$\pi N\to \eta N$ Data Require the Existence of the $N(1710)$ $P_{11}$ Resonance, Reducing the 1700-MeV Continuum Ambiguity

In spite of long-lasting discussions, the agreement on the existence of the $N(1710)$ $P_{11}$ resonance has not yet been reached, so the Particle Data Group declares it as a 3-star resonance only. We show that the proper inclusion of inelastic channels in the coupled-channel formalism indisputably demands the existence of the $N(1710)$ $P_{11}$ state, and that it presumably stays hidden within the continuum ambiguity of a typical single-channel partial-wave analysis. Consequently, the Particle Data Group confidence rating of this state should be raised to a 4-star resonance.

Figure 1

The agreement of the input $T_{\pi N\pi N}$ values with the results of the fit.

Figure 2

The agreement of the input $T_{\pi N\eta N}$ values with the results of the fit.

Figure 3

The prediction for the $T_{\pi N{\pi }^{2}N}$ amplitude for the best three- and the only four-bare-propagator pole solution.