In the previous paragraph we already stressed the need to have a general automated code that can generate, at the loop level, any cross section in supersymmetry. This is crucial for as precise predictions as possible, in par with the foreseen accuracy on the cosmological parameters as well as observables at the colliders.  Moreover, considering the issues of renormalisation schemes and parameter definitions, it is logical that the calculation of the relic density, which in our case will be incorporated into micrOMEGAs, be conducted in the same set-up and scheme as the cross sections calculations (in our case, fed to SFitter) and decays (in our case SDECAY). Considering that we know of no complete code even for cross sections at the colliders and that loop issues for the relic density pose more problem than for  high energy calculations, this part of the project is highly ambitious but since it has ramifications on many parts of our modular structure it is worth the challenge.  Moreover we have already tackled some important issues[20,21], like the loop induced monochromatic gamma ray signal through annihilation of neutralinos. Very recently an important foray in implementing a complete on-shell gauge invariant renormalisation has been made. Though there may remain challenges ahead we are certain that the SloopS project is realistic.

The development of this code within supersymmetry is very challenging and necessitates a major effort both at the technical level as well as at the theoretical level. In this proposal, a total of  4 months visitor (A. Semenov) is requested for the development of the code.  Also there is a need for a postdoc (24 months) to work mainly on the exploitation of this code for DM and collider studies.  Work on SloopS and its exploitation will cover at least the full duration of the grant. A detailed planning about this task is given in B-2-11.

  {mospagebreak title=From cosmology  to colliders}  From cosmology  to colliders and  future developments of  micrOMEGAs 

A relic density calculation involves the contribution from a daunting number of processes and involves a large number of parameters. Automation is therefore needed. Within micrOMEGAs all cross sections calculations are performed automatically, once a model has been properly specified, through LanHEP . The modular approach we have taken is well adapted for  extending  to different models of New Physics.  The DM candidate is readily identified by the code once a new parity, in lieu of R-parity for supersymmetry, is defined. The code will then generate the Feynman rules, the cross sections and perform the thermal averaging for the relic density prediction. We have in fact just completed a new version of micrOMEGAs within this spirit ready to incorporate any generic model for DM.   One of the objectives of the project is to now include and study specific models that provide an alternative to supersymmetry for solving the hierarchy problem, such as models with extra dimensions or little Higgs models.  Along side the working codes applicable to SUSY (MSSM, NMSSM, CP violation), these new physics codes will be interfaced to a generalisation of a tool such as SFitter for the extraction of parameters of the underlying theory at the colliders.  Indeed, micrOMEGAs is being set-up so that it also  generates, for a given scenario and a set of parameters, all cross sections in e+e- or at the LHC that are kinematically accessible, as well as a table of decays. It will therefore be ideally suited for analyses of parameter extraction at the collider and confrontation with more direct cosmological measurements. This is where an interface with SFitter, generalised to other models than supersymmetry (and mSUGRA), comes in.

For the incorporation and study of the extra-dimensions (Xdim) and little Higgs models, the invitation of expert model builders for a couple of months would be highly effective and beneficial.  For example, in the Xdim scenarii it would be interesting to see how one can go beyond the (minimal) Universal Extra-Dimension (UED). This should open up a variety of issues  linked to the cut-off scale, like contributions from brane terms that are expected from the underlying theory. It could be interesting how one could extract these new parameters from the data with a tool such as SFitter. In the little Higgs models, considerations on the nature of the lightest stable DM candidate (heavy U(1) or heavy neutrino) should be addressed and compared. We think we can already embark on this part of the project in the second year of the project.

Further improvements and precision in the interface between micrOMEGAs and SFitter will be made the context of supersymmetry by the incorporation, into SFitter, of more precise one-loop cross sections derived from SloopS and 1-loop QCD corrected decays from SDECAY. This should be attempted in the third year of the project. One can then critically review the required accuracy expected at the colliders to match the cosmological measurement, an issue we raised recently[1]. At the same time the possibility to include within micrOMEGAs, different scenarios of the post-inflation era is planned with the collaboration of the astrophysics team who suggested[2], as an example, an acceleration of the expansion of the universe by a period of primordial kination at the time of decoupling.

Another ongoing important development of micrOMEGAs, is carried out in close collaboration with both the theory and experimental astrophysics teams of the project.  micrOMEGAs will also provide the ``partonic" non relativistic cross sections for the annihilation of the DM particles (as might occur in the halo of the galaxy) into all standard model channels. Members of the AMS-HESS team are interfacing hadronisation and decay as well as adapting the codes for the propagation of anti-protons and positrons provided by the astroparticle theorists of the project (see next section) in order to have a global simulation tool for γ rays, pbar, e+ and neutrinos[24] with a plan of incorporating anti-deuterons[25].The success of such an ambitious program requires an important technical support, for further development of the code. For this we request 4 months visit for A. Pukhov and a post-doc working on the analysis of HESS data.

Another independent development of micrOMEGAs is the adjunction of a module for direct DM detection. Although some tree-level treatment is straightforward to implement[26], there are some interesting scenarios where one-loop effects are important[27].