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.

The response of a muon - a heavier sibling of an electron - to a weak external magnetic field that goes under the name of muon's anomalous magnetic moment can be measured and calculated to an exquisite precision, thereby providing extremely powerful tests of the framework we currently use to describe elementary particles and their interactions, namely the Standard Model. This quantity, in particular, is the subject of intense investigations by particle physicists worldwide due to a long-standing tension between its Standard Model evaluation and highly precise experimental results, which might be due to physics beyond the Standard Model. In order to match the precision of forthcoming measurements and ultimately establish size and nature of the discrepancy, more precise theory calculations with reliable uncertainties are required. In this context, the project focuses on one particularly challenging contribution due to the strong nuclear force, which is known as hadronic light-by-light and is responsible for a sizeable fraction of the present Standard Model uncertainty. Recently, a framework based on dispersion relations has been developed, which links the dominant low-energy contributions to hadronic light-by-light to measurable quantities like form factors and scattering amplitudes, thereby reducing model dependence. However, it remains an open issue how to include further suppressed contributions into this formalism and combine it with rigorous results for the high-energy contributions known as short-distance constraints. Tackling these two related problems is at the core of the project. We first proposed a method based on general parameter-dependent interpolating functions fulfilling all known constraints without resorting to any specific model. In this framework, the role played by parameters and assumptions can be studied in a very transparent and numerically efficient way, leading to improved numerical estimates. Our analysis clearly shows that an accuracy matching the precision goal of forthcoming experimental data can be achieved on the theory side by including a few additional contributions to hadronic light-by-light. Since it is currently not possible to calculate all of these in the above-mentioned approach, we developed a novel, suitably designed dispersive formalism that is for several aspects complementary to the previous one. We demonstrated that all relevant exclusive contributions can be computed in the novel approach, which, in addition, facilitates the matching with short-distance constraints. By comparing the two dispersive approaches, we provided the starting point for their combination, which should allow us to simultaneously exploit the advantages of both. Our results open the way for the first data-driven, model-independent determination of hadronic light-by-light compatible with all theoretical and experimental constraints, which will contribute to the most precise Standard Model evaluation of the muon's anomalous magnetic moment and thus to more stringent tests of our understanding of the fundamental laws of Nature.