Three-loop QCD corrections from massive quarks to deep-inelastic structure functions and operator matrix elements
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Date
2016
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Abstract
This thesis discusses higher-order contributions from heavy quarks to inclusive
deep-inelastic lepton-nucleon scattering. In this context, massive operator
matrix elements play an important role: they enter into the heavy flavour Wilson
coefficients through a factorisation relation in the asymptotic limit of large
virtualities. Furthermore, they also enter into the definition of the variable
flavour number scheme for parton distributions.
Here, we present the analytic calculation of of several such massive operator
matrix elements at the 3-loop level in perturbative quantum chromodynamics. In
particular, we review the necessary mathematical and computational methods for
these calculations and give results for the non-singlet and pure-singlet
operator matrix elements including their applications in the structure
functions, sum rules and and the variable flavour number scheme. Through this
calculation we also obtain the pure-singlet and non-singlet anomalous dimensions
at 3-loop order. Moreover, we discuss the calculation of certain representative
Feynman diagrams with ladder and V-topologies, which serve as a testing ground
for the calculational tools. Finally, also all Feynman diagrams of the gluonic
operator matrix element are calculated, which is required in a 3-loop
description of the variable flavour number scheme.
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Keywords
Quantenchromodynamik, Tief-inelastische Streuung, Strukturfunktion, Quantenfeldtheorie, Schweres Quark, Höhere Schleifenkorrektur