Matching of electroweak parameters for the parity violating interaction
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Abstract
This thesis investigates the formalism of matching in the electroweak sector of the Standard Model in the minimal modified subtraction scheme.
Two different effective models are used to derive an expression of the weak mixing angle below the particle threshold of the W-boson at one-loop order.
One model is based on a four-fermion contact interaction, while the other one resembles the electroweak sector of the Standard Model due to the introduction of a pseudo gauge boson Z', whose mass is not generated by the Higgs mechanism.
The findings are compared to already published results and shortcomings in the existing literature are pointed out.
It is demonstrated that the previously published matching condition of the weak mixing angle for integrating out the W-boson is not based on a well-defined effective theory and needs to be replaced, for example by a formula derived in this thesis.
The related concept of running coupling parameters in terms of the renormalization group equation is discussed in addition.
The perturbative treatment of the running electromagnetic coupling as can be found in the literature is presented in detail.
The overarching goal is the precise determination of the parity violating interaction at zero momentum transfer for which electroweak one-loop corrections are discussed including the role of the weak mixing angle.
It can be used to derive the parity violating asymmetry of elastic electron-proton--scattering which is going to be measured in the P2 experiment in Mainz to determine the weak mixing angle.