# Meson transition form factors in light-front holographic QCD

## Abstract

We study the photon-to-meson transition form factors (TFFs) F{sub M}{gamma}(Q{sup 2}) for {gamma}{gamma}{sup *}{yields}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 qq 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}{sup 0}{yields}{gamma}{gamma} and the pion TFF at the asymptotic limit, a probability for the qq component of the pion wave function P{sub qq}=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{sub qqqq}{approx}10%, which follows from analyzing the hadronmore »

- Authors:

- SLAC National Accelerator Laboratory, Stanford University, California 94309 (United States)
- Institute of Fundamental Sciences, Massey University, Private Bag 11 222, Palmerston North (New Zealand)
- Universidad de Costa Rica, San Jose (Costa Rica)

- Publication Date:

- OSTI Identifier:
- 21607815

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.84.075012; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; ANTI DE SITTER GROUP; ANTI DE SITTER SPACE; ASYMPTOTIC SOLUTIONS; COUPLING; DISTRIBUTION; FORM FACTORS; MATRIX ELEMENTS; PARTICLE DECAY; PHOTONS; PIONS; PROBABILITY; QUANTUM CHROMODYNAMICS; QUARKS; WAVE FUNCTIONS; BOSONS; DECAY; DIMENSIONLESS NUMBERS; ELEMENTARY PARTICLES; FERMIONS; FIELD THEORIES; FUNCTIONS; HADRONS; LIE GROUPS; MASSLESS PARTICLES; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; MESONS; PARTICLE PROPERTIES; PSEUDOSCALAR MESONS; QUANTUM FIELD THEORY; SPACE; SYMMETRY GROUPS

### Citation Formats

```
Brodsky, Stanley J., Cao Fuguang, and de Teramond, Guy F.
```*Meson transition form factors in light-front holographic QCD*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.84.075012.

```
Brodsky, Stanley J., Cao Fuguang, & de Teramond, Guy F.
```*Meson transition form factors in light-front holographic QCD*. United States. doi:10.1103/PHYSREVD.84.075012.

```
Brodsky, Stanley J., Cao Fuguang, and de Teramond, Guy F. Sat .
"Meson transition form factors in light-front holographic QCD". United States. doi:10.1103/PHYSREVD.84.075012.
```

```
@article{osti_21607815,
```

title = {Meson transition form factors in light-front holographic QCD},

author = {Brodsky, Stanley J. and Cao Fuguang and de Teramond, Guy F.},

abstractNote = {We study the photon-to-meson transition form factors (TFFs) F{sub M}{gamma}(Q{sup 2}) for {gamma}{gamma}{sup *}{yields}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 qq 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}{sup 0}{yields}{gamma}{gamma} and the pion TFF at the asymptotic limit, a probability for the qq component of the pion wave function P{sub qq}=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{sub qqqq}{approx}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}{sup '} mesons are also presented. The rapid growth of the pion TFF exhibited by the BABAR data at high Q{sup 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}{sup '} TFFs.},

doi = {10.1103/PHYSREVD.84.075012},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 7,

volume = 84,

place = {United States},

year = {2011},

month = {10}

}