(In)visible Z’ and dark matter

Alberto Romagnoni is a postdoc at LPT, Orsay. Dmitry.

In this post I discuss my recent work “(In)visible Z’ and dark matter”, done in collaboration with E. Dudas, Y. Mambrini and S. Pokorski. I think there are two main messages I should stress to summarize our paper. The first one is more interesting for its phenomenological consequences and a possible striking signature for dark matter. The second one is more important from a theoretical point of view, and concerns the so-called “decoupling” theorem.

The starting point is the attempt to answer the following question: “How is it possible to see an (in)visible Z’?”. Let me first define what is an “(in)visible” Z’ for us, and then discuss the main point about phenomenology of dark matter. Finally, I will briefly discuss the theoretical aspects of such a construction.

In the spirit of minimally extending the Standard Model (SM), a possibility is given by adding matter and/or gauge groups to it. One subject studied in details is clearly the simplest case, when one adds just an extra Abelian gauge group . This gauge symmetry is typically broken and a new massive gauge boson Z’ enters in the game. It is easy to imagine many different types of signatures for this kind of particle, most of all if Z’ couples to SM, or in other words, if the SM particles are charged under this extra . In particular, if Z’ mass is around TeV scale, there is the possibility to see the corresponding resonance in particles accelerators like LHC.

But, what happens if Standard Model spectrum is blind with respect to ? Clearly, if there is no way for Z’ to talk with SM, no signal will be possible. However, one can imagine that  an hidden sector of heavy fermions can couple to both SM and gauge groups. These new fields have obviously to satisfy some constraints, namely they have to arrange for the cancellation of all the anomalies, the Abelian and the mixed ones. Nonetheless, their presence induces loop effects that can be rephrased in terms of effective vertices for the vector fields. In other words, if the extra fermions are really heavier than the SM spectrum and the Z’ boson, they can be “integrated out” at a scale M, and in the effective Lagrangian, new interaction terms appear mainly as trilinear couplings of the form

,

multiplied by a factor roughly speaking proportional to , with a one-loop order parameter (), and the momentum entering in the vertex. These induced interactions can make the Z’ visible, or better, (in)visible.

There are in the literature some examples of LHC analysis for this and similar scenarios, but our purpose is slightly different and concerns Dark Matter (DM). The main idea is the following. Let suppose that the dark matter candidate is lighter than the fermionic sector which we integrated out, and uncharged with respect to SM gauge group. The unique tree level annihilation diagram is given by the exchange of Z’ . Then, Z’ can couple to the visible sector only via the couplings to the SM gauge bosons. In particular, the trilinear ones will be the dominant contributions, and the three channel  are opened. It is possible to show that a region exists in the parameter space (namely when the Z’ mass is near to the pole, ) where these processes contributes to the correct relic abundance measured by WMAP.

We computed the relic density using the last released version of the Micromegas code, modified to include the (in)visible Z’ and its couplings to the SM. The important point is that the same process produces a monochromatic gamma ray. In fact, it is a simple exercise to show that looking at the final state , the energy of the photon is fixed by the relation

.

Actually, this kind of effect is well known also in some other extensions of SM, namely in supersymmetric ones. However, since it comes loop suppressed with respect to the main annihilation channel of DM, usually this gamma-ray is completely invisible. In our model instead, since the gamma-ray is produced in the same diagram contributing to the relic density, it can easily be disentangled from the diffuse background and could be seen by the satellite GLAST/FERMI-LAT after 5 years of data taking. We used the Pythia Monte Carlo to simulate the gamma-ray spectrum, and an example of the results (for a choice of the parameters in the effective Lagrangian) is shown in the figure, for a classical NFW halo profile and .

A subtlety is given by the possible kinetic mixing between the Z’ and  the hypercharge field strengths, , also induced by loop effects. In principle, this term could induce SM millicharges for the DM candidate, and then allow direct annihilation in Z, and then in SM particles. However, in the parameter space region chosen before, its effects are not so important, and the gamma-ray remains visible.

Now, let me briefly discuss the origin of these trilinear terms. The “decoupling” theorem is a well known result in which the usual logic of renormalizable theories tells us that the interactions, mediated by heavy fermions running in loops, are generally suppressed by the masses of these fermions. However, a first type of counterexample has been done by D’Hoker and Farhi in 1984. They have shown that if the heavy  fermions “integrated out” contribute to the  anomalies, then gauge invariance constraints them to generate anomalous terms in the effective action, not suppressed by their mass scale. The reason is due to the topological nature, and then to the scale invariance of such anomalous terms. Our case is clearly different, since we integrate out an entire sector arranging for anomalies cancellation. This is the reason why all our vectorial trilinear terms are mass suppressed. However, in the paper we discuss the possibility to escape this fact, once one considers more than one extra Abelian gauge group. In fact, it is easy to construct an example of an heavy sector inducing trilinear terms like , with coefficient still of one-loop order, but not further mass suppressed. In this case, the gamma-ray effect should be still more enhanced. In our opinion, this could be an interesting subject of further analysis and it would be interesting to perform a systematic study of the effects of the effective operators at low-energy from a decoupling perspective.