We study the two-meson virtual cloud contribution to the self-energy of the $\mathrm{SU}(3)$ antidecuplet, to which the ${\Theta }^{+}$ pentaquark is assumed to belong. This is motivated by the large branching ratio of the $N(1710)$ decay into two pions and one nucleon. We derive effective Lagrangians that describe the $N(1710)$ decay into $N\pi \pi$ with two pions in s or p wave. We obtain increased binding for all members of the antidecuplet and a contribution to the mass splitting between states with different strangeness which is at least $20\%$ of the empirical one. We also provide predictions for three-body decays of the pentaquark antidecuplet.

• Received 1 December 2004

DOI:https://doi.org/10.1103/PhysRevC.71.045205