Modeling interactions of photons with pseudoscalar and vector mesons

We model the interaction of photons, pseudoscalars, and vector mesons within resonance chiral symmetric theory with SU(3) breaking. The couplings of the model are fitted to the experimental data. Within the developed model we predict the pseudoscalar-exchange light-by-light contributions to the muon anomalous magnetic moment $a_{\mu }^P=(82.8\pm 3.4)\times {10}^{-11}$. The error covers also the model dependence within the class of models considered in this paper. The model was implemented into the Monte Carlo event generator ekhara to simulate reactions $e^{+}{e}^{-}\to e^{+}{e}^{-}P$, $P={\pi }^0,\eta ,{\eta }^{\prime }$ and into the Monte Carlo event generator phokhara to simulate reactions $e^{+}{e}^{-}\to P\gamma (\gamma )$.

Figure 1

Transition form factors ${\gamma }^{*}\gamma P$ in the spacelike region compared to the data.

Figure 2

Experimental data for $\sigma (e^{+}{e}^{-}\to P\gamma )$ compared to the model predictions.

Figure 3

Experimental data for $\sigma (e^{+}{e}^{-}\to P\gamma )$ compared to the model predictions. The region of the $s$ has been limited to the $\omega$ peak.

Figure 4

Experimental data for $\sigma (e^{+}{e}^{-}\to P\gamma )$ compared to the model predictions. The region of the $s$ has been limited to the $\varphi$ peak.

Figure 5

Transition form factor ${\gamma }^{*}\gamma P$ in the timelike region compared to the data.

Figure 6

The form factor $\omega {\pi }^0\gamma$ in the timelike region compared to the data.

Figure 7

The form factor $\varphi P\gamma$ in the timelike region compared to the data.

Figure 8

The differential partial width of the decay $\eta \to {\pi }^0\gamma \gamma$ compared to the data.

Figure 9

The relative difference of differential cross sections calculated with $F_{{\gamma }^{*}{\gamma }^{*}P}(-Q^2,q_1^2)$ (full) and $F_{{\gamma }^{*}{\gamma }^{*}P}(-Q^2,0)$ (approx.). See text for details.

Figure 10

Comparison between LO and NLO cross sections. See text for details.