Determination of Supersymmetric Parameters with Neural Networks at the Large Hadron Collider

Abstract

The LHC is running and in the near future potentially some signs of new physics are measured. In this thesis it is assumed that the underlying theory of such a signal would be identified and that it is some kind of minimal supersymmetric extension of the Standard Model. Generally, the mapping from the measurable observables onto the parameter values of the supersymmetric theory is unknown. Instead, only the opposite direction is known, i.e. for fixed parameters the measurable observables can be computed with some uncertainties. In this thesis, the ability of artifical neural networks to determine this unknown function is demonstrated. At the end of a training process, the created networks are capable to calculate the parameter values with errors for an existing measurement. To do so, at first a set of mostly counting observables is introduced. In the following, the usefulness of these observables for the determination of supersymmetric parameters is checked. This is done by applying them on 283 pairs of parameter sets of a MSSM with 15 parameters. These pairs were found to be indistinguishable at the LHC by another study, even without the consideration of SM background. It can be shown that 260 of these pairs can be discriminated using the introduced observables. Without systematic errors even all pairs can be distinguished. Also with the consideration of SM background still most pairs can be disentangled (282 without and 237 with systematic errors). This result indicates the usefulness of the observables for the direct parameter determination. The performance of neural networks is investigated for four different parameter regions of the CMSSM. With the right set of observables, the neural network approach generally could also be used for any other (non–supersymmetric) theory. In each region, a reference point with around 1,000 events after cuts should be determined in the context of a LHC with a center of mass energy of 14 TeV and an integrated luminosity of 10/fb. The parameters m_0 and m_1/2 can be determined relatively well down to errors of around 4.5% and 1%, respectively. Increasing the integrated luminosity to 500/fb allows also a quite accurate determination of the other two continuous parameters tanβ and A_0. The parameter tanβ has relative errors as small as 4%, and the estimated standard deviations for A_0 are roughly between 25 and 35% of the true value of m_0.