Pentaquark masses in chiral perturbation theory

Heavy baryon chiral perturbation theory for pentaquarks is applied beyond leading order. The mass splitting in the pentaquark antidecuplet is calculated up to next-to-next-to-leading order in the absence of other exotic multiplets nearby in mass. An expansion in the coupling of the antidecuplet to nonexotic baryons simplifies calculations and makes the pentaquark masses insensitive to the pentaquark-nucleon mass difference. It is assumed that no other pentaquark multiplets are nearby in the mass spectrum. The possibility of determining coupling constants in the chiral Lagrangian on the lattice is discussed. Both positive and negative parities are considered.

Figure 1

(a) A pentaquark-meson-pentaquark vertex. (b) A pentaquark-meson-baryon vertex. This is the only diagram contributing to pentaquark decay at LO in the chiral expansion. (c) A quark mass insertion. This is the only diagram contributing to the pentaquark self-energy at NLO. Double lines are pentaquarks, single lines are baryons, and dashed lines are mesons.

Figure 2

Self-energy corrections appear at third order in the chiral expansion. Double lines are pentaquarks, single lines are baryons, and dashed lines are mesons.

Figure 3

Two insertions of the quark mass term in ${\mathcal{L}}_{PB}^{(2)}$.