Revisiting the dark photon explanation of the muon anomalous magnetic moment

A massive $U(1{)}^{\prime }$ gauge boson known as a “dark photon” or $A^{\prime }$, has long been proposed as a potential explanation for the discrepancy observed between the experimental measurement and theoretical determination of the anomalous magnetic moment of the muon ($g_{\mu }-2$) anomaly. Recently, experimental results have excluded this possibility for a dark photon exhibiting exclusively visible or invisible decays. In this work, we revisit this idea and consider a model where $A^{\prime }$ couples inelastically to dark matter and an excited dark sector state, leading to a more exotic decay topology we refer to as a semivisible decay. We show that for large mass splittings between the dark sector states this decay mode is enhanced, weakening the previous invisibly decaying dark photon bounds. As a consequence, $A^{\prime }$ resolves the $g_{\mu }-2$ anomaly in a region of parameter space the thermal dark matter component of the Universe is readily explained. Interestingly, it is possible that the semivisible events we discuss may have been vetoed by experiments searching for invisible dark photon decays. A reanalysis of the data and future searches may be crucial in uncovering this exotic decay mode or closing the window on the dark photon explanation of the $g_{\mu }-2$ anomaly.

Figure 1

Schematic diagram of dark photon decays in our scenario. Here the $A^{\prime }$ decays promptly to both visible and invisible particles, thereby evading the $A^{\prime }\to \overline{f}f$ resonance searches (where $f$ is a charged SM fermion) and missing energy searches for $A^{\prime }\to$ invisible decays.

Figure 2

Current limits on the dark photon semi-visible decay parameter space with benchmark parameters $\mathrm{\Delta }=0.4m_{{\chi }_1}$, $m_{A^{\prime }}=3m_{{\chi }_1}$ and ${\alpha }_D=0.1$. On the left panel we place constraints on the $\epsilon$ vs $m_{A^{\prime }}$ parameter space. On the right panel we include projections for a Belle II monophoton search as well as a BABAR displaced track reanalysis. We also color the various experimental constraints in grey for clarity and to bring attention to our region of parameter space. See text for details on the various bounds and projections.

Figure 3

Parameter space compatible with a dark photon decaying into thermal inelastic DM as an explanation for the Muon g-2 anomaly. On the left panel we plot ${\alpha }_D$ vs $m_{A^{\prime }}$ for a 40% mass splitting and $m_{A^{\prime }}=3m_{{\chi }_1}$. On the right panel we plot the ratio of mass splitting to $m_{{\chi }_1}$ as a function of $m_{{\chi }_1}$ for benchmark parameters ${\alpha }_D=0.5$ and $m_{A^{\prime }}=3m_{{\chi }_1}$. See text for details.