Contributions of semi-hadronic states $P\gamma;S\gamma, \pi^+\pi^-\gamma$ to amm of muon, in frames of Nambu-Jona-Lasinio model

TL;DR

This paper calculates the contributions of semi-hadronic states involving pseudoscalar and scalar mesons with photons to the muon's anomalous magnetic moment using the Nambu-Jona-Lasinio model, aligning with experimental data.

Contribution

It provides new estimates for semi-hadronic state contributions to the muon g-2 within the NJL model, including states not thoroughly analyzed before.

Findings

The $b0 ightarrow b0 ext{,}\eta$ contributions agree with previous results.

Estimated contributions for $b0 ext{,}\eta ext{,}\sigma$ and $b1b1 ext{,}\gamma$ states.

The total hadronic light-by-light contribution is estimated as $10.5 imes 10^{-10}$.

Abstract

We calculate the contribution of semi-hadronic states with pseudoscalar $P=\pi^0, \eta$ and scalar ($\sigma$(550))meson accompanied with real photon as an intermediate state of a heavy photon to the anomalous magnetic moment of muon. We consider the intermediate states with $\pi_0$ and $\sigma$ as a hadrons in frames of Nambu-Jona-Lasinio model. The contribution of $\pi_0\gamma$ state is in agreement with results obtained in previous theoretical considerations as well as with experimental data $a_\mu^{\pi_0\gamma}\approx 4.5 \times 10^{-10}$, besides we estimate $a_{\mu}^{\eta\gamma}=0.7 \times 10^{-10}, a_{\mu}^{\sigma\gamma} \sim 1.5 \times 10^{-11}, a_{\mu}^{\pi^+\pi^-\gamma} \sim 3.2 \times 10^{-10}.$ We discass as well the LbL mechanism with $a_{\mu}^{lbl}=10.5 \cdot 10^{-10}.$