Charmed baryon Λc in nuclear matter

Abstract

Density dependences of the mass and self-energies of Λc in nuclear matter are studied in the parity projected QCD sum rule. Effects of nuclear matter are taken into account through the quark and gluon condensates. It is found that the four-quark condensates give dominant contributions. As the density dependences of the four-quark condensates are not known well, we examine two hypotheses. One is based on the factorization hypothesis (F-type) and the other is derived from the perturbative chiral quark model (QM-type). The F-type strongly depends on density, while the QM-type gives a weaker dependence. It is found that, for the F-type dependence, the energy of Λc increases as the density of nuclear matter grows, that is, Λc feels repulsion. On the other hand, the QM-type predicts a weak attraction (∼ 20 MeV at the normal nuclear density) for Λc in nuclear matter. We carry out a similar analysis of the Λ hyperon and find that the F-type density dependence is too strong to explain the observed binding energy of Λ in nuclei. Thus we conclude that the weak density dependence of the four-quark condensate is more realistic. The scalar and vector self-energies of Λc for the QM-type dependence are found to be much smaller than those of the light baryons.

Recent progress in QCD condensate evaluations and sum rules

“…In Ref. [357] the sum rules were improved by taking into account α s corrections to the Wilson coefficients and employing the parity projected sum rules with a Gaussian kernel. In the same work, the treatment of the density dependence of four-quark condensates was studied in detail.…”

“…It was therefore concluded in Ref. [357] that only the PCQM prescription is suitable for this specific sum rule and hence also for the one of the Λ c . This then leads to an about 20 MeV attraction of the Λ c at normal nuclear matter density.…”

Fate of the charm baryon Λc in cold and hot nuclear matter

“…with the vector-type self-energy Σ v (T, µ), the effective mass M * (T, µ), q the three-dimensional momentum of the Λ c baryon [47] (see also Ref. [62].).…”

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

“…The prospect of an ample production of baryons with charm offered by facilities such as the LHC at CERN [1][2][3], RHIC at BNL [4], J-PARC and KEK in Japan [5,6], or FAIR in Germany [7][8][9] has led to a renewed interest in the in-medium properties of such baryons [10][11][12][13] and also in the question whether they, and notably the lightest charmed baryon, the Λ c (2286), could form bound states with ordinary matter [14][15][16][17][18][19]. In fact, there is a long history of speculations about possible bound systems involving the Λ c [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] that started soon after the discovery of charmed baryons [36,37] (see also the recent reviews [38,39]).…”