Search for a Spin-1 Intermediate Meson in Neutral Pion Photoproduction

If a spin-1 meson exists it might act as an intermediate particle in a meson current graph for neutral pion photoproduction. It is shown that the singularities from this graph are likely to be much closer to the physical region in the complex $x=cos\theta$ plane than any other singularities with the possible exception of those coming from a pion-pion interaction. Thus an extrapolation can be carried out in $x$ to determine the residue of the pole due to the spin-1 meson if it exists. This residue is calculated for vector ($V$) and pseudovector ($\mathrm{PV}$) mesons and is found to have the same negative sign for both cases, unlike in the spin-0 case. Experimental data at 300, 450, 700, and 800 Mev are used for the extrapolation which is carried out as a function of intermediate meson mass. It is found that the results are consistent with zero residue for all energies with the possible exception of 450 Mev where there is a slight evidence for a positive residue. Thus present evidence favors the conclusion that there is no contribution to neutral photoproduction from a spin-1 meson. One can place an upper limit of about 0.01 for the $V$ case and 0.05 for the $\mathrm{PV}$ case on the magnitude of $g^2{\left(\frac{\mathfrak{M}}{2m}\right)}^2$, where $g$ is the coupling constant between the nucleon and the spin-1 meson, and the latter has a mass $m$ and a magnetic moment $\mathfrak{M}$. A detailed analysis is also given of the error in the residue determined from a set of experimental data, as a function of the location and number of data points, the extrapolation distance, and the order of the extrapolating polynomial. It is concluded that the present error in the residue could be improved by a factor of 3 to 5 by an experiment measuring the differential cross section of neutral pion photoproduction at a photon energy of 800 Mev in the laboratory system at every 10° from 10° with an error of ±0.2 μb/sr on the individual measurements.