Comprehensive search for the ${\Theta }^{+}$ pentaquark on the lattice

We study spin $1/2$ isoscalar and isovector, even and odd parity candidates for the ${\Theta }^{+}(1540)$ pentaquark particle using large scale lattice QCD simulations. Previous lattice works led to inconclusive results because so far it has not been possible to unambiguously identify the known scattering spectrum and tell whether additionally a genuine pentaquark state also exists. Here we carry out this analysis using several possible wave functions (operators). Linear combinations of those have a good chance of spanning both the scattering and pentaquark states. Our operator basis is the largest in the literature, and it also includes spatially nontrivial ones with unit orbital angular momentum. The cross correlator we compute is $14\times 14$ with 60 nonvanishing elements. We can clearly distinguish the lowest scattering state(s) in both parity channels up to above the expected location of the pentaquark, but we find no trace of the latter. Based on that we conclude that there are most probably ($\approx 2\sigma /6\sigma$ levels in the negative/positive parity channels) no pentaquark bound states at our quark masses, corresponding to $m_{\pi }=400–630\mathrm{MeV}$. However, we cannot rule out the existence of a pentaquark state at the physical quark mass corresponding to $m_{\pi }=135\mathrm{MeV}$ or pentaquarks with a more exotic wave function.

Figure 1

The effective masses for the first two states in the negative (left panels) and positive (right panels) parity channel for $\kappa =0.1550$ (top panels) and $\kappa =0.1558$ (bottom panels). The lines indicate the fits according to Eq. (13).

Figure 2

The volume dependence of the two lowest states in the two parity channels (left panel: negative parity; right panel: positive parity). The dashed lines indicate the expected scattering states with 0 momentum and the first two nonvanishing momenta. The dotted line shows the experimental value of the pentaquark state.

Figure 3

The relative contribution of different operators to the lowest (left bar) and second lowest (right bar) eigenstate in the negative (left panels) and positive (right panels) parity channel for $\kappa =0.1550$ (top panels) and $\kappa =0.1558$ (bottom panels).