Deep Inelastic Structure Functions at two Loops

We present the analytic calculation of the Mellin moments of the structure functions F_2, F_3 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2, F_3 and F_L. We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven.Comment: 45 pages LaTe

Deep-inelastic structure functions: Reconstruction from Mellin moments

We summarize the method of calculating Mellin moments of deep-inelastic structure functions in perturbative QCD. We briefly discuss all steps to a complete analytical reconstruction of the perturbative corrrections in x-space.Comment: 6 pages LaTeX, presented at LL2000, Bastei (Germany

Lepton flavour violation in RS models with a brane- or nearly brane-localized Higgs

We perform a comprehensive study of charged lepton flavour violation in Randall-Sundrum (RS) models in a fully 5D quantum-field-theoretical framework. We consider the RS model with minimal field content and a "custodially protected" extension as well as three implementations of the IR-brane localized Higgs field, including the non-decoupling effect of the Kaluza-Klein (KK) excitations of a narrow bulk Higgs. Our calculation provides the first complete result for the flavour-violating electromagnetic dipole operator in Randall-Sundrum models. It contains three contributions with different dependence on the magnitude of the anarchic 5D Yukawa matrix, which can all be important in certain parameter regions. We study the typical range for the branching fractions of mu -> e gamma, mu -> 3e, mu N -> e N as well as tau -> mu gamma, tau -> 3 mu and the electron electric dipole moment by a numerical scan in both the minimal and the custodial RS model. The combination of mu -> e gamma and mu N -> e N currently provides the most stringent constraint on the parameter space of the model. A typical lower limit on the KK scale T is around 2 TeV in the minimal model (up to 4 TeV in the bulk Higgs case with large Yukawa couplings), and around 4 TeV in the custodially protected model, which corresponds to a mass of about 10 TeV for the first KK excitations, far beyond the lower limit from the non-observation of direct production at the LHC.Comment: 64 pages, 21 figures, LaTeX, v2: electron EDM analysis added, matches published versio

The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case

We present the next-to-next-to-leading order (NNLO) contributions to the main splitting functions for the evolution of longitudinally polarized parton densities of hadrons in perturbative QCD. The quark-quark and gluon-quark splitting functions have been obtained by extending our previous all Mellin-N calculations to the structure function g_1 in electromagnetic deep-inelastic scattering (DIS). Their quark-gluon and gluon-gluon counterparts have been derived using third-order fixed-N calculations of structure functions in graviton-exchange DIS, relations to the unpolarized case and mathematical tools for systems of Diophantine equations. The NNLO corrections to the splitting functions are small outside the region of small momentum fractions x where they exhibit a large double-logarithmic enhancement, yet the corrections to the evolution of the parton densities can be unproblematic down to at least x about 10^{-4}.Comment: 52 pages, Latex, 10 figures. FORM and Fortran files of the main results available with the sourc

The Quark Form Factor at Higher Orders

We study the electromagnetic on-shell form factor of quarks in massless perturbative QCD. We derive the complete pole part in dimensional regularization at three loops, and extend the resummation of the form factor to the next-to-next-to-leading contributions. These results are employed to evaluate the infrared finite absolute ratio of the time-like and space-like form factors up to the fourth order in the strong coupling constant. Besides for the pole structure of higher-loop QCD amplitudes, our new contributions to the form factor are also relevant for the high-energy limit of massive gauge theories like QED. The highest-transcendentality component of our results confirms a result recently obtained in N=4 Super-Yang-Mills theory.Comment: 16 pages, 1 figure, Late

First results for three-loop deep-inelastic structure functions in QCD

As a first step towards the complete calculation of deep-inelastic scattering at third order of massless perturbative QCD, we have computed the fermionic (nf) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic scattering. We briefly discuss the approach chosen for this calculation, the problems we encountered and the status of the project. We show the results for the corresponding anomalous dimension in both Mellin-N and Bjorken-x. Together with the nf part of A_3, our calculation facilitates the complete determination of the threshold-resummation coefficients B_2 and D_2^DIS. The latter quantity vanishes in the MSbar scheme.Comment: 5 pages, LaTeX. Talk given at RADCOR02, Kloster Ban

On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution

We discuss the prescription for the Dirac matrix gamma_5 in dimensional regularization used in most second- and third-order QCD calculations of collider cross sections. We provide an alternative implementation of this approach that avoids the use of an explicit form of gamma_5 and of its (anti-) commutation relations in the most important case of no more than one gamma_5 in each fermion trace. This treatment is checked by computing the third-order corrections to the structure functions F_2 and g_1 in charged-current deep-inelastic scattering with axial-vector couplings to the W-bosons. We derive the so far unknown third-order helicity-difference splitting function Delta P_ns^(2)s that contributes to the next-to-next-to-leading order (NNLO) evolution of the polarized valence quark distribution of the nucleon. This function is negligible at momentum fractions x >~ 0.3 but relevant at x << 1.Comment: 11 pages, Latex, 2 figures. FORM and Fortran files of the main results available with the sourc