Short distance constraints from HLbL contribution to the muon anomalous magnetic moment (2023)
Hadronic Light by Light (HLbL) scattering is not the biggest hadronic contribution to the muon’s anomalous magnetic moment, but it has the biggest relative uncertainty of all the contributions to that observable. With the tension between the Standard Model value prediction and the measurement at 4.2 σ, theoretical physicists have set their sights on reducing the HLbL contribution’s uncertainty to reduce the tension or push it beyond the discovery threshold. In such scenario, the high energy contribution of HLbL scattering to anomalous magnetic moment of the muon plays an important role. The aim of the research developed in this thesis is to study the HLbL leading order contribution in the maximally symmetric high energy region well above the hadronic threshold limit. This is achieved by performing an operator product expansion of the HLbL tensor, which we do systematically in the background field method. We consider our approach very efficient, also because it allows a straightforward renormalization of the field theoretical results. Our approach is also original and at the best of our knowledge not available in literature. The massless quark loop is the leading term and we compute it without neglecting its tensor structure. To this end, we use a tensor–loop–integral decomposition that does not in- troduce kinematic singularities. The resulting scalar loop integrals with shifted dimensions are computed with their full mass dependence using a Mellin–Barnes representation. Our original method of computation for the quark loop provides an independent check of recent literature results. Furthermore, by conserving the full tensor structure of the amplitude, we are able to perform an explicit check of a proposed kinematic–singularity–free tensor decomposition for the HLbL scattering amplitude that plays a central role in the dispersive computation in the low–energy regime. (Texto tomado de la fuente)