Soft and Coulomb resummation: squark and gluino production at the LHC

In this PhD thesis we have studied the production of massive particles at the Large Hadron Collider (LHC). We found very large corrections that can be compared with experimental results. The LHC is a big particle accelerator at CERN, Geneva where protons are collided against each other. After such high-energy proton collisions, different particles are produced, including massive particles. The experimentalists measure the cross section, which is related to the production rate, that specific massive particles are produced which are then subsequently compared with theoretical predictions from the theory called Quantum Chromodynamics (QCD). Because of the large mass of these particles, they have a small velocity after being produced and it can be shown in QCD that the cross section for their production can be expressed as a series in large numbers. These large numbers make it seem at first that the cross section does not converge, but in the last few decades methods have been developed that reorder the series such that it becomes possible to sum some subseries. The application of these methods is called resummation. In this thesis we have explained and reviewed the resummation method based on Effective Field Theories (EFT), performed directly in momentum space. We were interested in the production of squarks and gluinos that are massive particles that have not been detected up till now at the LHC. The squarks and gluinos are hypothetical particles which appear in some theories of supersymmetry (SUSY). These theories of SUSY have gained fame because of their ability to solve some of the fundamental problems in physics. Therefore, it is important to calculate the cross sections of squark and gluino production at the LHC as accurately as possible. The results of this thesis give a better and more accurate prediction of the cross sections by making use of resummation methods and are needed to make more reliable comparisons of SUSY models with the experimental results at the LHC