Full One-loop Calculation of Neutralino Annihilation into Two Photons

TL;DR

The paper delivers the first complete one-loop calculation of neutralino annihilation into two photons, $\tilde{\chi}^0_1\tilde{\chi}^0_1\to \gamma\gamma$, within the MSSM, including a new contribution that notably enhances the rate for TeV-scale higgsino-like neutralinos. The amplitude is decomposed into four diagram classes and expressed in a form where the cross section scales as $v\sigma_{2\gamma} = \frac{\alpha^2 M_\chi^2}{16\pi^3} |\tilde{\mathcal{A}}|^2$, with all four-point integrals reducible to three-point functions; the imaginary parts are cross-checked with Cutkosky rules and a sign correction relative to prior works is reported. Extensive SUSY parameter scans reveal large variability in the rate, with pure higgsino cases at TeV masses yielding $vσ_{2\gamma}$ around $1.2\times10^{-28}$ cm$^3$ s$^{-1}$, and show that the $3c$ diagram can dominate, especially as higgsino content increases. The work also recalculates the $\tilde{\chi}^0_1\tilde{\chi}^0_1\to 2g$ channel and analyzes halo-model uncertainties, concluding that gamma-ray line searches are a promising dark-matter probe, though halo structure (including clumps) strongly affects flux predictions and may reconcile some observational claims depending on the model.

Abstract

For the first time, a full one-loop calculation of the process $χχ\to 2γ$ is performed, where $χ$ is the lightest neutralino in the minimal supersymmetric extension of the Standard Model. This process is of interest for dark matter detection, since it would give a sharp $γ$ ray line with $E_γ=m_χ$. We improve upon and correct published formulas, and give cross sections for supersymmetric models with $χ$ masses between 30 GeV and several TeV. We find a new contribution, previously neglected, which enhances the $2γ$ rate for TeV higgsinos by up to an order of magnitude. As a byproduct, we obtain a new expression for the related process $χχ\to 2 gluons$, which on the other hand is generally smaller than previously calculated. There has been a recent claim that evidence for a 3.5 TeV higgsino annihilating into a $γ$ line may already exist from balloon emulsion and Air Cherenkov Telescope data. We comment on attractive features and problems with this interpretation.

Figures (6)

• Figure 1: Feynman diagrams contributing, at one loop level, to neutralino annihilation into two photons. Diagrams with exchanged initial and final states are not shown.
• Figure 2: Annihilation rate of neutralinos into 2$\;\gamma$ for a broad scan in supersymmetric parameter space (the parameter range is identical to that of the "generous scan" of Table 2.2 in [34,30]).
• Figure 3: Annihilation rate of neutralinos into 2$\;\gamma$ for more extensive scans in the low- and high-mass regions.
• Figure 4: In Fig. (a) ratio $2\,v\sigma_{2\gamma}\,/\,v\sigma_{WW}$ as a function of the gaugino fraction $Z_g$; in Fig. (b) ratio $2\,v\sigma_{2\gamma}\,/\,v\sigma_{WW}$ for the sampled supersymmetric models of Fig. (a), the unitarity lower bound of [20] (dashed line) and the pure higgsino rate obtained in this work (solid line). Adding loop corrections to neutralino masses [33] (not done in these plots) one may find points closer to the solid line.
• Figure 5: Normalized flux $\Phi_\gamma$ for the same models as those in Fig. 2.