Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.
Electromagnetic decays of the neutral pion
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abstract
We complement studies of the neutral pion transition form factor pi^0 --> gamma^(*) gamma^(*) with calculations for the electromagnetic decay widths of the processes pi^0 --> e^+ e^-, pi^0 --> e^+ e^- gamma and pi^0 --> e^+ e^- e^+ e^-. Their common feature is that the singly- or doubly-virtual transition form factor serves as a vital input that is tested in the non-perturbative low-momentum region of QCD. We determine this form factor from a well-established and symmetry-preserving truncation of the Dyson-Schwinger equations. Our results for the three- and four-body decays match results of previous theoretical calculations and experimental measurements. For the rare decay we employ a numerical method to calculate the process directly by deforming integration contours, which in principle can be generalized to arbitrary integrals as long as the analytic structure of the integrands are known. Our result for the rare decay is in agreement with dispersive calculations but still leaves a 2 sigma discrepancy between theory and experiment.
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hep-ph 2years
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background 1representative citing papers
Chiral effective field theory and resonance chiral theory yield cross sections for e+e- to four pions that are one to two orders smaller than data, with hadronic vacuum polarization contributions to (g-2)μ of (0.680±0.062)×10^{-16} and (0.597±0.058)×10^{-16} for the two charge modes.
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Improved Standard-Model predictions for $\eta^{(\prime)}\to \ell^+ \ell^-$
Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.
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Study of electron-positron annihilation into four pions within chiral effective field theory in the low energy region
Chiral effective field theory and resonance chiral theory yield cross sections for e+e- to four pions that are one to two orders smaller than data, with hadronic vacuum polarization contributions to (g-2)μ of (0.680±0.062)×10^{-16} and (0.597±0.058)×10^{-16} for the two charge modes.