Search for a muonic dark force at BaBar

Many models of physics beyond the standard model predict the existence of new Abelian forces with new gauge bosons mediating interactions between “dark sectors” and the standard model. We report a search for a dark boson $Z^{\prime }$ coupling only to the second and third generations of leptons in the reaction $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{Z}^{\prime },Z^{\prime }\to {\mu }^{+}{\mu }^{-}$ using $514{\mathrm{fb}}^{-1}$ of data collected by the BABAR experiment. No significant signal is observed for $Z^{\prime }$ masses in the range 0.212–10 GeV. Limits on the coupling parameter $g^{\prime }$ as low as $7\times {10}^{-4}$ are derived, leading to improvements in the bounds compared to those previously derived from neutrino experiments.

Figure 1

The distribution of the four-muon invariant mass, $m(4\mu )$, for data taken at the $\mathrm{\Upsilon }(4S)$ peak together with Monte Carlo predictions of various processes normalized to data luminosity. The $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ Monte Carlo does not include ISR corrections.

Figure 2

The distribution of the reduced dimuon mass, $m_R$, together with Monte Carlo predictions of various processes normalized to data luminosity. Four combinations per event are included. The fit of the ratio between reconstructed and simulated events is shown as a light blue dashed line. The $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ Monte Carlo does not include ISR or other efficiency corrections (see text).

Figure 3

The measured $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{Z}^{\prime }$, $Z^{\prime }\to {\mu }^{+}{\mu }^{-}$ cross section together with its statistical significance, $S_S$ (see text for definition), as a function of the $Z^{\prime }$ mass. The uncertainty on each point is shown as light gray error bars. The dark gray band indicates the region excluded from the analysis.

Figure 4

The 90% CL upper limits on the cross section $\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}{Z}^{\prime },Z^{\prime }\to {\mu }^{+}{\mu }^{-})$ as a function of the $Z^{\prime }$ mass. The dark gray band indicates the region excluded from the analysis.

Figure 5

The 90% CL upper limits on the new gauge coupling $g^{\prime }$ as a function of the $Z^{\prime }$ mass, together with the constraints derived from the production of a ${\mu }^{+}{\mu }^{-}$ pair in ${\nu }_{\mu }$ scattering (“Trident” production) [29, 30]. The region consistent with the discrepancy between the calculated and measured anomalous magnetic moment of the muon within $2\sigma$ is shaded in red.