Peter Stoffer

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion–photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for γ⁎γ⁎→ππ.

Dispersive approach to hadronic light-by-light scattering

A bstractBased on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from ππ intermediate states to the partial waves for the process γ*γ*→ ππ. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

Remarks on higher-order hadronic corrections to the muon g−2

Recently, it was shown that insertions of hadronic vacuum polarization at O(α4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g−2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.

Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon

We present a first model-independent calculation of ππ intermediate states in the hadronic-light-by-light (HLBL) contribution to the anomalous magnetic moment of the muon (g-2)_{μ} that goes beyond the scalar QED pion loop. To this end, we combine a recently developed dispersive description of the HLBL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box a_{μ}^{π box}=-15.9(2)×10^{-11}. We then construct a suitable input for the γ^{*}γ^{*}→ππ helicity partial waves, based on a pion-pole left-hand cut and show that for the dominant charged-pion contribution, this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to our final estimate for the sum of these two contributions a_{μ}^{π box}+a_{μ,J=0}^{ππ,π-pole  LHC}=-24(1)×10^{-11}.

VIRTUAL PHOTON–PHOTON SCATTERING

Based on analyticity, unitarity, and Lorentz invariance the contribution from hadronic vacuum polarization to the anomalous magnetic moment of the muon is directly related to the cross section of e+e− → hadrons. We review the main difficulties that impede such an approach for light-by-light scattering and identify the required ingredients from experiment. Amongst those, the most critical one is the scattering of two virtual photons into meson pairs. We analyze the analytic structure of the process γ*γ* → ππ and show that the usual Muskhelishvili–Omnes representation can be amended in such a way as to remain valid even in the presence of anomalous thresholds.

Isospin breaking effects in K_{\ell 4} decays

In the framework of chiral perturbation theory with photons and leptons, the one-loop isospin-breaking effects in

Low-energy effective field theory below the electroweak scale: operators and matching

K_{\ell 4}

Isospin breaking effects in

Kℓ4 decays due to both the photonic contribution and the quark and meson mass differences are computed. A comparison with the isospin-breaking corrections applied by recent high statistics