AbstractsPhysics

Nowadays there is an increasing amount of efforts in searching for answers to a plethora of questions about the world around us. It seems that in the Large Hadron Collider's (LHC) era, those efforts are coming to fruition, and at the same time new triggering questions appear. Among them, the most important are questions about the nature of dark energy, the particle nature of dark matter, the existence of extra dimensions, the verification of the mechanism that gives mass to the particle content of the Standard Model (SM) of particle physics, the existence of supersymmetric particles etc. In this thesis, motivated by experimental results in direct connection with some of the questions above, we first examined scenarios of dark matter interaction with SM leptons, focusing to the study of low energy recoiling electrons and found promising results that can be verified in near future experiments. In order to extent these findings, the dark matter annihilation into photons brought us into the study of triple vertices with external photons or different gauge bosons in general. Within this framework we studied in detail the triple gauge boson one-loop vertex containing virtual heavy fermions and reproduced the most general, analytical expression for that vertex. From a calculational point of view we developed a new approach to the problem by exclusively performing calculations in four dimension and by using physical arguments to handle infinities or anomalously behaved quantities. Analyzing further the triple gauge boson vertex we examined the decoupling effects that arise when the virtual fermions mass become very large. The interesting point here was the realization that in fact these heavy fermions do not decouple completely from the theory. They leave remnants that are necessary to guaranty the self-consistency of the theory. Moreover, we work out quite interesting applications of these results in the SM framework, as well as in theories beyond the SM. Furthermore, by using the same techniques we clarified some computational issues about W gauge boson one-loop contribution to Higgs boson decay into two photons. Performing the calculation in the unitary gauge and strictly in four dimensions, we encountered divergent quantities that we managed to handle by inserting arbitrary four-vectors. The remaining ambiguities were restored by exploiting physical arguments. The results obtained by using the combination of these two techniques (introducing four-vectors to reduce divergencies and using physical considerations to determine unambiguously the result), verify previous similar results. The validity of those results has been also tested by the use of a new proposed method (Four Dimensional Regularization) FDR. Certainly there are open problems that the techniques described above, could answer. These problems constitute the inspiration for further extension of this work. Στις μέρες μας όλο και περισσότερο αυξάνουν οι προσπάθειες εξεύρεσης απαντήσεων σε ερωτήματα σχετικά με τον κόσμο γύρω μας. Φαίνεται πως στην εποχή του…