Infrared Parton Shower Dynamics and the Top Quark Mass

With a weight of about the mass of a gold atom, the top quark is the heaviest of the known elementary particles. It thus has a particular relation to the Higgs boson which gives mass to all the elementary particles. A precise measurement of the top quark mass is therefore of great importance for the Standard Model of elementary particle physics as well as extensions of it. The most precise measurements of the top quark mass are based on the so-called direct reconstruction method, which by now at the Large Hadron Collider (LHC) has reached errors of around half the proton mass. Here, properties of jets and lepton that come from decays of top quarks are compared with simulations from multipurpose Monte-Carlo event generators (MMCs). Measurement values for the top quark mass are then obtained from a fit procedure. These MMCs form the backbone of all experimental measurements of physical quantities at the LHC, and there are well tested methods to reliably estimate the measurement errors. When using MMCs for measuring the top quark mass, however, a unique problem arises: the top quark is not a physical quantity, but a theoretical and scheme dependent one. This issue is related to the well-known fact that quarks exist, but are not directly observable particles. So, values of the quark masses can only be obtained from the comparison of experimental data with corresponding theoretical predictions that are calculated in a particular quark mass scheme. In MMCs this scheme dependence is, however, not yet understood. This results in an additional uncertainty of the top mass measurements, which up to now could not be fully clarified. It is the aim of the project to analyze and quantify the theoretical scheme dependence of the top quark mass in MMCs for observables that enter the direct reconstruction method. In a recent work on eventshapes it was found that the infrared cutoff of the parton shower evolution, which is the perturbative component in MMCs, is the essential property that determines this scheme dependence. In the proposed project the parton shower algorithms shall be solved analytically for the observables mentioned above and compared with theoretical factorization computations in which the same infrared cutoff is accounted for. In this way the perturbative component of the scheme dependence of the top quark mass in MMCs can be quantified coherently for observables that enter the direct reconstruction method. In addition, also non- perturbative corrections and effects of the finite top quark lifetime shall be analyzed in a systematic manner.

In the project, a method was presented for the first time that allows to relate the top quark mass parameter in Monte Carlo event generators, which are used in experimental analyses at the Large Hadron Collider, in a concrete and precise manner to field-theoretically well-defined renormalization schemes. This problem is important because the experimental uncertainties in so-called 'direct' top quark mass measurements have become so small that a definitive solution to the problem has become necessary. The developed method requires various theoretical calculations of the infrared cutoff dependence of the parton shower algorithms of the event generators and a precise knowledge of the hadronization corrections for the simulated observables. Additionally, it must be ensured that the parton shower algorithm meets certain accuracy requirements and that the hadronization model implemented in the event generator is capable of reproducing the essential dynamical aspects of the parton shower algorithm. The method is based on so-called tuning analyses, where simulations for different values of the parton shower cutoff are performed and compared using fits. This method has been tested and applied for the first time to so-called jet mass observables simulated by the HERWIG event generator. Using this method, it was found that the existing Herwig cluster hadronization model needs improvement. These enhancements were developed in the project and implemented within a new dynamic cluster hadronization model. With the new dynamic cluster hadronization model, both the scheme of hadronization effects and the top quark mass parameter can now be controlled with high accuracy within the framework of Herwig simulations. Furthermore, results have been developed in the project to apply this method to observables that are differential with respect to the decay of the top quark.