Relativistic five-quark equations and negative parity pentaquarks

The relativistic five-quark equations are found in the framework of the dispersion relation technique. The solutions of these equations using the method based on the extraction of the leading singularities of the amplitudes are obtained. The five-quark amplitudes for the low-lying pentaquarks including the $u$, $d$, $s$ quarks are calculated. The poles of these amplitudes determine the masses of the negative parity pentaquarks with $I=0,1$ and $J^P={\frac{3}{2}}^{-},{\frac{5}{2}}^{-}$. The mass of the lowest pentaquark with $I=0$ and $J^P={\frac{3}{2}}^{-}$ is equal to 1514 MeV.

Figure 1

Graphic representation of the equations for the five-quark subamplitudes $A_k$ ($k=1–7$) corresponding to the ${\theta }^{+}$ pentaquark.

Figure 2

Graphic representation of the equations for the five-quark subamplitudes $A_k$ ($k=1–6$) corresponding to the ${\theta }^{++}({\theta }^0)$ pentaquark.