Study of pentaquarks on the lattice with overlap fermions

We present a quenched lattice QCD calculation of spin-$1/2$ five-quark states with $uudd\overline{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either $I=0$ or $I=1$. The states we found are consistent with $KN$ scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results are based on overlap-fermion propagators on two lattices, ${12}^3\times 28$ and ${16}^3\times 28$, with the same lattice spacing of 0.2 fm, and pion mass as low as $\sim 180\mathrm{M}\mathrm{e}\mathrm{V}$.

Figure 1

Nucleon and kaon masses as a function of $m_{\pi }^2$ for the 3.2 fm lattice. Experimental values are represented by the star symbols.

Figure 2

Correlation functions for the positive-parity (first column) and the negative-parity (second column) for 2.4 fm (first row) and 3.2 fm (second row), respectively, (at a pion mass around 200 MeV). One should notice that the scale in the top left figure is different than the others. This shows that for the positive-parity channel the ghost state is more prominent for the smaller lattice, while no ghost state is detected for the negative-parity channel.

Figure 3

Correlation functions for the positive-parity (first column) and the negative-parity (second column) for 2.4 fm (first three rows) and 3.2 fm (second three rows) lattices, respectively. These correlation functions are for three pion masses (in MeV). One should notice that there are negative dips in the positive-parity channel which indicate the presence of ghost states. These $KN{\eta }^{\prime }$ ghost states decouple from the correlation function at pion mass above $\sim 300\mathrm{M}\mathrm{e}\mathrm{V}$.

Figure 4

The computed ground state mass in the $I(J^P)=0(1/2^{-})$ channel as a function of $m_{\pi }^2$ for the two lattices $L=2.4\mathrm{f}\mathrm{m}$ and $L=3.2\mathrm{f}\mathrm{m}$. The curve is the $KN$ threshold energy in the $S$-wave $E_{KN}(n=0)=m_K+m_N$. The bottom figure is an enlarged version of the top figure for the small quark mass region.

Figure 5

The computed ground state mass in the $I(J^P)=1(1/2^{-})$ channel as a function of $m_{\pi }^2$. As in Fig. 4, the curve is the $KN$ threshold energy in the $S$-wave $E_{KN}(n=0)=m_K+m_N$, and the bottom figure is an enlarged version of the top figure for the small quark mass region.

Figure 6

The computed masses in the $I(J^P)=0(1/2^{-})$ (top) $1(1/2^{-})$ (bottom) channels as a function of $m_{\pi }^2$ (for 3.2 fm lattice). The first excited states (square) are shown along with the ground state (circle). The first few scattering states corresponding to different discrete momenta (for $n=0,1,2,3\mathrm{\text{and}}4$) are shown by dashed lines.

Figure 7

The computed mass in the $I(J^P)=0(1/2^{+})$ channel as a function of $m_{\pi }^2$ for the two lattices $L=2.4\mathrm{f}\mathrm{m}$ and $L=3.2\mathrm{f}\mathrm{m}$. The two lower curves are the $KN$ threshold energies in the $P$-wave $E_{KN}(n=1)$. The two higher curves represent the energies of the noninteracting ghost states.

Figure 8

The computed mass in the $I(J^P)=1(1/2^{+})$ channel as a function of $m_{\pi }^2$ for the two lattices $L=2.4\mathrm{f}\mathrm{m}$ and $L=3.2\mathrm{f}\mathrm{m}$. The two lower curves are the $KN$ threshold energies in the $P$-wave $E_{KN}(n=1)$. The two higher curves represent the energies of the noninteracting ghost states. The bottom figure is an enlarged version of the top figure in the lower quark mass region.

Figure 9

A comparison of ground state masses as a function of $m_{\pi }^2$ for $I=0$ and $I=1$ channels both for the negative (top) and the positive (bottom) parities.

Figure 10

Ratio of spectral weights on the two lattices in the negative-parity $I=0$ (top figure) and $I=1$ (bottom figure) channels. The line at 2.37 is the expected volume dependence of the spectral weight.

Figure 11

Ratio of spectral weights of the two lattices for $I(J^P)=1(1/2^{+})$ channel. The line at 2.37 is the expected volume dependence of the spectral weight.