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Meson Form Factors

Johan Bijnens

TL;DR

This paper surveys light-meson form factors (pion, kaon, eta, eta') as probes of strong interactions in external-current processes. It outlines the main theoretical frameworks used to compute these quantities, including Chiral Perturbation Theory, dispersion relations, lattice QCD, modelling, and perturbative QCD, and discusses their respective domains of validity. It then reviews the vector, scalar, and transition form factors for each meson, covering radiative decays such as π_l2γ and the kaon analogues, with key relations such as the pion vector normalization $F_V(0)=1$ and the charge radii entering FV(q^2)=1+(rV^2/6)q^2+... . The discussion emphasizes the role of these form factors in extracting Standard Model parameters like $V_{us}$ and in testing QCD and precision SM predictions such as the muon anomalous magnetic moment, noting the dependence of radii on the probe. It also highlights the need for consistent experimental and theoretical treatments due to the probe-dependent nature of hadronic sizes.

Abstract

We give an introduction to and a short overview of light meson form factors. We first discuss the classical picture and how it then fits in with amplitudes in quantum field theory. We give a short overview of the main theoretical methods and then discuss pion, kaon, eta and eta' form factors.

Meson Form Factors

TL;DR

This paper surveys light-meson form factors (pion, kaon, eta, eta') as probes of strong interactions in external-current processes. It outlines the main theoretical frameworks used to compute these quantities, including Chiral Perturbation Theory, dispersion relations, lattice QCD, modelling, and perturbative QCD, and discusses their respective domains of validity. It then reviews the vector, scalar, and transition form factors for each meson, covering radiative decays such as π_l2γ and the kaon analogues, with key relations such as the pion vector normalization and the charge radii entering FV(q^2)=1+(rV^2/6)q^2+... . The discussion emphasizes the role of these form factors in extracting Standard Model parameters like and in testing QCD and precision SM predictions such as the muon anomalous magnetic moment, noting the dependence of radii on the probe. It also highlights the need for consistent experimental and theoretical treatments due to the probe-dependent nature of hadronic sizes.

Abstract

We give an introduction to and a short overview of light meson form factors. We first discuss the classical picture and how it then fits in with amplitudes in quantum field theory. We give a short overview of the main theoretical methods and then discuss pion, kaon, eta and eta' form factors.
Paper Structure (26 sections, 21 equations, 1 figure)

This paper contains 26 sections, 21 equations, 1 figure.

Table of Contents

  1. Meson Form Factors
  2. Introduction
  3. Theoretical methods
  4. Chiral perturbation theory
  5. Dispersive
  6. Lattice QCD
  7. Modelling
  8. Perturbative QCD
  9. Pion form factors
  10. Vector form factor
  11. Scalar form factor
  12. Transition form factor
  13. $\pi_{\ell2\gamma}$
  14. Kaon form factors
  15. Vector form factors
  16. ...and 11 more sections

Figures (1)

  • Figure 1: Electron-pion scattering with a pointlike photon-electron coupling but the photon-pion coupling depends on its internal structure depicted by the shaded circle.