Prospects for detecting a net photon circular polarization produced by decaying dark matter

If dark matter interactions with Standard Model particles are $CP$ violating, then dark matter annihilation/decay can produce photons with a net circular polarization. We consider the prospects for experimentally detecting evidence for such a circular polarization. We identify optimal models for dark matter interactions with the Standard Model, from the point of view of detectability of the net polarization, for the case of either symmetric or asymmetric dark matter. We find that, for symmetric dark matter, evidence for net polarization could be found by a search of the Galactic center by an instrument sensitive to circular polarization with an efficiency-weighted exposure of at least $50,000{\mathrm{cm}}^2\mathrm{yr}$, provided the systematic detector uncertainties are constrained at the 1% level. Better sensitivity can be obtained in the case of asymmetric dark matter. We discuss the prospects for achieving the needed level of performance using possible detector technologies.

Figure 1

Feynman diagrams of relevant processes: (a) and (b) one-loop decay of $X$ to photon pairs; (c) tree-level decay of $X$ to $e^{+}{e}^{-}$; (d) vertex correction contributed by $X$ .

Figure 2

A contour plot of the net circular polarization $R$ as a function of $x$ and $\phi$. The star represents the benchmark point as in Table 1.

Figure 3

The decay rate and polarization as a function of $x$. The dashed vertical line represents our benchmark $x$ as shown in Table 1.

Figure 4

Contour plots in the $(x,\phi )$-plane of the $N_{\mathrm{pol}}^{\mathrm{GC}}$ (left panel) and $N_{\mathrm{pol}}^{\mathrm{GC}}/N_{\text{total}}^{\mathrm{GC}}$ (right panel), assuming at each point that $|\lambda {|}^2$ is chosen to have the maximum value consistent with observational constraints. The plot range is $0.002\le x\le 0.998$ and $0.01\pi \le \phi \le 0.99\pi$. These two plots are made with the typical ACT parameters given at the beginning of Sec. 4b. The star denotes the benchmark point described in Table 1.

Figure 5

Contour plots in the $(x,\phi )$-plane of the effective exposure $A^2{I}_{\exp }{e}_p/\epsilon$ (black solid contours) necessary for $3\sigma$ evidence of a net circular polarization, assuming at each point that $|\lambda {|}^2$ is chosen to have the maximum value consistent with observational constraints. The blue dashed lines are contours of $R(x,\phi )$, and the star denotes the benchmark point described in Table 1.