A new determination of the $\gamma \pi \to \pi \pi$ anomalous amplitude via ${\pi }^{-}{e}^{-}\to {\pi }^{-}{e}^{-}{\pi }^0$ data

Abstract

We discuss the reaction ${\pi }^{-}{e}^{-}\to {\pi }^{-}{e}^{-}{\pi }^0$ with the purpose of obtaining information on the $\gamma \pi \to \pi \pi$ anomalous amplitude ${\mathcal{F}}_{3\pi }$. We compare a full calculation at $\mathcal{O}(p^6)$ in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia {\em et al}. By integrating our theory results using Monte Carlo techniques we obtain $\sigma =2.05$ nb at $\mathcal{O}(p^6)$ and $\sigma =2.17$ nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross section of $\sigma =(2.11\pm 0.47)$ nb. On the basis of the ChPT results one would extract from the the experimental cross section as amplitudes ${\mathcal{F}}_{3\pi }^{(0)\mathrm{extr}}=(9.9\pm 1.1)$ GeV${}^{-3}$ and ${\mathcal{F}}_{3\pi }^{(0)\mathrm{extr}}=(9.6\pm 1.1)$ GeV${}^{-3}$, respectively, which have to be compared with the low-energy theorem ${\mathcal{F}}_{3\pi }=e/(4{\pi }^2{F}_{\pi }^3)=9.72{GeV}^{-3}$. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain ${\mathcal{F}}_{3\pi }$ with smaller uncertainty.

arXiv comment23 pages, 14 figures, discussion of the ChPT calculation extended

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Cited by in corpus (11)

• QCD and strongly coupled gauge theories: challenges and perspectives
• Dispersive analysis of the pion transition form factor
• Extracting the chiral anomaly from gamma pi --> pi pi
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• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Leading logarithms in the anomalous sector of two-flavour QCD
• Chiral perturbation theory - Success and challenge
• Transition form-factor of $\gamma \to 3\pi$ in nonlocal quark model
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• Tests of Three-Flavor Chiral Perturbation Theory