ΛcNbound states revisited

Abstract

The one-boson exchange potential model for à c N is constructed and the possibility of à c N bound states is examined. We consider an effective Lagrangian for the charmed baryons, à c , AE c , and AE à c , reflecting the heavy quark symmetry, chiral symmetry, and hidden local symmetry. We determine the coupling constants using various methods. With the derived nonrelativistic potentials, we study the bound state problem of the à c N system and relevant coupled channel effects. It is found that molecular bound states of à c N are plausible, for which the channel couplings of AE c N and AE à c N are essential.Lagrangians satisfying the heavy quark symmetry for heavy baryons, chiral symmetry for pions, and hidden local symmetry for vector mesons. The Lagrangian is analogous to the heavy meson version presented in Ref. [42]. As for the unknown coupling constants, we turn to the quark model, chiral multiplets, vector meson dominance, and QCD sum rule. Extension of the study to the bottom case is also interesting, but we would not explore it here. Our paper is organized as follows. After the introduction, we present the effective Lagrangians in Sec. II. Then we determine the coupling constants with various methods in Sec. III. In Sec. IV, we present the derived potentials. The numerical results for the S-wave spin-singlet and triplet à c N are given in Secs. V and VI, respectively. Finally, we present our discussions and conclusions in Sec. VII. II. THE LAGRANGIANHere, we consider the S-wave à c N states and the channels which couple to them, i.e., the I ¼ 1 2 and J P ¼ 0 þ or 1 þ two-baryon states. We consider the contributions from the AE c N and AE à c N channels. It is a 3-channel problem for J P ¼ 0 þ and 7-channel problem for J P ¼ 1 þ . The labels are listed in Table I. Because of the higher mass, we assume that the Áð1232Þ contributions are negligible.In the heavy quark limit, the ground state heavy baryons Qqq form SUð3Þ antitriplet with J P ¼ 1 2 þ and two degenerate sextets with J P ¼ ð 1 2 ; 3 2 Þ þ . As in Ref.[43], we use B" 3 , B 6 , and B à 6 to denote these multiplets. To write down the compact form of the Lagrangians, we use the notation of the superfield S , which is defined by

Hidden-charm and bottom meson-baryon molecules coupled with five-quark states

“…[102]. For the coupling g 4 , this value can also be fixed by the Σ ( * ) c → Λ c π decay, and agrees with the one obtained by the quark model [102].…”

“…The phase factor δ is set at δ = −1, as discussed in Ref. [102]. The heavy baryon fieldsΛ c andΣ ( * ) c(µ) are expressed bŷ…”

The hidden-charm pentaquark and tetraquark states

“…The effective Lagrangians, which were constructed with the heavy quark symmetry and chiral symmetry [253,254,255,256,257,258], were adopted to obtain the OPE effective potentials of the Σ c (2455)D * and Σ * c (2520)D * systems,…”

Exotic baryons as a hadronic molecule in the heavy quark region

“…G i j α (α = π, ρ, ω, σ) is the constant of the (i, j) component given by the coupling constants of the Lagrangians. O i 1 and O j 2 are the (transition) spin operator of the heavy meson and heavy baryon vertices, respectively [31][32][33]40].…”

“…The potential for the isovector mesons, π and ρ, is multiplied by the isospin factor, √ with the dipole-type form factor F(Λ, q) for spatially extended hadrons [14,[31][32][33]40]…”