Interpolation categories for homology theories

For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions we construct a tower of interpolation categories. These are categories over which the functor factorizes and which capture more and more information according to the injective dimension of the images of the functor. The categories are obtained by proving the existence of truncated versions of resolution or $E_2$-model structures. Examples of functors fitting in our framework are given by every generalized homology theory represented by a ring spectrum satisfying the Adams-Atiyah condition. The constructions are closely related to the modified Adams spectral sequence and give a very conceptual approach to the associated moduli problem and obstruction theory. As application we establish an isomorphism between certain E(n)-local Picard groups and some Ext-groups.Comment: 40 pages, corrected version of second part of the replaced version, first part will appear sepparately as "Truncated resolution model structures", to appear in JPA

Full NLO electroweak corrections to Z-boson pair production at the Large Hadron Collider

We report on a recent calculation of the full next-to-leading-order electroweak corrections to Z-boson pair production with subsequent decays into four charged leptons. Using the complete matrix elements at leading order and next-to-leading order in the electroweak coupling for the processes $pp\to\mu^+\mu^-e^+e^-$ and $pp \to\mu^+\mu^-\mu^+\mu^-$, this includes all off-shell effects of intermediate massive vector bosons and photons. We employ a gauge-invariant splitting for the electroweak corrections into purely weak and photonic corrections. The latter show the well-known radiative tails near kinematical thresholds or resonances. The former are generically at the level of $\sim-5\%$ for the fiducial cross section and reach several $-10\%$ in the high-energy tails of distributions due to logarithms of electroweak origin. The impact of interference effects due to equal-flavour leptons in the final state can reach the order of $5\%$ in off-shell-sensitive regions. Photon-induced contributions are included in our calculation, but turn out to be phenomenologically unimportant.Comment: Proceedings to the XXV International Workshop on Deep-Inelastic Scattering and Related Subjects, 3-7 April 2017, Birmingham, U

Calculus of functors and model categories II

This is a continuation, completion, and generalization of our previous joint work with B. Chorny. We supply model structures and Quillen equivalences underlying Goodwillie's constructions on the homotopy level for functors between simplicial model categories satisfying mild hypotheses.Comment: 47 pages. Version 3 contains a new introduction and further small changes, based on suggestions of the referee. To appear in "Algebraic and Geometric Topology

Optimal designs for multivariable spline models

In this paper, we investigate optimal designs for multivariate additive spline regressionmodels. We assume that the knot locations are unknown, so must be estimated from thedata. In this situation, the Fisher information for the full parameter vector depends on theunknown knot locations, resulting in a non-linear design problem. We show that locally,Bayesian and maximin D-optimal designs can be found as the products of the optimaldesigns in one dimension. A similar result is proven for Q-optimality in the class of allproduct design

Electroweak corrections to vector-boson scattering

We report on a recent calculation of the complete NLO QCD and electroweak corrections to the process $pp\to\mu^+\nu_\mu e^+\nu_ejj$, i.e. like-sign charged vector-boson scattering. The computation is based on the complete amplitudes involving two different orders of the strong and electroweak coupling constants at tree level and three different orders at one-loop level. We find electroweak corrections of $-13\%$ for the fiducial cross section that are an intrinsic feature of the vector-boson scattering process. For differential distributions, the corrections reach up to $-40\%$ in the phase-space regions explored. At the NLO level a unique separation between vector-boson scattering and irreducible background processes is not possible any more at the level of Feynman diagrams.Comment: 6 pages, 8 eps figures, Prodeedings of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austri