We present the first measurement of the cross correlation of weak gravitational lensing and the extragalactic $\gamma$-ray background emission using data from the Canada-France-Hawaii Lensing Survey and the Fermi Large Area Telescope. The cross correlation is a powerful probe of signatures of dark matter annihilation, because both cosmic shear and gamma-ray emission originate directly from the same dark matter distribution in the Universe, and it can be used to derive constraints on the dark matter annihilation cross section. We show that the measured lensing-$\gamma$ correlation is consistent with a null signal. Comparing the result to theoretical predictions, we exclude dark matter annihilation cross sections of $⟨\sigma v⟩={10}^{-24}–{10}^{-25}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for a 100 GeV dark matter. If dark matter halos exist down to the mass scale of ${10}^{-6}{M}_{\odot }$, we are able to place constraints on the thermal cross sections $⟨\sigma v⟩\sim 5\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for a 10 GeV dark matter annihilation into ${\tau }^{+}{\tau }^{-}$. Future gravitational lensing surveys will increase sensitivity to probe annihilation cross sections of $⟨\sigma v⟩\sim 3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ even for a 100 GeV dark matter. Detailed modeling of the contributions from astrophysical sources to the cross correlation signal could further improve the constraints by $\sim 40\%–70\%$.

• Received 22 April 2014

DOI:https://doi.org/10.1103/PhysRevD.90.063502