Search for the pentaquark resonance signature in lattice QCD

Claims concerning the possible discovery of the ${\Theta }^{+}$ pentaquark, with minimal quark content $uudd\overline{s}$, have motivated our comprehensive study into possible pentaquark states using lattice QCD. We review various spin-$\frac{1}{2}$ pentaquark interpolating fields in the literature and create a new candidate ideal for lattice QCD simulations. Using these interpolating fields we attempt to isolate a signal for a five-quark resonance. Calculations are performed using improved actions on a large ${20}^3\times 40$ lattice in the quenched approximation. The standard lattice resonance signal of binding at quark masses near the physical regime, observed for established baryon resonances, is not observed for spin-$\frac{1}{2}$ pentaquark states. Thus we find no evidence supporting the existence of a spin-$\frac{1}{2}$ pentaquark resonance in quenched QCD.

Figure 1

Mass difference between the lowest-lying negative-parity excited nucleon bound state, the $I(J^P)=\frac{1}{2}({\frac{1}{2}}^{-})N^{*}(1535)$, and the $S$-wave $N+\pi$ two-particle scattering state.

Figure 2

Mass difference between the $I(J^P)=\frac{3}{2}({\frac{3}{2}}^{+})\Delta (1232)$ and the $P$-wave $N+\pi$ two-particle scattering state.

Figure 3

Effective mass of the $I(J^P)=0({\frac{1}{2}}^{-})$ color-singlet $NK$-type pentaquark interpolator, ${\chi }_{NK}$. The data correspond to $m_{\pi }\simeq 830\mathrm{MeV}$ (squares), 700 MeV (circles), and 530 MeV (triangles).

Figure 4

As in Fig. 3, but for the $I(J^P)=0({\frac{1}{2}}^{-})$ color-fused $NK$-type pentaquark interpolator, ${\chi }_{\widetilde{NK}}$.

Figure 5

As in Fig. 3, but for the $I(J^P)=0({\frac{1}{2}}^{-})$ $PS$-type pentaquark interpolator, ${\chi }_{PS}$.

Figure 6

Masses of the $I(J^P)=0({\frac{1}{2}}^{-})$ states extracted with the color-singlet $NK$, color-fused $\widetilde{NK}$, and $PS$-type pentaquark interpolating fields as a function of $m_{\pi }^2$. For comparison, the masses of the $S$-wave $N+K$, $N+K^{*}$, and $N^{\prime }+K$ two-particle states are also shown. Some of the points have been offset horizontally for clarity.

Figure 7

Effective mass difference between the $I(J^P)=0({\frac{1}{2}}^{-})$ state extracted with the color-singlet $NK$-type pentaquark interpolator, ${\chi }_{NK}$, and the $S$-wave $N+K$ two-particle state. The data correspond to $m_{\pi }\simeq 830\mathrm{MeV}$ (squares), 700 MeV (circles), and 530 MeV (triangles).

Figure 8

As in Fig. 7, but for the $I(J^P)=0({\frac{1}{2}}^{-})$ $PS$-type interpolating field, ${\chi }_{PS}$.

Figure 9

Mass difference between the $I(J^P)=0({\frac{1}{2}}^{-})$ state extracted with the $NK$-type pentaquark interpolating field and the $S$-wave $N+K$ two-particle state.

Figure 10

Mass difference between the $I(J^P)=0({\frac{1}{2}}^{-})$ state extracted with the $PS$-type pentaquark interpolating field and the $S$-wave $N+K$ two-particle state.

Figure 11

Effective mass of the $I(J^P)=1({\frac{1}{2}}^{-})$ state corresponding to the $NK$-type pentaquark “state 1” for several values of $m_{\pi }$, $m_{\pi }\simeq 830\mathrm{MeV}$ (squares), 700 MeV (circles), and 530 MeV (triangles).

Figure 12

As in Fig. 11, but for the $I(J^P)=1({\frac{1}{2}}^{-})$ $NK$-type pentaquark “state 2.”

Figure 13

As in Fig. 11, but for the $I(J^P)=1({\frac{1}{2}}^{-})$ $SS$-type interpolator, ${\chi }_{SS}$.

Figure 14

Masses of the $I(J^P)=1({\frac{1}{2}}^{-})$ states extracted with the $NK$- and $SS$-type pentaquark interpolating fields as a function of $m_{\pi }^2$, compared with the masses of the $S$-wave $N+K$, $N+K^{*}$, and $\Delta +K^{*}$ two-particle states. Some of the points have been offset horizontally for clarity.

Figure 15

Mass difference between the $I(J^P)=1({\frac{1}{2}}^{-})$ state corresponding to the $NK$-type pentaquark “state 1” and the $S$-wave $N+K$ two-particle state.

Figure 16

Mass difference between the $I(J^P)=1({\frac{1}{2}}^{-})$ state corresponding to the $NK$-type pentaquark “state 2” and the $S$-wave $N+K^{*}$ two-particle state.

Figure 17

Mass difference between the $I(J^P)=1({\frac{1}{2}}^{-})$ state extracted with the $SS$-type pentaquark interpolating field and the $S$-wave $N+K$ two-particle state.

Figure 18

Effective mass of the $I(J^P)=0({\frac{1}{2}}^{+})$ color-singlet $NK$-type pentaquark interpolator, ${\chi }_{NK}$, for $m_{\pi }\simeq 830\mathrm{MeV}$ (squares), 700 MeV (circles), and 530 MeV (triangles).

Figure 19

As in Fig. 18, but for the $I(J^P)=0({\frac{1}{2}}^{+})$ $PS$-type pentaquark interpolator, ${\chi }_{PS}$.

Figure 20

Masses of the $I(J^P)=0({\frac{1}{2}}^{+})$ states extracted with the color-singlet $NK$- and $PS$-type pentaquark interpolating fields as a function of $m_{\pi }^2$. For comparison, the masses of the $P$-wave $N+K$ and $N+K^{*}$ and $S$-wave $N^{*}+K$ two-particle states are also shown. Some of the points have been offset horizontally for clarity.

Figure 21

Mass difference between the $I(J^P)=0({\frac{1}{2}}^{+})$ state extracted with the $NK$-type pentaquark interpolating field and the $P$-wave $N+K$ two-particle state.

Figure 22

Mass difference between the $I(J^P)=0({\frac{1}{2}}^{+})$ state extracted with the $PS$-type pentaquark interpolating field and the $P$-wave $N+K$ two-particle state.

Figure 23

Effective mass of the $I(J^P)=1({\frac{1}{2}}^{+})$ color-singlet $NK$-type pentaquark interpolator, ${\chi }_{NK}$. The data correspond to $m_{\pi }\simeq 830\mathrm{MeV}$ (squares) and 700 MeV (circles).

Figure 24

As in Fig. 23, but for the $I(J^P)=1({\frac{1}{2}}^{+})$ $SS$-type pentaquark interpolator, ${\chi }_{SS}$.

Figure 25

Masses of the $I(J^P)=1({\frac{1}{2}}^{+})$ states extracted with the color-singlet $NK$- and $SS$-type pentaquark interpolating fields as a function of $m_{\pi }^2$. For comparison, the masses of the $P$-wave $N+K$, $S$-wave $N^{*}+K$, and $P$-wave $N+K^{*}$ two-particle states are also shown. Some of the points have been offset horizontally for clarity.

Figure 26

Mass difference between the $I(J^P)=1({\frac{1}{2}}^{+})$ state extracted with the $NK$-type pentaquark interpolating field and the $P$-wave $N+K$ two-particle state.

Figure 27

Mass difference between the $I(J^P)=1({\frac{1}{2}}^{+})$ state extracted with the $SS$-type pentaquark interpolating field and the $P$-wave $N+K$ two-particle state.

Figure 28

Compilation of results for the lowest-lying $I(J^P)=0({\frac{1}{2}}^{-})$ state from lattice QCD pentaquark studies.