Effective Field Theories for Physics Beyond the Standard Model

Under the assumption that the mass scale M of physics beyond the Standard Model(BSM) is far above the electroweak scale v, effective field theories (EFTs) are the suitablemethod for a consistent separation of the physical processes at these disparate mass scales.We construct EFT frameworks for the generic description of physics BSM - covering thetwo relevant cases that particles of the BSM sector can or can not be produced on-shellat the Large Hadron Collider (LHC) or a future collider.In the first scenario we focus on the case where a new heavy resonance S with massMS far above v is discovered at a collider. We assume that the BSM sector contains further yetundiscovered particles with masses of order M ~ MS. We discuss the case where S is ascalar Standard-Model (SM) gauge singlet and formulate an EFT to describe the decays ofS into SM particles. We demonstrate that for a consistent separation of the mass scalesM and v the appropriate operators in the EFT are non-local Soft-Collinear-Effective-Theory (SCET) operators rather than higher-dimensional local operators. We constructthe effective Lagrangian up to the next-to-next-to-leading order in the power-countingparameter v/M and consider the renormalisation-group (RG) equations which allowthe resummation of large logarithms of M/v. Our approach provides a template forthe construction of analogous EFTs which are suited to describe resonances of differentcharges and spin. We illustrate our framework in two examples. In the first example wedemonstrate that our EFT applies also in the case of the double hierarchy v MS In the second example we consider a BSM model, where S and heavy, vector-like fermionsare added to the SM. We perform the matching of the BSM model to the EFT and showthat resummation yields sizeable effects in phenomenologically relevant decay channels.In the second scenario we consider the case where the mass scale M of the BSM modelis above the energy reach of the collider. We apply the Standard-Model Effective Theory(SMEFT) in collider studies for the processes dijet- and dilepton production. We derivebounds on the contributing Wilson coefficients and on the mass scale M. For the firsttime in analyses of this type we employ a consistent expansion in the EFT series in powersof 1/M. We truncate our signal predictions for the cross sections at the next-to-leading order in 1/M andintroduce a theory uncertainty to model the terms of higher power. In our analysis weallow for multiple SMEFT operators to contribute at a time. We identify and bound twodistinct linear combinations of Wilson coefficients in both studies. The bounds arisingin our approach are generically weaker than the overly stringent bounds obtained inprevious studies without appropriate theory uncertainties. The method developed in thiswork can be applied to further processes and the bounds obtained in our approach mayserve as an important input for future global fits in the SMEFT framework.The two frameworks developed and applied in this thesis provide a toolbox for the consistentEFT description of BSM physics in the cases described above.