Observation of the $p{\eta }^{\prime }$ Cusp in the New Precise Beam Asymmetry $\mathrm{\Sigma }$ Data for $\gamma p\to p\eta$

Data on the beam asymmetry $\mathrm{\Sigma }$ in the photoproduction of $\eta$ mesons off protons are reported for tagged photon energies from 1130 to 1790 MeV (mass range from $W=1748\mathrm{MeV}$ to $W=2045\mathrm{MeV}$). The data cover the full solid angle that allows for a precise moment analysis. For the first time, a strong cusp effect in a polarization observable has been observed that is an effect of a branch-point singularity at the $p{\eta }^{\prime }$ threshold [$E_{\gamma }=1447\mathrm{MeV}$ ($W=1896\mathrm{MeV}$)]. The latest BnGa partial wave analysis includes the new beam asymmetry data and yields a strong indication for the $N(1895){\frac{1}{2}}^{-}$ nucleon resonance, demonstrating the importance of including all singularities for a correct determination of partial waves and resonance parameters.

Figure 1

New beam asymmetry $\mathrm{\Sigma }$ data (blue points) shown as a function of $\cos {\theta }_{\eta }^{\mathrm{cm}}$ for five different energy bins. The systematic uncertainties are given by the gray area. In the left-hand column, the new $\mathrm{\Sigma }$ data are compared to existing data from the GRAAL collaboration (black triangles) [33] and from the CLAS collaboration (green squares) [34], and with different PWA predictions [BnGa-2014-02 (dotted red line) [9], JüBo-2015-FitB (dash-dotted green line) [14], and $\eta \mathrm{MAID}$-2003 (dashed black line) [12] ]. In the right-hand column, the data are compared to the BnGa-2014-02 (dotted red line) [9] and their latest solution BnGa-2019 (solid red line) [10], which includes the new $\mathrm{\Sigma }$ data.

Figure 2

Fit coefficient $(a_4{)}_4^{\check{\mathrm{\Sigma }}}$. Top: The energy dependence of the fit coefficient $(a_4{)}_4^{\check{\mathrm{\Sigma }}}$ is shown for the $p\eta$ final state (blue points) as extracted from the new CBELSA/TAPS data according to Eq. (3). The continuous curves are evaluated using the BnGa-2019 PWA [10] and truncating at different ${\ell }_{\max }$. Bottom: The GRAAL (black triangles) [33] and the CLAS beam asymmetry data (green squares) [34] were analyzed according to Eq. (3), and the results for the fit coefficient $(a_4{)}_4^{\check{\mathrm{\Sigma }}}$ are compared to the ones of the new CBELSA/TAPS data (blue points). The curve for ${\ell }_{\max }=4$ is shown for the BnGa-2014-02 PWA [9] (dashed black line) and the BnGa-2019 PWA [10] (solid black line).

Figure 3

The $E_{0+}$ multipole of $p\eta$. The real part (upper plot), imaginary part (middle plot), and absolute square (lower plot) of the $E_{0+}$ multipole are depicted for the $p\eta$ final state for several different PWA. The imaginary and real parts are not shown for the $\eta \mathrm{MAID}$-2018 PWA due to different phase conventions [13].