Scrutinizing the evidence for $N\left(1685\right)$

The helicity-dependent observable $E$ for the reaction $\gamma d\to \eta n\left(p\right)$ with a spectator proton was recently measured by the A2 Collaboration at MAMI in Mainz. The data were interpreted as further evidence for a narrow resonance with spin and parity $J^P=1/2^{+}$ $(P_{11}$ wave). However, a full partial-wave analysis without any narrow resonance leads to an excellent description of the data. Imposing a narrow resonance with the properties suggested by the A2 Collaboration leads to a significant deterioration of the fit quality: there is no need for a narrow resonance.

Figure 1

Legendre coefficients ${\mathrm{A}}_1$ of the angular distributions of ${\sigma }_{1/2},{\sigma }_{3/2}$ [25], and ${\sigma }_{\mathrm{tot}}$ for the reaction $\gamma d\to \eta n\left(p\right)$, where ${\sigma }_{\mathrm{tot}}$ is calculated as $({\sigma }_{1/2}+{\sigma }_{3/2})/2$ as functions of the invariant mass $W$. The experimental results (red circles) are compared to a BnGa fit to the data of Refs. [4, 5] without a narrow resonance (solid curve) or a fit imposing a narrow resonance (dotted curve).

Figure 2

Excitation functions ${\sigma }_{1/2}$ and ${\sigma }_{3/2}$ for five bins in $cos{\theta }_{\eta }^{*}$ for the reactions $\gamma d\to \eta p\left(n\right)$ (top 2 rows) and $\gamma d\to \eta n\left(p\right)$ (bottom 2 rows). Statistical and systematic errors are added quadratically. The solid curves represent the new BnGa fit (which include the data from Ref. [25]) without an additional narrow resonance; the dashed lines represent a fit in which a narrow resonance is imposed with the properties given in Ref. [4]. The two numbers give the ${\chi }^2$ contribution of the bin, the upper number without and the lower number including the narrow resonance.

Figure 3

The total cross sections ${\sigma }_{1/2}$ and ${\sigma }_{3/2}$ for the reactions $\gamma d\to \eta p\left(n\right)$ (top panels) and $\gamma d\to \eta n\left(p\right)$ (bottom panels) and new BnGa fits. The solid lines represent a fit without a narrow resonance, and the dashed lines in the bottom figure represent a fit in which a narrow resonance is imposed with the properties given in Ref. [4].

Figure 4

Increase of ${\chi }^2$ when a narrow resonance with mass $M=1670$ MeV, width $\mathrm{\Gamma }=30$ MeV, and $J^P=1/2^{+}$ is imposed as a function of the signal strength $\tilde{a}=\sqrt{Br\left(\eta n\right)}{A}_n^{1/2}$. The number of data points is 1150.