$\rho$ meson photoproduction at low energies

The $\sigma$-exchange and $f_2$-exchange mechanisms for $\rho$ meson photoproduction are reexamined. Then the commonly employed $\sigma$-exchange amplitude is revised by using the recent information from the analyses on the $\rho \to {\pi }^0{\pi }^0\gamma$ decay and the $\sigma NN$ coupling constant from Bonn potential. Instead of relying on the Pomeron-$f$ proportionality assumption, the $f_2$ meson exchange amplitude is established from an effective Lagrangian which is constructed from the tensor structure of the $f_2$ meson. Phenomenological information together with tensor meson dominance and vector meson dominance assumptions are used to estimate the $f_2$ coupling constants. As a first step to improve the current theoretical models, we have also explored the effects due to the uncorrelated $2\pi$-exchange amplitude with $\pi N$ intermediate state. This leading-order $2\pi$-exchange amplitude can be calculated using the coupling constants determined from the study of pion photoproduction and the empirical width of $\rho \to \pi \pi$ decay. In comparing with the existing differential cross section data, we find that a model with the constructed $2\pi$, $\sigma$, and $f_2$ exchanges is comparable to the commonly used $\sigma$-exchange model in which the $\sigma$ coupling parameters are simply adjusted to fit the experimental data. We suggest that experimental verifications of the predicted single and double spin asymmetries in the small $\mid t\mid \left(<2{\text{GeV}}^2\right)$ region will be useful for distinguishing the two models and improving our understanding of the nonresonant amplitude of $\rho$ photoproduction. Possible further improvements of the model are discussed.

Figure 1

Models for $\rho$ photoproduction. (a,b) $t$-channel Pomeron and one-meson exchanges $\left(M=f_2,\pi ,\eta ,\sigma \right)$, (c,d) $s$- and $u$-channel nucleon pole terms.

Figure 2

$2\pi$ exchange in $\rho$ photoproduction. The intermediate meson state $M$ includes $\pi$, and the baryon $B$ includes the nucleon.

Figure 3

Differential cross sections of model (A) at $E_{\gamma }=\left(\mathrm{a}\right)2.8$, (b) 3.28, (c) 3.55, and (d) $3.82\text{GeV}$. The dot-dashed lines are from $\sigma$ exchange and the dashed lines are without $\sigma$ exchange. The solid lines are the full calculation. Experimental data are from Ref. 52 (open squares) and Ref. 3 (filled circles).

Figure 4

Differential cross sections of model (B) at $E_{\gamma }=\left(\mathrm{a}\right)2.8$, (b) 3.28, (c) 3.55, and (d) $3.82\text{GeV}$. The dot-dashed lines are from $f_2$ exchange, the dashed lines are from $2\pi$ and $\sigma$ exchanges, and the dotted lines are from the other processes, i.e., without $f_2$, $2\pi$, and $\sigma$ exchanges. The solid lines are the full calculation. Experimental data are from Ref. 52 (open squares) and Ref. 3 (filled circles).

Figure 5

Differential cross sections of model (A) and (B) at $E_{\gamma }=\left(1\right)2.8$, (b) 3.28, (c) 3.55, and (d) $3.82\text{GeV}$. The dashed lines are the results of model (A) and the solid lines are those of model (B). Experimental data are from Refs. 3, 52.

Figure 6

Single spin asymmetries of model (A) and (B) at $E_{\gamma }=3.55\text{GeV}$. Notations are the same as in Fig. 5. The definitions of the spin asymmetries are from Ref. 37.

Figure 7

Double spin asymmetries $C_{zx}^{\text{BT}}$, $C_{zz}^{\text{BT}}$, $C_{z{x}^{\prime }}^{\text{BR}}$, and $C_{z{z}^{\prime }}^{\text{BR}}$ of model (A) and (B) at $E_{\gamma }=3.55\text{GeV}$. Notations are the same as in Fig. 5.

Figure 8

Spin asymmetries $P_{\sigma }$ and ${\Sigma }_{\varphi }$ of model (A) and (B) at $E_{\gamma }=3.55\text{GeV}$. Notations are the same as in Fig. 5.

Figure 9

$f_2\to \gamma \gamma$ decay in vector meson dominance.

Figure 10

$f_2\to V\gamma$ decay in vector meson dominance.