Dark sectors charged under a new Abelian interaction have recently received much attention in the context of dark matter models. These models introduce a light new mediator, the so-called dark photon ($A^{\prime }$), connecting the dark sector to the standard model. We present a search for a dark photon in the reaction $e^{+}{e}^{-}\to \gamma A^{\prime }$, $A^{\prime }\to e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$ using $514{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector. We observe no statistically significant deviations from the standard model predictions, and we set 90% confidence level upper limits on the mixing strength between the photon and dark photon at the level of $10^{-4}-10^{-3}$ for dark photon masses in the range $0.02–10.2\mathrm{GeV}$. We further constrain the range of the parameter space favored by interpretations of the discrepancy between the calculated and measured anomalous magnetic moment of the muon.

Searches for lepton-flavor-violating decays of a $\tau$ lepton to a lighter mass lepton and a photon have been performed with the entire data set of $(963\pm 7)\times {10}^6\tau$ decays collected by the BABAR detector near the ${\rm Y}(4S)$, ${\rm Y}(3S)$ and ${\rm Y}(2S)$ resonances. The searches yield no evidence of signals and we set upper limits on the branching fractions of $\mathcal{B}({\tau }^{\pm }\to e^{\pm }\gamma )<3.3\times {10}^{-8}$ and $\mathcal{B}({\tau }^{\pm }\to {\mu }^{\pm }\gamma )<4.4\times {10}^{-8}$ at 90% confidence level.

We search for single-photon events in $53{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BABAR detector at the PEP-II $B$-Factory. We look for events with a single high-energy photon and a large missing momentum and energy, consistent with production of a spin-1 particle $A^{\prime }$ through the process $e^{+}{e}^{-}\to \gamma A^{\prime }$; $A^{\prime }\to \text{invisible}$. Such particles, referred to as “dark photons,” are motivated by theories applying a $U(1)$ gauge symmetry to dark matter. We find no evidence for such processes and set 90% confidence level upper limits on the coupling strength of $A^{\prime }$ to $e^{+}{e}^{-}$ in the mass range $m_{A^{\prime }}\le 8\mathrm{GeV}$. In particular, our limits exclude the values of the $A^{\prime }$ coupling suggested by the dark-photon interpretation of the muon $(g-2{)}_{\mu }$ anomaly, as well as a broad range of parameters for the dark-sector models.

A precise measurement of the cross section of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ from threshold to an energy of 3 GeV is obtained with the initial-state radiation (ISR) method using $232{\mathrm{fb}}^{-1}$ of data collected with the BABAR detector at $e^{+}{e}^{-}$ center-of-mass energies near 10.6 GeV. The ISR luminosity is determined from a study of the leptonic process $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}(\gamma ){\gamma }_{\mathrm{ISR}}$, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ is obtained with a systematic uncertainty of 0.5% in the dominant $\rho$ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $\pi \pi$ cross section from threshold to 1.8 GeV is $(514.1\pm 2.2(\mathrm{stat})\pm 3.1(\mathrm{syst}))\times {10}^{-10}$.

We study the reaction $e^{+}{e}^{-}\to e^{+}{e}^{-}{\pi }^0$ in the single tag mode and measure the differential cross section $d\sigma /d{Q}^2$ and the $\gamma {\gamma }^{*}\to {\pi }^0$ transition form factor in the momentum transfer range from 4 to $40{\mathrm{GeV}}^2$. At $Q^2>10{\mathrm{GeV}}^2$ the measured form factor exceeds the asymptotic limit predicted by perturbative QCD. The analysis is based on $442{\mathrm{fb}}^{-1}$ of integrated luminosity collected at PEP-II with the BABAR detector at $e^{+}{e}^{-}$ center-of-mass energies near 10.6 GeV.