Heavy quark masses from jets using effective field theory

Currently the most precise experimental measurements of the top quark mass are obtained from determinations of the top mass parameter in the Monte-Carlo event generator used for the experimental analyses based on kinematic fits to top quark events. However, the exact relation of the Monte-Carlo top mass parameter to a quantum-field-theoretically well-defined top quark mass is unknown. Thus the interpretation of these measurements is limited, because the results contain an intrinsic ambiguity, which has not even been quantified reliably up to now. The proposed project has the aim to remedy the situation by reaching two goals not achieved in the literature before. The first goal is a high precision theoretical calculation of so-called event shape distributions such as thrust for massive quark production at the observable particle level. Event shape distributions have a strong sensitivity to the quark mass and the precise calculation requires the implementation of quark mass definitions consistent at the quantum level. The required computations are carried out using effective field theory methods. These allow for a systematic summation of so-called large logarithmic corrections in perturbation theory as well as a consistent account of so-called hadronization corrections which describe the transition from quarks and gluons to the experimentally observable particles. The second goal is to analyze systematically the relation between the Monte-Carlo top quark mass parameter and field-theoretical top quark mass definitions by comparing the theory calculations of the electron-positron eventshape distributions with the corresponding Monte-Carlo results. This analysis will be carried out using numerical fits and will provide the information how the Monte-Carlo top quark mass parameter can be converted to a well-defined field-theoretic top quark mass definition.

The top quark is the heaviest known elementary particle and weighs approximately the same as a single gold atom. The top quark mass is an essential input parameter for many predictions in particle physics, and it also plays an important role in the understanding of the stability of the vacuum in which we and our universe exist. Currently the most precise experimental measurements of the top quark mass are made at the Large-Hadron-Collider (LHC) and are obtained from determinations of the top mass parameter in the Monte-Carlo event generator used for the experimental analyses using fits to kinematic distributions. While Monte-Carlo event generators are very versatile tools to simulate what happens after the protons at the LHC collide, their theoretical precision is relatively limited. As a consequence, prior to the project, the exact relation of the Monte-Carlo top mass parameter to a quantum-field-theoretically well-defined top quark mass was unknown, and the interpretation of the previously mentioned measurements was limited. To remedy this situation the project has made two important contributions. First, it has provided important results to increase the precision of the theoretical predictions of jet mass related event-shape distributions, which are highly sensitive to the top quark, and to clarify a number of open conceptual issues that are relevant for the understanding of the field theoretic methods to make such systematic predictions. This included a complete second order calculation of the massive quark jet function, a high-precision analysis of the relation between different quark mass renormalisation schemes, the study of different conventions to define quark mass sensitive event shapes and the up-to-date most precise calculation of the jet mass distribution in the peak region where the mass sensitivity is maximal. Furthermore, for the first time so-called grooming techniques have been accounted for in the theoretical description of the mass distribution for top quark initiated jets. The grooming allows to apply the results also for the collisions at the Large-Hadron-Collider (LHC). Second, a calibration procedure was developed which allows to numerically relate the Monte-Carlo top quark mass parameter and theoretically well-defined top quark mass schemes by fitting the theoretical predictions of the jet mass distribution to Monte-Carlo pseudo data. This procedure was first developed for electron-positron collisions and then extended to the proton-proton collisions a the LHC in cooperation with the LHC-ATLAS collaboration.