Virtuality Distributions in Application to $γγ^* \to π^0$ Transition Form Factor at Handbag Level

A. V. Radyushkin

doi:10.1016/j.physletb.2014.06.078

paper

Virtuality Distributions in Application to $γ γ^{*} \to π^{0}$ Transition Form Factor at Handbag Level

arXiv:1404.7032 · doi:10.1016/j.physletb.2014.06.078

Abstract

We outline basics of a new approach to transverse momentum dependence in hard processes. As an illustration, we consider hard exclusive transition process $γ^{*} γ \to π^{0}$ at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal $O (0, z)$ ) describing a hadron with momentum $p$ . Treated as functions of $(p z)$ and $z^{2}$ , they are parametrized through virtuality distribution amplitudes (VDA) $Φ (x, σ)$ , with $x$ being Fourier-conjugate to $(p z)$ and $σ$ Laplace-conjugate to $z^{2}$ . For intervals with $z^{+} = 0$ , we introduce the transverse momentum distribution amplitude (TMDA) $Ψ (x, k_{⊥})$ , and write it in terms of VDA $Φ (x, σ)$ . The results of covariant calculations, written in terms of $Φ (x, σ)$ are converted into expressions involving $Ψ (x, k_{⊥})$ . Starting with scalar toy models, we extend the analysis onto the case of spin-1/2 quarks and QCD. We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. We also discuss how one can generate high- $k_{⊥}$ tails from primordial soft distributions.

arXiv comment9 pages, 8 figures; Bibliography fixed

Virtuality Distributions in Application to $γ γ^{*} \to π^{0}$ Transition Form Factor at Handbag Level

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Virtuality Distributions in Application to $γ γ^{*} \to π^{0}$ Transition Form Factor at Handbag Level