Positive parity pentaquarks in a Goldstone boson exchange model

We study the stability of the pentaquarks uuddQ, uudsQ and udssQ (Q = c, b, or t) of positive parity in a constituent quark model based on Goldstone boson exchange interaction between quarks. The pentaquark parity is the antiquark parity times that of a quark excited to a p-shell. We show that the Goldstone boson exchange interaction favors these pentaquarks much more than the negative parity ones of the same flavour content but all quarks in the ground state. We find that the nonstrange pentaquarks are stable against strong decays. The existence of particles made of more than three quarks is an important issue of QCD inspired model. The interest has been raised so far by particles described by the colour state [222]C , the tetraquarks q q, the pentaquarks qq and the hexaquarks q. The present study is devoted to pentaquarks, first proposed independently by Gignoux, Silvestre-Brac and Richard [1] and Lipkin [2] about ten years ago. Within a constituent quark model based on one-gluon exchange (OGE) interaction, these authors found that the states P 0 cs = |uudsc〉 and P cs = |uddsc〉 and their conjugates are stable against strong decays. Within better approximations, they turned out to be unstable [3,4]. A systematic theoretical study [5] in a model with OGE interaction suggested several candidates for stability, and among them ∗e-mail : [email protected] 1 especially those with strangeness S = -1 or -2. In particular, the uudsc system was bound by -52 MeV. The nonstrange systems uuddQ (Q = c or b) were unbound. Calculations done within an instanton model [6] or a Skyrme model [7] show that pentaquarks, irrespective of their strangeness, appear as bound or near-threshold resonances depending on the model parameters. Moreover, the lowest pentaquark states predicted in Ref. [7] have positive parity (L = 1). If bound, the lifetime of the pentaquark uudsc or uddsc is expected to be similar to that of the D s meson. Using various mechanisms, the typically estimated pentaquark production cross section is of the order of 1 % that of D s [8]. Based on the above theoretical predictions, experiments are being planned and the first search for the pentaquarks P 0 cs and P cs , performed at Fermilab, has just been reported [9]. The decay P 0 cs → φπp was analyzed for two different pentaquark masses : M = 2.75 GeV, being the lowest mass expected from the OGE model and M = 2.86 GeV, the value at which the largest number of events was observed. No convincing evidence for pentaquarks decaying to φπp was observed yet. The theoretical predictions are definitely model-dependent. In a previous work [10], we studied the stability of heavy-flavoured pentaquarks within a chiral constituent quark model [11–13] originally proposed by Glozman and Riska [11]. In this model, the hyperfine splitting in hadrons is obtained from the short-range part of the Goldstone boson exchange (GBE) interaction between quarks, instead of the OGE interaction of conventional models, as discussed above. The main merit of the GBE interaction is that it reproduces the correct ordering of positive and negative parity states in all parts of the considered spectrum [12–14] in contrast to any other OGE model. In Ref. [10], we considered pentaquarks with strangeness ranging from S = -3 to S = 0. There, we assumed that all light quarks are identical and the ground-state orbital (O) wave function is symmetric under permutation of light quarks, i.e. it corresponds to the Young diagram [4]O. The subsystem of light quarks must necessarily be in a colour 3, or alternatively a [211]C state. Then, the Pauli principle allows a certain number of spin [f ]S and flavour [f ]F states to be combined with [4]O and [211]C to give a total antisymmetric 2 four-quark state. We found that any of these states combined with a heavy antiquark Q where Q = c or b gave rise to a pentaquark energy which was at least 300-400 MeV above the dissociation threshold nucleon plus meson, i.e. the considered pentaquark cannot be a bound compact object. Its parity is P = -1, due to the antiquark. The novelty of this study is that, within the same GBE model, we analyse the stability of pentaquarks with P = +1. In such a case, the parity of the pentaquark is given by P = (−)L + 1, thus the light quarks must carry an angular momentum L odd. Here, we consider the case L = 1, which implies that the subsystem of four light quarks must be in a state of orbital symmetry [31]O. Although the kinetic energy of such a state is higher than that of the totally symmetric [4]O state, a schematic estimate [14] suggests that the [31]O symmetry would lead to a stable pentaquark. In the following, we give the arguments of Ref. [14] based on a simplified GBE interaction of the form