A. von Manteuffel

W+ W- production at hadron colliders in next to next to leading order QCD.

Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for onshell WW production that include, for the first time, QCD effects up to next-to-next-to-leading order in perturbation theory. As compared to next-to-leading order, the inclusive WW cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the WW cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free WW production in the four and five flavour number schemes, we demonstrate that top-quark resonances can be separated from the inclusive WW cross section without significant loss of theoretical precision.Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for on-shell W+ W- production that include, for the first time, QCD effects up to next to next to leading order in perturbation theory. As compared to next to leading order, the inclusive W+ W- cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the W+ W- cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free W+ W- production in the four and five flavor number schemes, we demonstrate that top-quark resonances can be separated from the inclusive W+ W- cross section without a significant loss of theoretical precision.

Stability and symmetry breaking in the general two-Higgs-doublet model

A method is presented for the analysis of the scalar potential in the general two-Higgs-doublet model. This allows us to give the conditions for the stability of the potential and for electroweak symmetry breaking in this model in a very concise way. These results are then applied to two different Higgs potentials in the literature, namely the MSSM and the two-Higgs-doublet potential proposed by Gunion et al. The known results for these models follow easily as special cases from the general results. In particular, for the potential of Gunion et al. we can clarify the stability and symmetry-breaking properties of the model with our method.

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

Abstract Three loop ladder and V -topology diagrams contributing to the massive operator matrix element A Q g are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter e . Given these representations, the desired Laurent series expansions in e can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin–Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist–Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product–sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V -topologies.

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

We evaluate the two-loop QCD diagrams contributing to the leading color coefficient of the heavy-quark pair production cross section in the gluon fusion channel. We obtain an analytic expression, which is valid for any value of the Mandelstam invariants s and t and of the heavy-quark mass m. Our findings agree with previous analytic results in the small-mass limit and with recent results for the coefficients of the IR poles.

The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function F2(x,Q2) and transversity

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function F2(x,Q 2 ) in the asymptotic region Q 2 ≫ m 2 and the associated operator matrix element A (3),NS qq,Q (N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This matrix element is associated to the vector current and axial vector current for the even and the odd moments N, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to O(NF) and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in N space and harmonic polylogarithms inx-space. Numerical results are presented for the non-singlet charm quark contribution to F2(x,Q 2 ).

The 3-loop pure singlet heavy flavor contributions to the structure function F2(x,Q2) and the anomalous dimension

The pure singlet asymptotic heavy flavor corrections to 3–loop order for the deep–inelastic scattering structure function F2(x,Q 2 ) and the corresponding transition matrix element A (3),PS Qq in the variable flavor number scheme are computed. In Mellin-N space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contributionto the structure function F2(x,Q 2 ) are presented.

Slepton production at e + e- and e-e- linear colliders

Abstract.High-precision analyses are presented for the production of scalar sleptons, selectrons and smuons in supersymmetric theories, at future e + e- and e-e- linear colliders. Threshold production can be exploited for measurements of the selectron and smuon masses, an essential ingredient for the reconstruction of the fundamental supersymmetric theory at high scales. The production of selectrons in the continuum will allow us to determine the Yukawa couplings in the selectron sector, scrutinizing the identity of the Yukawa and gauge couplings, which is a basic consequence of supersymmetry. The theoretical predictions are elaborated at the one-loop level in the continuum, while at threshold non-zero width effects and Sommerfeld rescattering corrections are included. The phenomenological analyses are performed for e + e- and e-e- linear colliders with energy up to about 1 TeV and with high integrated luminosity up to 1 ab-1 to cover the individual slepton channels separately with high precision.

The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(\alpha_s^3)

Abstract We calculate the massive unpolarized operator matrix element A g q ( 3 ) ( N ) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O ( α s 3 ) . A first independent recalculation is performed for the contributions ∝ N F of the 3-loop anomalous dimension γ g q ( 2 ) ( N ) .

CP violation in the general two-Higgs-doublet model: a geometric view

We discuss the CP properties of the potential in the general two-Higgs-doublet model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these invariant functions, parametrising the gauge orbits of the Higgs fields, is isomorphic to the forward light cone and its interior. CP transformations are shown to correspond to reflections in the space of the gauge invariant functions. We consider CP transformations where no mixing of the Higgs doublets is taken into account as well as the general case where the Higgs basis is not fixed. We present basis independent conditions for explicit CP violation which may be checked easily for any THDM potential. Conditions for spontaneous CP violation, that is CP violation through the vacuum expectation values of the Higgs fields, are also derived in a basis independent way.

The O(αs3TF2) contributions to the gluonic operator matrix element

Abstract The O ( α s 3 T F 2 C F ( C A ) ) contributions to the transition matrix element A g g , Q relevant for the variable flavor number scheme at 3-loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In x -space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines.