Development, Testing and Future Outlook of a Penalized Spline as a Representation of the Standard Model Background in Dijet Searches

Abstract: The aim of this thesis is to develop, test and evaluate a penalized basis spline as a method for representing the Standard Model background in dijet searches from proton-proton collisions at the Large Hadron Collider. Current representations of the Standard Model background are complex and dependent on current assumptions of the Standard Model. Using a P-spline is interesting because of its simplicity and independence from assumptions of the data. Its performance will be tested by fitting $p+p\rightarrow j+j$ generated events from MadGraph and ATLAS data with different penalization parameters of the spline. The test is evaluated using a $\chi^2$ goodness-of-fit test. The distribution of $\chi^2$ for 100 simulated dijet events peaked at 1, showing that the spline has no problem representing the Standard Model background. The spline can also perform a good fit on ATLAS data. This thesis concludes that the P-spline can represent the Standard Model background and perform a good fit on ATLAS data. To conclude that the P-spline can be used as a tool to aid particle searches, further research needs to be done where the P-spline is tested with signal injection.