Resummed photon spectra for WIMP annihilation

Searches for photons from decaying or annihilating dark matter are a focus of many current and future experiments. Precise theoretical predictions are required for the correct interpretation of experimental exclusions or discoveries, however, it is well known that large corrections due both to Sommerfeld enhancement and Sudakov double logarithms are present. The all orders resummation of these corrections for the exclusive final state $\gamma \gamma$ and the totally inclusive $\gamma +X$ has been considered, and give differing conclusions on the importance of logarithmic corrections due to their different assumptions on the final state. In reality, the experimental resolution significantly constrains the final state $X$ in $\gamma+X$, introducing another scale, namely the detector resolution, which appears in Sudakov double logarithms. In this paper we develop a comprehensive effective field theory framework to compute the photon spectrum for annihilating or decaying dark matter, which allows for a resummation of all large logarithmic contributions, properly treating the effect of the experimental resolution on the $\gamma+X$ final state. Our framework combines techniques from non-relativistic effective field theories, soft-collinear effective theory, and recent advances in multi-scale effective theories developed in the context of jet substructure. From the effective field theory perspective we find a number of interesting features, including the simultaneous presence of SCET$_{\text{I}}$ and SCET$_{\text{II}}$ modes, as well as collinear-soft modes at the electroweak scale. We compute all ingredients to one-loop, demonstrating the consistency of our factorization, and discuss the merging onto the fully exclusive $\gamma \gamma$ factorization, and the fully inclusive $\gamma+X$ factorization. We present numerical results and update current limits on dark matter, as well as present predictions for future experiments where the improved resolution further enhances the importance of the effects studied here.