Final Report Summary - PARTNERS (Top Partners at the LHC) The main aim of this project has been to study simple, minimal effective descriptions of possible new physics at the LHC; to constrain these models, using both theoretical and experimental inputs; and to study the phenomenology of these particles at the LHC. In addition, the study of quantum corrections to particle behaviour at the LHC was a significant interest. Since the beginning of the project, the research has developed in two major directions. The first of these directions was motivated by the problem of baryogenesis. The importance of this problem cannot be underestimated, for it concerns the matter which makes up our world. The question is: where did this matter come from? The standard model of particle physics does not have a satisfactory answer to this question. Indeed, it is known that physics beyond the standard model is necessary to produce the matter we are made of. It could well be that the LHC will provide an answer to this fundamental question. Our research in this direction began by building a simple model for the new physics which could be responsible for allowing the necessary baryogenesis to occur at energy scales which the LHC can probe. Indeed, we learned that is enough to add a scalar particle to the standard model, which interacts directly only with the Higgs field. Because the behaviour of this particle at the LHC is rather similar to the behaviour of the Higgs boson (although its mass is presumably different) we were able to place powerful constraints on the model using present LHC data. The theoretical requirement that the new particle does indeed allow for baryogenesis further constrained the model, resulting in rather sharp predictions for how such a particle can behave if it exists in nature. Future LHC data may detect this particle; if this does not happen, the remaining parameter space of the model will be shrunk to a very small island.The second major direction of research concerned quantum corrections to the behaviour of particles. The calculation of these corrections is required for understanding precision LHC data---it is worth emphasising that the performance of the LHC has been truly spectacular, and has allowed for much more detailed, high precision observations than were initially expected. With many years of the LHC program in the future, the precision of LHC observations will require more and more precise theoretical calculations of the predictions of the standard model to allow for a careful comparison of experiment and theory. The computation of the predictions of the standard model of particle physics is a very challenging problem. Therefore, there has been a very considerable effort by particle theorists in recent years to develop new calculational tools. One such tool is called colour-kinematics duality. The advantage of this approach is that it related complicated parts of the calculation of some effect to simpler (so-called planar) parts of the calculation. This is an exciting development, but it remains unclear under what circumstances the method applies. Our work in this area focused on one-loop calculations, which are the largest quantum corrections. We demonstrated has to exploit colour-kinematics duality in an infinite class of these processes, assuming that the particles interacting were all circularly polarised in the same direction.