The muon anomaly (also known as g−2) is one of the most precisely known quantities in all of Physics. The comparison between its recent measurements from the E989 experiment at Fermilab and the Standard Model prediction from the Muon g−2 Theory Collaboration shows that the presence of a New Physics signature in this observable is inconclusive. A faithful comparison with the experiment requires reducing theoretical uncertainties by a factor of 4, which, at current precision, is dominated by two non-perturbative hadronic contributions: the Hadronic Vacuum Polarization (HVP) and the Hadronic Light-by-Light (HLbL) scattering.
One of the leading sources of uncertainty in the HLbL contribution to the muon g−2 is the tower of spin-2 resonances, beginning with the f2(1270). We present progress in evaluating these effects within a new dispersive framework in triangle kinematics, motivated by the study of the vector-vector-axial correlator, which permits a description of higher-spin states with reduced model dependence. A key ingredient is the analysis of the γ*T → π+π− subprocess in the P wave, identifying T with the f2(1270). After deriving its dispersive solution using the Muskhelishvili–Omnès (MO) representation, we discuss its role in constructing the tensor T → γ*γ* transition form factors (TFFs), previously measured by Belle only in the singly-virtual region. We show how the MO solution, in conjunction with the TFFs, can yield a robust estimate of the HLbL spin-2 contribution to the muon g−2.
