3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS
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Date
2014-01-13
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Abstract
Die vorliegende Dissertation behandelt die Berechnung höherer Korrekturen zu den Strukturfunktionen der tiefinelastischen Streuung. Insbesondere werden Effekte schwerer Quarks in QCD-Korrekturen auf dem
Drei-Schleifen-Niveau bestimmt. In dem asymtotischen Bereich Q^2 >>m^2 ergeben sich die schweren Wilsonkoeffizienten aus den leichten Wilsonkoeffizienten und den massiven Operatormatrixelementen (OMEs).
Es werden neue Beiträge zu den OMEs A_{gq,Q} und A_{gg,Q} berechnet. Ferner werden Methoden für die computeralgebraische Berechnung von Leiterdiagrammen angegeben, wobei von Darstellungen generalisierter
hypergeometrischer Funktionen und Appell-Funktionen Gebrauch gemacht wird. Hierbei kommen symbolische Summationstechniken zum Einsatz. Für die Berechnung von Graphen mit zwei disjunkten massiven Zyklen werden diese Methoden erweitert um Mellin-Barnes-Integrale und Eigenschaften iterierter Integrale. Schliesslich werden für den Fall
der tiefinelastischen Streuung im geladenen Strom die kompletten Zwei-Schleifen-Korrekturen für die schweren Wilsonkoeffizienten konstruiert und im x- und N-Raum angegeben. Die Ergebnisse sind notwendig für eine präzise Bestimmung der Partondichten (PDFs) und der starken Kopplungskonstante zu Drei-Schleifen-Präzision.
The present thesis presents the calculation of higher order corrections to the structure functions of deep-inelastic scattering. In particular heavy quark effects in QCD corrections are determined on the 3-loop level. In the asymptotic region Q^2 >> m^2, the heavy flavor Wilson coefficients can be represented in terms of the light flavor Wilson coefficients and the massive operator matrix elements (OMEs). New contributions to the OMEs A_{gq,Q} and A_{gg,Q} are obtained. Furthermore, methods for the computer algebraic computation of ladder diagrams are given, making use of different representations of generalized hypergeometric functions and Appell functions. Here symbolic summation techniques are applied. For the calculation of graphs with two disjoint massive cycles, these methods are altered including Mellin-Barnes integrals and properties of iterated integrals. Finally, for the process of charged current deep-inelastic scattering, the complete 2-loop corrections to the heavy flavor Wilson coefficients are constructed and given in x-space and Mellin-space. The results of the thesis are necessary for the precise determination of the parton densities (PDFs) and the strong coupling constant at 3-loop precision.
The present thesis presents the calculation of higher order corrections to the structure functions of deep-inelastic scattering. In particular heavy quark effects in QCD corrections are determined on the 3-loop level. In the asymptotic region Q^2 >> m^2, the heavy flavor Wilson coefficients can be represented in terms of the light flavor Wilson coefficients and the massive operator matrix elements (OMEs). New contributions to the OMEs A_{gq,Q} and A_{gg,Q} are obtained. Furthermore, methods for the computer algebraic computation of ladder diagrams are given, making use of different representations of generalized hypergeometric functions and Appell functions. Here symbolic summation techniques are applied. For the calculation of graphs with two disjoint massive cycles, these methods are altered including Mellin-Barnes integrals and properties of iterated integrals. Finally, for the process of charged current deep-inelastic scattering, the complete 2-loop corrections to the heavy flavor Wilson coefficients are constructed and given in x-space and Mellin-space. The results of the thesis are necessary for the precise determination of the parton densities (PDFs) and the strong coupling constant at 3-loop precision.
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QCD, Tief-inelastische Streuung, Strukturfunktion, Wilson-Koeffizient, Schweres Quark, Partondichte, Höhere Schleifenkorrektur, Summationstechnik, Geladener Strom