Photoproduction of the ϕ meson off the deuteron near threshold

We discuss coherent and incoherent ϕ meson photoproduction off the deuteron at low energy and small momentum transfer with the aim of checking whether the recent experimental data need for their interpretation an inclusion of exotic channels. Our analysis of the differential cross section and spin-density matrix elements shows that new data on the $\gamma D\to \varphi X$ reaction at $E_{\gamma }~2$ GeV may be understood on the basis of conventional dynamics. However, a certain ambiguity of the deviation between the model predictions and the data from the laser electron photon beamline at SPring-8 (LEPS) on the $\gamma p\to \varphi p$ reaction still remains. To make a firm conclusion about a possible manifestation of exotic channels, one has to improve the resolution of the data by providing additional information on the channels with spin- and double-spin-flip transitions which are sensitive to the properties of the photoproduction amplitude in the $\gamma p$ and $\gamma D$ reactions. This information may be used as an additional independent test of the ϕ meson photoproduction mechanism.

Figure 1

Diagrammatic representation of coherent [(a), (b)] and incoherent [(c), (d)] ϕ meson photoproduction in the $\gamma D$ reactions with single [(a), (c)] and double [(b), (d)] scattering contributions.

Figure 2

Differential cross section of the $\gamma p\to \varphi p$ reaction as a function of momentum transfer $t$ at $E_{\gamma }=2.02$ GeV. The Pomeron and pseudoscalar exchange contributions and total cross section are shown by dot-dashed, dashed, and solid curves, respectively. Data are from LEPS [11], SAPHIR [22], Bonn [23], and JLab [24].

Figure 3

Differential cross section of the $\gamma p\to \varphi p$ reaction at $t=t_{\max }$ ($\theta =0$) as a function of the photon energy. Experimental data are from Refs. [11, 25].

Figure 4

Dependence of the structure factor $Z$ on $t=t_D$.

Figure 5

Differential cross section of the $\gamma D\to \varphi D$ reaction as a function of momentum transfer $t$ ($t=t_D$), with LEPS [15] and CLAS [16] data.

Figure 6

Differential cross section of the $\gamma D\to \varphi D$ reaction at $t=t_{\max }$ ($t=t_D$) as a function of the photon energy. Experimental data are from Ref. [15].

Figure 7

Differential cross section of ϕ meson photoproduction off the proton (solid curve) and off the isoscalar nucleon in the $\gamma D$ reaction. Experimental data are from Refs. [11, 15].

Figure 8

Differential distribution of $[\gamma D,\varphi ]$ missing mass in $\gamma D\to \varphi X$ reactions at different energies. The curves correspond to the cross sections of incoherent $\gamma D\to \varphi (\mathit{pn})$ (dashed) reactions, the coherent $\gamma D\to \gamma D$ (dot-dashed), and their sum (solid). The arrows mark the position of the maximum of the missing mass distribution.

Figure 9

Distribution of $[\gamma D,\varphi ]$ missing mass for the $\gamma D\to \varphi X$ reaction. The histogram corresponds to the experimental data [28]. The theoretical curves are scaled by the factor 3.7 $(\mu {\mathrm{b}}^{/}){}^{-1}$ (see details in text).

Figure 10

Energy dependence of ${\rho }_{00}^0$ for the $\gamma D\to \varphi D$ reaction at (a) $t_0=t_{\max }$ and (b) $t_0=-0.2$ GeV${}^2$; ${\Delta }_t=0.2$ GeV${}^2$. Curves correspond to the explicit $\gamma D$ reactions (solid), the $\gamma D$ reaction with reduced cross sections (dot-dashed), and photoproduction off the free isoscalar nucleon (dashed).

Figure 11

Estimates of ${\rho }_{00}^0$ given by Eq. (33) for $\gamma p$ and $\gamma D$ reactions.

Figure 12

Energy dependence of ${\rho }_{00}^0$ with (a) $t_0=t_{\max }$ and (b) $t_0=-0.2$ GeV${}^2$ . Experimental data are from Ref. [11].

Figure 13

Angular distribution $W(\cos \Theta )$ for the $\gamma D\to \varphi D\to K^{+}{K}^{-}D$ reaction in the helicity frame at $E_{\gamma }=3.1$ GeV and $-t_0=0.3$ GeV${}^2$. Experimental data for two energy intervals and $\left|t\right|=0.35$–0.8 GeV${}^2$ are taken from Ref. [16].

Figure 14

Spin-density matrix elements ${\rho }_{00}^0$ in the helicity and Gottfried-Jackson frames at $\left|t\right|-\left|t_0\right|<0.2$ GeV${}^2$ and $t_0=-0.2$ GeV${}^2$.

Figure 15

Same as Fig. 12, but for $\mathrm{Re}{\rho }_{1-1}^0$.

Figure 16

Same as Fig. 12, but for ${\rho }_{1-1}^1$. Experimental data are from Refs. [11, 15].

Figure 17

Angular distribution $W^L(\Phi -\Psi )$ for the reaction $\gamma p\to \varphi p\to p{K}^{+}{K}^{-}$ at $\left|t\right|-\left|t_{\max }\right|⩽0.2$ GeV${}^2$ for energy intervals (a) $E_{\gamma }=1.97$–2.17 and (b) $E_{\gamma }=2.17$–2.37 GeV. Experimental data are from Ref. [30].

Figure 18

Angular distribution $W^L(\Phi -\Psi )$ for the reaction $\gamma D\to \varphi X\to X{K}^{+}{K}^{-}$ ($X=D,\mathit{np}$) at $\left|t\right|-\left|t_{\max }\right|⩽0.1$ GeV${}^2$. (a) and (b) correspond to the $[\gamma D,\varphi ]$ missing mass smaller or larger than 1.89 GeV, respectively. Experimental data are from Ref. [15].

Figure 19

Energy dependence of $2{\rho }_{11}^1+{\rho }_{00}^1$ for $t_0=t_{\max }$ and $t_0=-0.2$ GeV${}^2$.