Next-to-Leading Order QCD Corrections to Heavy-Flavour Production in Neutral Current DIS

In the last few decades Quantum Chromo Dynamics (QCD) became a major field for high energy physics. Large experiments have been and will be built to investigate all implications that are predicted by its master formula, the Lagrangian density. The Large Hadron Collider (LHC), the “largest machine of mankind”, was built to test the predictions of the standard model (SM) to a very high accuracy and so we finally arrived in the era of high precision physics. The demand for precision requires more and more effort to compute all necessary pieces. In this PhD thesis we close one of the last missing pieces in the set of next-to-leading order (NLO) QCD calculations. We discuss the production of a heavy quark pair in deeply inelastic scattering (DIS) and compute all parts that are required at NLO accuracy. We settle the needed frameworks and notations before computing the matrix elements first at leading order (LO) and then for all contributions at NLO. We compute two different decompositions of the required phase space to realize two different numerical codes, which in turn specialize in different experimental observables. Along the way, we give useful tips and tricks and highlight some of the mathematical challenges on the road of NLO calculations. Finally, we discuss the possibilities to apply these calculations to the planned spin physic program at a future Electron-Ion Collider (EIC). The discussed charm quark production can improve the determination of polarized parton distribution functions (pPDFs). On the other hand, we discuss the possibilities to obtain a further improved calculation of heavy quark structure functions by including the Z-boson exchange in neutral current (NC) DIS