Sum rule for the Compton amplitude and implications for the proton–neutron mass difference

The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $$m_{\mathrm{QED}}^{p-n}=0.58\pm 0.16\,\text {MeV}$$ m QED p - n = 0.58 ± 0.16 MeV .

Hadronic vacuum polarization and vector-meson resonance parameters from $$\varvec{e^+e^-\rightarrow \pi ^0\gamma }$$

We study the reaction $$e^+e^-\rightarrow \pi ^0\gamma $$ e + e - → π 0 γ based on a dispersive representation of the underlying $$\pi ^0\rightarrow \gamma \gamma ^*$$ π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the $$\pi ^0\gamma $$ π 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $$a_\mu ^{\pi ^0\gamma }\big |_{\le 1.35\,\text {GeV}}=43.8(6)\times 10^{-11}$$ a μ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $$\omega $$ ω and $$\phi $$ ϕ . We observe good agreement with the $$e^+e^-\rightarrow 3\pi $$ e + e - → 3 π channel, explaining a previous tension in the $$\omega $$ ω mass between $$\pi ^0\gamma $$ π 0 γ and $$3\pi $$ 3 π by an unphysical phase in the fit function. Combining both channels we find $${\bar{M}}_\omega =782.736(24)\,\text {MeV}$$ M ¯ ω = 782.736 ( 24 ) MeV and $${\bar{M}}_\phi =1019.457(20)\,\text {MeV}$$ M ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The $$\phi $$ ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from the $${\bar{K}} K$$ K ¯ K channel, demonstrating consistency with $$3\pi $$ 3 π and $$\pi ^0\gamma $$ π 0 γ . For the $$\omega $$ ω mass, our result is consistent but more precise, exacerbating tensions with the $$\omega $$ ω mass extracted via isospin-breaking effects from the $$2\pi $$ 2 π channel.

Hadronic vacuum polarization: three-pion channel

The 3π-channel contribution to hadronic vacuum polarization (HVP) in the anomalous magnetic moment of the muon (g−2)µ is examined based on a dispersive representation of the γ* → 3π amplitude. This decay amplitude is reconstructed from dispersion relations, fulfilling the low-energy theorem of QCD. The global fit function is applied to the data sets of the 3π channel below 1.8 GeV, which constitutes the secondlargest exclusive contribution to HVP and its uncertainty. The dominant ωand φ-peak regions in the e+e− → 3π cross section as well as the non-resonant regions are precisely described to obtain our best estimate. The final result, $ a_\mu ^{3\pi }\left| { \le 1.8\,{\rm{GeV}}\,{\rm{ = }}\,{\rm{46}}{\rm{.2(6)(6)}} \times {\rm{1}}{{\rm{0}}^{ - 10}}} \right. $, reduces the model dependence owing to the fundamental principles of analyticity and unitarity and provides a cross check for the compatibility of the different e+e− → 3π data sets. A combination of the current analysis and the recent similar treatment of the 2π channel yields a dispersive determination of almost 80% of the entire HVP contribution. Our analysis reaffirms the muon anomaly at 3.4σ level, when the rest of the contributions is taken from the literature.

Hadronic light-by-light contribution to (g - 2)μ: a dispersive approach

After a brief introduction on ongoing experimental and theoretical activities on (g - 2)μ, we report on recent progress in approaching the calculation of the hadronic light-by-light contribution with dispersive methods. General properties of the four-point function of the electromagnetic current in QCD, its Lorentz decomposition and dispersive representation are discussed. On this basis a numerical estimate for the pion box contribution and its rescattering corrections is obtained. We conclude with an outlook for this approach to the calculation of hadronic light-by-light.

THE ANOMALOUS PROCESS γπ → ππ AND ITS IMPACT ON THE π0 TRANSITION FORM FACTOR

The process γπ → ππ, in the limit of vanishing photon and pion energies, is determined by the chiral anomaly. This reaction can be investigated experimentally using Primakoff reactions, as currently done at COMPASS. We derive a dispersive representation that allows one to extract the chiral anomaly from cross-section measurements up to 1 GeV, where effects of the ρ resonance are included model-independently via the ππ P-wave phase shift. We discuss how this amplitude serves as an important input to a dispersion-theoretical analysis of the π0 transition form factor, which in turn is a vital ingredient to the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.