Meson transition form factors in light-front holographic QCD

We study the photon-to-meson transition form factors (TFFs) $F_{M\gamma }(Q^2)$ for $\gamma {\gamma }^{*}\to M$ using light-front holographic methods. The Chern-Simons action, which is a natural form in five-dimensional anti–de Sitter (AdS) space, is required to describe the anomalous coupling of mesons to photons using holographic methods and leads directly to an expression for the photon-to-pion TFF for a class of confining models. Remarkably, the predicted pion TFF is identical to the leading order QCD result where the distribution amplitude has asymptotic form. The Chern-Simons form is local in AdS space and is thus somewhat limited in its predictability. It only retains the $q\overline{q}$ component of the pion wave function, and further, it projects out only the asymptotic form of the meson distribution amplitude. It is found that in order to describe simultaneously the decay process ${\pi }^0\to \gamma \gamma$ and the pion TFF at the asymptotic limit, a probability for the $q\overline{q}$ component of the pion wave function $P_{q\overline{q}}=0.5$ is required, thus giving indication that the contributions from higher Fock states in the pion light-front wave function need to be included in the analysis. The probability for the Fock state containing four quarks $P_{q\overline{q}q\overline{q}}\sim 10\%$, which follows from analyzing the hadron matrix elements for a dressed current model, agrees with the analysis of the pion elastic form factor using light-front holography including higher Fock components in the pion wave function. The results for the TFFs for the $\eta$ and ${\eta }^{\prime }$ mesons are also presented. The rapid growth of the pion TFF exhibited by the BABAR data at high $Q^2$ is not compatible with the models discussed in this article, whereas the theoretical calculations are in agreement with the experimental data for the $\eta$ and ${\eta }^{\prime }$ TFFs.

Figure 1

The $\gamma {\gamma }^{*}\to {\pi }^0$ transition form factor shown as $Q^2{F}_{\pi \gamma }(Q^2)$ as a function of $Q^2=-q^2$. The dotted curve is the asymptotic result predicted by the Chern-Simons form. The dashed and solid curves include the effects of using a confined EM current for twist-2 and twist-2 plus twist-4, respectively. The data are from 19, 22, 23.

Figure 2

Same as Fig. 1 for $F_{\pi \gamma }(Q^2)$.

Figure 3

Leading-twist contribution (a) and twist-4 contribution (b) to the process $\gamma {\gamma }^{*}\to {\pi }^0$.

Figure 4

The $\gamma {\gamma }^{*}\to \eta$ transition form factor shown as $Q^2{F}_{\eta \gamma }(Q^2)$ as a function of $Q^2=-q^2$. The dotted curve is the asymptotic result. The dashed and solid curves include the effects of using a confined EM current for twist-2 and twist-2 plus twist-4, respectively. The data are from 19, 22, 23.

Figure 5

Same as Fig. 4 for the $\gamma {\gamma }^{*}\to {\eta }^{\prime }$ transition form factor shown as $Q^2{F}_{{\eta }^{\prime }\gamma }(Q^2)$.

Figure 6

Same as Fig. 4 for the $\gamma {\gamma }^{*}\to \eta$ transition form factor shown as $F_{\eta \gamma }(Q^2)$.

Figure 7

Same as Fig. 4 for the $\gamma {\gamma }^{*}\to {\eta }^{\prime }$ transition form factor shown as $F_{{\eta }^{\prime }\gamma }(Q^2)$.