Abstract
We construct an effective field theory (EFT) description of the hard photon spectrum for heavy WIMP annihilation. This facilitates precision predictions relevant for line searches, and allows the incorporation of non-trivial energy resolution effects. Our framework combines techniques from non-relativistic EFTs and soft-collinear effective theory (SCET), as well as its multi-scale extensions that have been recently introduced for studying jet substructure. We find a number of interesting features, including the simultaneous presence of SCETI and SCETII modes, as well as collinear-soft modes at the electroweak scale. We derive a factorization formula that enables both the resummation of the leading large Sudakov double logarithms that appear in the perturbative spectrum, and the inclusion of Sommerfeld enhancement effects. Consistency of this factorization is demonstrated to leading logarithmic order through explicit calculation. Our final result contains both the exclusive and the inclusive limits, thereby providing a unifying description of these two previously-considered approximations. We estimate the impact on experimental sensitivity, focusing for concreteness on an SU(2)W triplet fermion dark matter — the pure wino — where the strongest constraints are due to a search for gamma-ray lines from the Galactic Center. We find numerically significant corrections compared to previous results, thereby highlighting the importance of accounting for the photon spectrum when interpreting data from current and future indirect detection experiments.
Highlights
Below will hold for a wide class of heavy WIMPs
With this understanding of the correct treatment of the scales as we transition to the fully exclusive endpoint, and how they are implemented in our final factorization formula, we show that our leading logs (LL) expression in the endpoint region correctly reproduces the LL in both the exclusive and operator product expansion (OPE) regions
We provided a new factorization formula, which allows for a resummation of all large logarithmic contributions, properly treating the effects due to electroweak symmetry breaking, the experimental resolution on the γ + X final state, and the Sommerfeld enhancement
Summary
An outline of this paper is as follows. In section 2 we carefully review the kinematics of indirect detection, highlighting the different regions of the photon spectrum, the appropriate field theoretic techniques that are required for their description, and the differing approximations made in previous presentations. While we have attempted to make the presentation as self contained as possible, in particular by reviewing the relevant technology, these sections necessarily assume a higher level of familiarity with EFT techniques, and are as such more mathematically intensive. These sections provide the details which yield the final prediction, but can be skipped without affecting one’s big picture understanding of this work. The main results of our study are shown in graphical form, where we highlight the numerical impact of the resummation of logarithms of zcut, and compare with numerical results from previous approximations This clearly illustrates the importance of properly including the finite resolution of the experiments.
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