• new physics
• muon g-2
• hadronic cross section

The standard Model (SM) of particle physics provides an accurate an well-tested description of
elementary particle interactions observed at laboratory experiments. For this reason, the importance
and predictivity of the SM has triggered a large experimental effort to obtain reliable and precise
data. In particular, the measurement of the muon anomalous magnetic moment by the Muon g-2 collaboration at Fermilab, together with the previous Brookhaven measurement of this
quantity, suggests a 5.1 σ.
Among virtual corrections, crucial for the computation of the theoretical prediction of the
anomalous magnetic moment is the Hadronic Vacuum Polarization (HVP) contribution, which
represents the largest source of uncertainty. It is defined as a hadronic blob inside a photon propagator, and QCD effects are relevant. At the present time, two consolidated approaches have been
developed to compute the hadronic vacuum polarization: the longstanding dispersive approach and
lattice QCD. However, the measure of the HVP contribution to g-2 deriving from these techniques
is at odd, revealing an intriguing and complicated theoretical scenario. Indeed, the more recent
results from several lattice QCD collaborations reveal a disagreement with the SM prediction by
2.1 σ and an agreement with the experimental measure. The discrepancy between the dispersive
prediction and the lattice QCD computation leads to the ”new muon g-2 puzzle”, the main topic
of this thesis. We will focus on the dispersive approach to devise feasible solutions to this puzzle.
We ask whether modifying the hadronic cross section with New Physics (NP) contribution could be resolutive of the new muon g-2. We present three different scenarios of NP that give new contributions to the hadronic cross section. We introduce a NP model where a light Z′ boson couples to the first generation of quarks and leptons. In the first part, we analyze a scenario where a Z′ particle appears at tree level. The propagator is schematized with the Breit-Wigner approximation, which is valid if the resonance is narrow. Then, we present an improvement of this first approach by replacing the Breit-Wigner propagator with a Kallen-Lehmann representation, with the aim of weakening the narrow resonance assumption and refine the previous analysis. Lastly, we invoke NP in loop processes and Final State Radiation (FSR). The final chapter is dedicated to the numerical analysis of NP contributions to the dispersive integral.