khanna,et al.  Λ+c, Σc, Ξcand Λbhypernuclei in the quark–meson coupling model , 2004 .

[11]  Yu-Hong Tan,et al.  Heavy flavored baryon hypernuclei in a relativistic mean-field model , 2004 .

[12]  F. Khanna,et al.  Properties of charmed and bottom hadrons in nuclear matter: A Plausible study , 2002, nucl-th/0207036.

[13]  Adelaide,et al.  $\Lambda^+_c$- and $\Lambda_b$-hypernuclei , 2002, nucl-th/0207077.

[14]  A. Polls,et al.  Hyperon properties in finite nuclei using realistic YN interactions , 1998, nucl-th/9805032.

[15]  Müther,et al.  Width of the Delta resonance in nuclei. , 1994, Physical review. C, Nuclear physics.

[16]  J. Speth,et al.  Meson-exchange hyperon-nucleon interactions in free scattering and nuclear matter , 1994 .

[17]  J. Hao,et al.  Hypernucleus [sub [Lambda]][sup 16]O and accurate hyperon-nucleon [ital G]-matrix interactions , 1993 .

[18]  Halderson.  g-matrix calculations in finite hypernuclei. , 1993, Physical review. C, Nuclear physics.

[19]  A. Polls,et al.  Effects of short-range correlations on the self-energy in the optical model of finite nuclei , 1992 .

[20]  N. Starkov,et al.  On production of charmed nuclei in charm exchange (D, π) reactions at thecτ-factory , 1991 .

[21]  V. Lyukov.  Study of hypernuclear production and search for supernuclei in proton-nuclear interactions in photoemulsion at 70 and 250 GeV , 1989 .

[22]  F. Iazzi,et al.  Production of heavy flavours in nuclei at the ARES facility , 1989 .

[23]  G. Bhamathi.  Binding in nuclear matter of hyperons and charmed baryons , 1989 .

[24]  H. Bandō.  Chapter VII. Flavor Nuclei , 1985 .

[25]  B. Gibson,et al.  Binding energy estimates for charmed few-body systems , 1983 .

[26]  H. Bandō,et al.  Flavor Nuclei and One-Boson-Exchange Potentials , 1983 .

[27]  H. Bandō.  ?c5He and ?c9Be charmed nuclei versus ?5He and ?9Be hypernuclei , 1982 .

[28]  G. Bhamathi.  Light supernuclei and SU(4) symmetry , 1981 .

[29]  L. A. Ponomarev,et al.  Rescattering by a nucleus of (Nπ) and (3π) beams after their coherent formation , 1981 .

[30]  N. Kolesnikov,et al.  HYPERNUCLEI AND SUPERNUCLEI. (IN RUSSIAN) , 1981 .

[31]  R. Gatto,et al.  Stable charmed hyperfragments , 1978 .

[32]  S. Kahana,et al.  Possibility of Charmed Hypernuclei , 1977 .

[33]  S. Kahana,et al.  Bound states of charmed baryons and antibaryons , 1977 .

[34]  E. Haacke,et al.  A calculation of SU(4) Clebsch–Gordan coefficients , 1976 .

[35]  M. Binkley,et al.  Observation of a Narrow anti-Baryon State at 2.26-GeV/c**2 , 1976 .

[36]  Alam,et al.  Observation in e+e- annihilation of a narrow state at 1865 MeV/c2 decaying to Kπ and Kπππ , 1976 .

[37]  G. E. Fischer,et al.  Observation of a narrow charged state at 1876 MeV/c2 Decaying to an exotic combination of Kππ , 1976 .

[38]  P. Connolly,et al.  Evidence for Delta S = - Delta Q Currents or Charmed Baryon Production by Neutrinos , 1975 .

[39]  S. Wu,et al.  Experimental Observation of a Heavy Particle $J$ , 1974 .

[40]  G. E. Fischer,et al.  Discovery of a Narrow Resonance in $e^+ e^-$ Annihilation , 1974 .