Short-Distance Constraints on Hadronic Light-by-Light

Anomalous magnetic moment (AMM) of leptons have played a central role in establishing quantum field theory as a successful language to describe the fundamental laws of Nature. Nowadays, they still represent benchmark observables being among the most accurately measured and predicted quantities in particle physics.

The AMM of the muon, in particular, enjoys a special status since it is one of the very few observables to exhibit a significant discrepancy with respect to its Standard Model (SM) determination. The origin of this discrepancy is unknown and its explanation is a top priority for particle physicists worldwide. In order to clarify this issue, two new experiments have been designed with the concrete goal to improve in the next few years the already astonishing accuracy of 0.54 parts per million reached by previous measurements. This strongly calls for improved theory predictions.

SM uncertainties are dominated by virtual low-energy strong interaction effects that cannot be computed using perturbative methods. In particular, the hadronic light-by-light (HLbL) contribution is emerging as a potential roadblock. In order to evaluate it, we had to rely so far on hadronic models, which introduce sources of systematic errors that are impossible to quantify. In a recent theory breakthrough, we have set up a novel dispersive formalism for the first data-driven determination of the HLbL and produced first numerical estimates of HLbL within this approach. This framework exploits the general principles of unitarity and analyticity to rigorously define contributions to HLbL and link them to experimentally accessible quantities (form factors and cross sections). One of the most pressing open issues is that short-distance constraints on HLbL scattering are not yet incorporated into our formalism. The proposed project will fill this gap.

Using perturbative and non-perturbative quantum field theory techniques, we will work out for the first time all constraints on HLbL from kinematic configurations where Lorentz invariants are taken in turn to be large, considering all possible hierarchies among them. The importance of those constraints in the determination of the muon AMM will be assessed via a thorough numerical analysis. We will provide a theoretical guidance for controlled interpolations across all relevant kinematic regimes in terms of consistent dispersion relations for HLbL and will systematically study the role played in this context by hadronic resonances.

The proposed research represents a crucial and timely step forward for the completion of our data-driven determination of HLbL with controlled uncertainties, with the aim of being sufficiently accurate to make forthcoming measurements of the muon AMM a decisively stringent test of the SM.