Correlation between muon $g-2$ and $\mu \to e\gamma$

While the muon $g-2$ anomaly can be successfully explained by some new physics models, most of them are severely constrained by the $\mu \to e\gamma$ bound. This tension is more transparent from the effective field theory perspective, in which the two phenomena are encoded in two very similar operators. However, with the $\mathcal{O}(1)$ Wilson coefficients, the current upper bound on $\mu \to e\gamma$ indicates a new physics cutoff scale being 5 orders smaller than that needed to eliminate the $(g-2{)}_{\mu }$ anomaly. By summarizing all the formulas from the one-loop contributions to the muon $g-2$ with the internal-particle spin not larger than 1, we point out two general methods to reconcile the conflict between the muon $g-2$ and $\mu \to e\gamma$: the Glashow-Iliopoulos-Maiani mechanism and the nonuniversal couplings. For the latter method, we use a simple scalar leptoquark model as an illustration.

Figure 1

Effective operators for (a) $(g-2{)}_{\mu }$ and (b) $\mu \to e\gamma$.

Figure 2

One-loop diagrams contributing to $(g-2{)}_{\mu }$.

Figure 3

The integration parts of (a) $\delta a_{\mu }^S$ and (b) $\delta a_{\mu }^P$ in the limits of $M_S\gg m_{\mu },M_{f_i^{\prime }}$.

Figure 4

Contours of $\delta a_{\mu }=287\times {10}^{-11}$ (upper curve) and $\mathcal{B}(\mu \to e\gamma )=5.7\times {10}^{-13}$ (lower curve) in the plane of the couplings ${\lambda }^{(\prime )}$ and the leptoquark mass $m_{X_1}$, where ${\lambda }^{(\prime )}$ is the coupling related to $\mu \to e\gamma$ ($(g-2{)}_{\mu }$).