Meson Transition Form Factors in Light-Front Holographic QCD

TL;DR

This paper uses light-front holographic QCD and the Chern-Simons action in AdS space to predict meson transition form factors, highlighting the importance of higher Fock states for accurate modeling.

Contribution

It introduces a holographic approach to compute photon-to-meson transition form factors, emphasizing the role of higher Fock components in the pion wavefunction.

Findings

The pion TFF matches leading order QCD results with asymptotic distribution amplitude.

A qar{q} wavefunction probability of 0.5 is needed to fit decay and TFF data.

Higher Fock states contribute significantly, with a 10% probability for four-quark components.

Abstract

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 5-dimensional anti-de Sitter (AdS) space, 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 \bar q component of the pion wavefunction, 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 \rightarrow gamma gamma and the pion TFF at the asymptotic limit, a probability for the q \bar q component of the pion wavefunction P_{q \bar q}=0.5 is required; thus giving indication that the contributions from higher Fock states in the pion light-front wavefunction need to be included in the analysis. The probability for the Fock state containing four quarks (anti-quarks) which follows from analyzing the hadron matrix elements, P_{q \bar q q \bar q} \sim 10 %, agrees with the analysis of the pion elastic form factor using light-front holography including higher Fock components in the pion wavefunction. 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.