Top Quark Mass, Parton Showers and UV Subtraction
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Abstract
Increasing the accuracy of theoretical predictions is an ongoing task in today's high energy physics. In this thesis, we investigate two different aspects that are part of the theoretical modelling of collider events.
In the first part of this thesis, we focus on the parton shower and particularly the role of the top quark mass in the parton shower simulation. Therefore, we analyze the depence of the peak position of the thrust distribution on the shower cutoff value. Thrust is an observable that is highly sensitive to the mass of the top quark. For our analysis, we use the dipole parton shower algorithm. We compare the outcome of our parton shower simulations to a relation of the dependence from analytic computations. These calculations are based on soft-colliner effective theory and the coherent branching formalism. We show that the result of the parton shower simulations and the analytic computation are in good agreement.
The second part of the thesis is dedicated to fixed-order calculations concerning the field of scattering amplitudes. For processes with more than two particles in the final state, one is particularly interested in computational methods that are suited for automation. One promising approach is found in loop-tree duality combined with numerical loop integration. In the loop-tree duality method at next-to-next-to-leading order, one encounters two-loop diagrams that have a one-loop self-energy insertion on one of the internal lines of the outer loop. This leads to Feynman integrals with raised propagators, i.e. propagators with higher powers. For calculations in the loop-tree duality approach, one needs to calculate the residue for the case that a raised propagator goes on-shell. This calculation involves the calculation of derivatives and is, hence, process-dependent. We show that it is possible to construct ultraviolet counterterms at the integrand level that make the residues vanish in the on-shell scheme. This relocates the problem of raised propagators to a process-independent part of the calculation. Additionally, we provide suitable forms of these counterterms for scalar $\phi^3$-theory and QCD.