TeV scale dark matter and electroweak radiative corrections

Recent anomalies in cosmic rays data, namely, from the PAMELA Collaboration, can be interpreted in terms of TeV scale decaying/annihilating dark matter. We analyze the impact of radiative corrections coming from the electroweak sector of the standard model on the spectrum of the final products at the interaction point. As an example, we consider virtual one loop corrections and real gauge bosons emission in the case of a very heavy vector boson annihilating into fermions. We find electroweak corrections that are relevant, but not as big as sometimes found in the literature; we relate this mismatch to the issue of gauge invariance. At scales much higher than the symmetry breaking scale, one loop electroweak effects are so big that eventually higher orders/resummations have to be considered: we advocate for the inclusion of these effects in parton shower Monte Carlo models aiming at the description of TeV scale physics.

Figure 1

Amplitude squared that contributes to the primary particle spectrum (see text). (a)–(c) describe real emission contributions, while (d) is an example of a virtual correction.

Figure 2

Ward identity relevant for the process considered in this paper.

Figure 3

Gauge boson emission diagrams (the wavy line is a $Z$ or a $W$) for the case of a heavy scalar decaying into a fermion or an antifermion.

Figure 4

Spectrum $\frac{dN}{dz}$ of the primary particle (antimuon) coming from the decay of a heavy $Z^{\prime }$ ($M=10\mathrm{TeV}$) after inclusion of one loop virtual corrections and EW gauge bosons emission. Here and in the following figures $z=2E/M$, with $E$ being the antimuon energy. An “optimal resolution” is assumed (see text).

Figure 5

The same as Fig. 4 but zoomed in the region $z\approx 1$ and with the contributions coming from $\gamma$, $W$, and $Z$ emission drawn separately.

Figure 6

Continuous line: the same as Fig. 4 but with an experimental resolution $\Delta E(\mu )=30\mathrm{GeV}$. Dashed line: tree level distribution with no electroweak corrections.