A ′ A ′ ℓ + ℓ + − ℓ − DM DM A ′ DM DM* Nucleus Nucleus FIG. 2: Left: Dark matter annihilation into the dark photon A $^{′}$, which decays into charged leptons such as electrons and/or muons, can explain the cosmic-ray electron and/or positron excesses seen by PAMELA, Fermi, ATIC, HESS, and other exper- iments. Right: Dark matter scattering into an excited state off nuclei through A ′ exchange in direct dark matter detection experiments can explain the annual modulation signal observed by DAMA/LIBRA, and the null results of other direct detection experiments. C. Current Limits on Light U (1) Gauge Bosons ing is dominated by an inelastic process, in which the dark matter χ scatters off a nucleus N into an excited state χ ∗ with mass splitting δ ≈ 100 keV [67]. The kinematics of these reactions is also remark- ably consistent with all the distinctive properties of the nuclear recoil spectrum reported by DAMA/LIBRA. In addition, the INTEGRAL telescope [71] has reported a 511keV photon signal near the galactic center, indicating a new source of ∼ 1-10 MeV electrons and positrons. This excess could be explained by collisions of O (100 GeV-1 TeV) mass dark matter into O (MeV) excited states in the galaxy [72] — dark matter excited by scattering de- cays back to the ground state by emitting a soft e $^{+}$e − pair. The 511keV excess then arises from the subsequent annihilation of the produced positrons. Constraints on new A ′ ’s that decay to e $^{+}$e − and the search reach of an experiment using the spectrometers of Hall A at Jefferson Laboratory are summarized in Fig- ure 1. Shown are constraints from electron and muon anomalous magnetic moment measurements, a$_{e}$ and a$_{µ}$ [27], the BaBar search for Υ(3 S ) → γA ′ → γµ $^{+}$µ − , and three beam dump experiments, E137, E141, and E774 [3]. The constraints from a$_{µ}$ and the BaBar search as- sume that the A ′ couples to muons — this is the case, for example, if it mixes with the photon. If it only couples to electrons, then the constraints on α ′ /α and m$_{A}$ ′ in the region to which the proposed experiment is sensitive are weaker than α ′ /α ≲ 10 − $^{4}$. χ N → χ ∗ N, (9) We refer the reader to [3, 27] for details on exist- ing constraints. Here, we briefly review the constraint on e $^{+}$e − → γA ′ → γµ $^{+}$µ − derived from the BaBar search [75]. If the A ′ couples to both electrons and muons, this is the most relevant constraint in the re- gion probed by the proposed experiment. The analy- sis of [75] was in fact a search for Υ(3 S ) decays into a pseudoscalar a , Υ(3 S ) → γa → γµ $^{+}$µ − , but can be in- terpreted as a limit on A ′ production because the final states are identical. Using L int ∼ 30 fb − 1 of data con- taining ∼ 122 × 10 6 Υ(3 S ) events, a 90% C.L. upper limit of roughly (1 − 4) × 10 − 6 on the γµ $^{+}$µ − branch- ing fraction was found for m$_{A}$ ′ ∼ 2 m$_{µ}$ − 1 GeV. This search would thus be sensitive to about ∼ 100 − 500 events with e $^{+}$e − → γA ′ → γµ $^{+}$µ − . Requiring that σ ( e $^{+}$e − → γA ′ ) × BR ( A ′ µ $^{+}$µ − ) × L int ≲ 500, where BR ( A ′ µ $^{+}$µ − ) = 1 / (2 + R ( m$_{A}$ ′ )) for m$_{A}$ ′ > 2 m$_{µ}$ with R = σ ( e $^{+}$e $^{−}$→ hadrons; E = m$_{A}$ ′ ) σ ( e $^{+}$e µ $^{+}$µ $^{−}$; E = m$_{A}$ ′ ) , and rescaling the resulting The existence of an A ′ may also help explain various other particle physics anomalies [27] such as the anoma- lous magnetic moment of the muon (( g − 2)$_{µ}$) [73] and the HyperCP anomaly [74]. While these experimental hints provide an urgent mo- tivation to look for an A ′ , it is important to emphasize the value of these searches in general. There has never been a systematic search for new GeV-scale force car- riers that are weakly coupled to Standard Model parti- cles. Nothing forbids their existence, and their discovery would have profound implications for our understand- ing of nature. A relatively simple experiment using the facilities available at, for example, Jefferson Laboratory and Mainz will probe a large and interesting range of A ′ masses and couplings. 6