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Unitarity and Higher-Order Corrections in Neutralino Dark Matter Annihilation into Two Photons

Junji Hisano, Sh. Matsumoto, Mihoko M. Nojiri

Abstract

The neutralino pair annihilation into two photons in our galactic halo gives a robust dark matter signal, since it would give a quasi-monotonic gamma ray. This process is radiatively-induced, and the full-one loop calculation was done previously. However, for the heavy wino-like or Higgsino-like neutralino, the one-loop cross section violates unitarity, therefore the higher-order corrections may be important. We construct a non-relativistic theory for chargino and neutralino two-body states, and estimate all-order QED corrections and two-loop corrections by $Z$ and/or $W$ exchange. We find that the critical mass, above that the two-loop contribution is larger than one-loop one, is about 8 TeV (O(10) TeV) in the limit where neutralino is wino (Higgsino)-like, respectively. Around and above the critical mass, the all-order Z and/or W exchange must be included to estimate the cross section. On the other hand, the QED corrections depend on the mass difference between the neutralino and chargino. In the wino-like limit where neutralino is highly degenerate with chargino in mass, we find that QED corrections enhance the pair annihilation cross section by 1.5-2.

Unitarity and Higher-Order Corrections in Neutralino Dark Matter Annihilation into Two Photons

Abstract

The neutralino pair annihilation into two photons in our galactic halo gives a robust dark matter signal, since it would give a quasi-monotonic gamma ray. This process is radiatively-induced, and the full-one loop calculation was done previously. However, for the heavy wino-like or Higgsino-like neutralino, the one-loop cross section violates unitarity, therefore the higher-order corrections may be important. We construct a non-relativistic theory for chargino and neutralino two-body states, and estimate all-order QED corrections and two-loop corrections by and/or exchange. We find that the critical mass, above that the two-loop contribution is larger than one-loop one, is about 8 TeV (O(10) TeV) in the limit where neutralino is wino (Higgsino)-like, respectively. Around and above the critical mass, the all-order Z and/or W exchange must be included to estimate the cross section. On the other hand, the QED corrections depend on the mass difference between the neutralino and chargino. In the wino-like limit where neutralino is highly degenerate with chargino in mass, we find that QED corrections enhance the pair annihilation cross section by 1.5-2.

Paper Structure

This paper contains 34 equations, 5 figures.

Figures (5)

  • Figure 1: Ladder diagrams in the calculation of the forward-scattering amplitude (${\cal T}_{pp}$). The crossing points correspond to the annihilation term for chargino.
  • Figure 2: The ladder diagrams of photon exchange relevant to the calculation of the forward-scattering amplitude. $A_0$ is the one-loop amplitude; $A_0 \sim \alpha\alpha_2 m/m_W$.
  • Figure 3: a) The leading $\tilde{\chi}^0_1\tilde{\chi}^0_1\rightarrow 2\gamma$ cross section taking into account all-order QED effect, $\sigma v$, as a function of the neutralino mass $m$ (solid lines). For comparison, result of the one-loop calculation Eq. (\ref{['one-loop result']}) is also shown (dashed lines). b) The contours of $\sigma/\sigma_{\rm 1-loop}$ in a ($m$, $\delta m$) plane.
  • Figure 4: The ratio between the next-to-leading order amplitude and the leading-order amplitude as a function of the neutralino mass $m$. a) and b) are for the wino- and the Higgsino-like neutralino, respectively.
  • Figure 5: Diagrams which contribute to next-to-leading order correction. a) and b) are for the wino- and Higgsino-like neutralino DM, respectively.