The Θ+ (1540) as a heptaquark with the overlap of a pion, a kaon and a nucleon

We study the very recently discovered Θ+ (1540) at SPring-8, at ITEP and at CLASThomas Jefferson Lab. We apply the same RGM techniques that already explained with success the repulsive hard core of nucleon-nucleon, kaon-nucleon exotic scattering, and the attractive hard core present in pion-nucleon and pion-pion non-exotic scattering. We find that the K −N repulsion excludes the Θ+ as a K −N s-wave pentaquark. We explore the Θ+ as heptaquark, equivalent to a N + π + K borromean boundstate, with positive parity and total isospin I = 0. We find that the kaon-nucleon repulsion is cancelled by the attraction existing both in the pion-nucleon and pionkaon channels. Although we are not yet able to bind the total three body system, we find that the Θ+ may still be a heptaquark state. In this talk we study the exotic hadron Θ+ [1] (narrow hadron resonance of 1540 MeV decaying into a nK+) very recently discovered at Spring-8 [2], and confirmed by ITEP [3] and by CLAS at the TJNL [4]. This is an extremely exciting state because it may be the first exotic hadron to be discovered, with quantum numbers that cannot be interpreted as a quark and an anti-quark meson or as a three quark baryon. Very recent studies propose that the Θ+ is a pentaquark state [5]. Exotic multiquarks are expected since the early works of Jaffe [6, 7], and some years ago Diakonov, Petrov and Polyakov [8] applied skyrmions to a precise prediction of the Θ+. The nature of this particle, and its isospin, parity [9] and angular momentum are yet to be determined. We start in this talk by reviewing the Quark Model (QM) and the Resonating Group Method (RGM) [10], which are adequate to study states where several quarks overlap. We show that the QM, together with chiral symmetry, produces hard core hadronhadron potentials, which can be either repulsive or attractive. First we apply the RGM to show [11, 12] that the exotic N −K hard core s-wave interaction is repulsive. This is consistent with the experimental data [13], see Fig. 1. We think that this excludes the Θ+ as a bare s-wave pentaquark uddus̄ state or a tightly bound s-wave N −K narrow resonance. The observed mass of the Θ+ is larger than the sum of the K and N masses by 1540− 939− 493 = 118 MeV , and this does not suggest a simple K −N binding. However a π could also be present in this system, in which case the binding energy would be of the order of 20 MeV . Moreover this state of seven quarks would have a positive parity, and would have to decay to a p-wave N−K system, which is suppressed by angular momentum, thus explaining the narrow width of the Θ+. With this natural description in mind we then apply the RGM to show that the π −N and π −K hard core interactions are attractive. Finally we put together the π −N, π −K and N −K interactions to show that the Θ+ is possibly a borromean [14] three body s-wave bound ····· ····· ····· ····· ····· ····· ····· ····· ····· ····· ····· ····· ····· ····· ····· · 0.5 1 1.5 2 2.5 -0.4 -0.3 -0.2 -0.1 plab [Fm−1]