Including gauge corrections to thermal leptogenesis

This thesis provides the first approach of a systematic inclusion of gauge corrections to leading order to the ansatz of thermal leptogenesis. We have derived a complete expression for the integrated lepton number matrix including all resummations needed. For this purpose, a new class of diagram has been invented, namely the cylindrical diagram, which allows diverse investigations into the topic of leptogenesis such as the case of resonant leptogenesis. After a brief introduction of the topic of the baryon asymmetry in the universe and a discussion of its most promising solutions as well as their advantages and disadvantages, we have presented our framework of thermal leptogenesis. An effective model was described as well as the associated Feynman rules. The basis for using nonequilibrium quantum field theory has been built in chapter 3. At first, the main definitions have been presented for equilibrium thermal field theory, afterwards we have discussed the Kadanoff-Baym equations for systems out of equilibrium using the example of the Majorana neutrino. The equations have also been solved in the context of leptogenesis in chapter 4. Since gauge corrections play a crucial role throughout this thesis, we have also repeated the naive ansatz by replacing the free equilibrium propagator by propagators including thermal damping rates due to the Standard Model damping widths for lepton and Higgs fields. It is shown that this leads to a comparable result to the solutions of the Boltzmann equations for thermal leptogenesis. Thus it becomes obvious that Standard Model corrections are not negligible for thermal leptogenesis and therefore need to be included systematically from first principles. In order to achieve this we have started discussing the calculation of ladder rung diagrams for Majorana neutrinos using the HTL and the CTL approach in chapter 5. All gauge corrections are included in this framework and thus it has become the basis for the following considerations. Furthermore, we have computed the Majorana neutrino production rate itself in chapter 6 to test our numerical procedure. In this context we have calculated the tree-level result as well as the gauge corrected result for the Majorana neutrino production rate. Finally in chapter 7, we have implemented the Majorana neutrino ladder rung diagram into our setup for leptogenesis: As a first consideration, we have collected all gauge corrected diagrams up to three-loop order for the asymmetry-causing two-loop diagrams. However, the results of chap. 5 showed that it is not sufficient to just include diagrams up to three-loop level. Due to the necessity of resumming all n-loop diagrams, we have constructed a cylindrical diagram that fulfils this condition. This diagram is the link between the Majorana neutrino ladder rung diagram calculated before on the one hand and the lepton asymmetry on the other. Therefore we have been able to derive a complete expression for the integrated lepton number matrix including all leading order corrections. The numerical analysis of this lepton number matrix needs a great computational effort since for the resulting eight-dimensional integral two ordinary differential equations have to be computed for each point the routine evaluates. Thus the result remains yet inaccessible. Research perspectives: Summarising, this thesis provides the basis for a systematic inclusion of gauge interactions in thermal leptogenesis scenarios. As a next step, one should evaluate the expression for the integrated lepton number numerically to gain a value, which can be used for comparison to earlier results such as the solutions of the Boltzmann equations as well as the Kadanoff-Baym ansatz with the implemented Standard Model widths. This numerical result would be the first quantitative number, which contains leading order corrections due to all interactions of the Majorana neutrino with the Standard Model particles. Further corrections by means of including washout effects and the Hubble expansion are expected to be reasonably small. Furthermore, it is very interesting to apply this result to the case of resonant leptogenesis. This is is the scenario where there is degeneracy or quasi-degeneracy of the Majorana masses, thus none of the heavy neutrino masses can be integrated out. By using the versatile cylindrical diagram first described in this thesis, it is not far to seek that this case can be considered easily. For the sake of completeness one has to mention that it is also possible to give constraints of the gravitino production and, thus, to test supersymmetric theories. If the lightest superparticle is the gravitino, which can be a dominant component of dark matter, also supergravity might be tested at the LHC in the near future.