LHC 750 GeV diphoton excess and muon $(g-2)$

We consider implications of the diphoton excess recently observed at the LHC on the anomalous magnetic dipole moment of the muon $(g-2)_\mu = 2 a_\mu$, hypothesizing that the possible 750 GeV resonance is a (pseudo)scalar particle. The (pseudo)scalar-$\gamma$-$\gamma$ interaction implied by the diphoton events might generically contribute to $a_\mu$ via 2-loop Barr-Zee type diagrams in a broad class of models. If the scalar is an $SU(2)_L$ singlet, the new contribution to $a_\mu$ is much smaller than the current anomaly, $\Delta a_\mu \equiv a_\mu^{\rm exp}-a_\mu^{\rm SM} \approx (30 \pm 10) \times 10^{-10}$, since the scalar can complete the Barr-Zee diagrams only through its mixing with the Standard Model Higgs boson. If the (pseudo)scalar belongs to an $SU(2)_L$ doublet in an extended Higgs sector, then by contrast, $\Delta a_\mu$ can be easily accommodated with the aid of an enhanced Yukawa coupling of the (pseudo)scalar to the muon such as in the Type-II or -X two Higgs doublet model.