Multi-Parton Contributions to B̄ → Xs γ at Next-To-Leading Order in QCD

The calculation of the branching ratio for the inclusive decay B̄ → Xs γ has been an
active field of research for multiple decades, yielding results that work very well as a
standard candle of the Standard Model of Particle Physics (SM). The large interest
in this observable has already led to an almost complete expression for the next-
to-leading order (NLO) part and a large number of next-to-next-to-leading order
(NNLO) contributions to the theoretical prediction. With results from colliders
becoming ever more precise, the need for higher precision of theoretical predictions
arises.
In this work, we calculate the remaining pieces for the branching ratio of the four-
body decay of a b quark into an s quark, a photon γ and two additional quarks qq̄ at
NLO in the strong coupling αs . The calculation of this one-loop process b → sγqq̄,
which includes a virtual gluon, has to be supplemented by b → sγqq̄g, since the
loop calculation results in infrared divergences that have to be cancelled by the real-
emission counterparts.
One focus of this thesis is the computation of the occurring four- and five-body
phase space integrals and the calculational techniques that are crucial in obtaining
them. These include the latest iterations of integration-by-parts (IBP) methods that
we used to obtain our sets of master integrals and a description of the differential
equations we used to solve them. We further lay out the different methods we used
to determine the necessary boundary conditions for these, tailored to the different
challenges we encountered.
Furthermore we describe our methods of renormalization and regularization. We
are using dimensional regularization throughout this work and, in this framework,
treating the final state quarks massless leads to residual collinear divergences. For
these remaining divergent expressions, we employ splitting-function regularization
to switch the regularization scheme from dimensional regularization to logarithms of
the quark masses. We also give an overview over the ongoing effort in the calculation
of the last missing piece for the future completion of the perturbative contributions
at O(αs ) which is tied to the next-to-leading order splitting function.
Using these techniques, we calculate the analytic results for our correction to the
decay width of B̄ → Xs γ as one of the missing pieces for the NLO branching
fraction. The expressions are made publicly available online in Mathematica format
for further use. Finally, we discuss future steps for obtaining a numerical result.