Understanding Pentaquark States in QCD

We estimate the mass of the pentaquark state with QCD sum rules and find that pentaquark states with isospin $I=0,1,2$ lie close to each other around $(1.55\pm 0.15)\mathrm{G}\mathrm{e}\mathrm{V}$. The experimentally observed baryon resonance ${\Theta }^{+}(1540)$ with $S=+1$ can be consistently identified as a pentaquark state if its $J^P={\frac{1}{2}}^{-}$. Such a state is expected in QCD. If its parity is positive, this pentaquark state is really exotic. The outstanding issue now is to determine its quantum numbers experimentally.

Figure 1

The variation of the $I=2$ pentaquark state mass $M_2$ with the Borel parameter $T^2$ (in units of ${\mathrm{G}\mathrm{e}\mathrm{V}}^2$) and the continuum threshold $s_0$. From bottom to top the curves correspond to $s_0=3.61,4.0,4.41{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, respectively.

Figure 2

The variation of the $I=0$ pentaquark state mass $M_0$ with the Borel parameter $T^2$ (in units of ${\mathrm{G}\mathrm{e}\mathrm{V}}^2$) and the continuum threshold $s_0$. From bottom to top the curves correspond to $s_0=3.61,4.0,4.41{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, respectively.