Heavy quark symmetry and the Skyrme model

Abstract

We present a consistent way of describing heavy baryons containing a heavy quark as bound states of an SU (2) soliton and heavy mesons. The resulting mass formula reveals the heavy quark symmetry explicitly. By extending the model to the orbitally excited states, we establish the generic structure of the heavy baryon spectrum. As anticipated from the heavy quark spin symmetry, the c-factor denoting the hyperfine splitting constant vanishes and the baryons with the same angular momentum of light degrees of freedom form degenerate doublets. This approach is also applied to the pentaquark exotic baryons, where the conventional c-factor plays no more a role of the hyperfine constant. After diagonalizing the Hamiltonian of order N −1 c , we get the degenerate doublets, which implies the vanishing of genuine hyperfine splitting.

Heavy-quark solitons: towards realistic masses

“…In addition to these bound states in the k = 0 channel, which carry positive energy eigenvalues, solutions with G = 1=2 exist in the k = 1 channel possessing, however, negative energy eigenvalues, the so{called pentaquark states [8]. These solutions describe an antiheavy meson bound to the Skyrmion and correspond to (qqqq Q) states in the quark model.…”

“…We also investigate the so-called pentaquark states [8] in the present model. These are postulated states of the form qqqq Q.…”

“…Many aspects of this interesting but technically involved problem have been treated by various groups [4]{ [8] The baryons under study have the schematic quark structure qqQ, where q stands for a light quark and Q for a heavy quark. In the given approach they are realized as heavy mesons ( qQ) bound to light baryons (qqq).…”

Solitons bound to heavy mesons

“…Diagonalization of those potential matrices yields the results of Refs. [12,13]; that is, degenerate heavy-meson-soliton bound states with binding energy − In case of k π ℓ = 0 + , we have only one state x|k ℓ = 0, 0 3 . Although this state is made of ℓ = 1 angular momentum basis, the associated singularity in the centrifugal energy is canceled by the same one of υ(x) in the potential, and the resulting effective potential is finite at the origin.…”

“…Based on the model Lagrangian of Ref. [11], we have carefully examined this picture to study the heavy baryon states with higher spin [12] and also to study nonstrange pentaquark exotic baryons [13] 3 .…”