Abstract
We discuss status and prospects of a dispersive analysis of the π0, η, and η ′ transition form factors. Particular focus is put on the various pieces of experimental information that serve as input to such a calculation. These can help improve on the precision of an evaluation of the light pseudoscalar pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.**
Highlights
Intermediate statesThe pion vector form factor FπV (s) as extracte√d from τ− → π−π0ντ decays, e.g., can be described very accurately by a representation (3) up to s = 1 GeV, employing a linear polynomial R(s) ≡ P11(s) = 1 + αV s—at higher energies, the nonlinear effects of inelastic resonances become important [9]
The uncertainty of the Standard-Model prediction of the anomalous magnetic moment of the muon is entirely dominated by hadronic contributions [2]
The various contributions to hadronic light-by-light scattering are organized in terms of their analytic structure, according to the cuts and poles in the different energy variables that are dictated by the above principles
Summary
The pion vector form factor FπV (s) as extracte√d from τ− → π−π0ντ decays, e.g., can be described very accurately by a representation (3) up to s = 1 GeV, employing a linear polynomial R(s) ≡ P11(s) = 1 + αV s—at higher energies, the nonlinear effects of inelastic resonances become important [9]. The power of the universality of final-state interactions lies in the fact that an Omnès representation (3) will apply everywhere where two pions are produced from a point source in a relative P-wave; the process-dependence can be reduced to the coefficients of the multiplicative polynomial Such a representation can in particular be used for the decays η(′) → π+π−γ [10]: they are driven by the chiral anomaly and require the pion pair to be in an odd partial wave, the assumption of dominance by the P-wave f1(s) is entirely justified. It can be modeled well using the vector-meson-dominance assumption, with the necessary coupling constants extracted directly from the partial decay widths for η′ → ωγ and ω → l+l− as well as φ → η′γ and φ → l+l−
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