Abstract
We evaluate the hadronic contribution to the $g-2$ of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization. The low-energy limit is a non-local Nambu--Jona-Lasinio (NJL) model that has all the parameters fixed from QCD, and the only experimental input used is the confinement scale that is known from measurements of hadronic physics. Our estimations provide a novel analytical alternative to the current lattice computations and we find that our result is close to the similar computation performed from experimental data. We also comment on how this analytical approach technique, in general, may provide prospective estimates for hadronic computations from dark sectors and its implication in BSM model-building in future.
Highlights
Since the original computation for the electron from first principles [1], originating from Dirac equation, the lepton anomalous magnetic moments continue to be very important observables for precision tests of the Standard Model (SM) [2]
We evaluate the hadronic contribution to the g − 2 of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization
To summarize, using technique devised by Bender, Milton, and Savage, in Ref [15] the Dyson-Schwinger equations for quantum chromodynamics in differential form was revisited
Summary
Since the original computation for the electron from first principles [1], originating from Dirac equation, the lepton anomalous magnetic moments continue to be very important observables for precision tests of the Standard Model (SM) [2]. The Budapest-Marseille-Wuppertal Collaboration has put forward their latest results [10], showing that the HVP correction they obtain moves the ballpark of the muon g − 2 value back into the SM field This would imply that the technique using experimental values from the colliders probably underestimates this contribution. Due to the large set of undetermined parameters entering in such effective theories, this kind of approach in this early, primitive stage was abandoned in favor of the use of experimental data and lattice QCD calculations. Based on these first principles, we will evaluate the HVP contribution to the muon (g − 2)
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