Strong tW Scattering at the LHC

Deviations of the top electroweak couplings from their Standard Model values imply that certain amplitudes for the scattering of third generation fermions and longitudinally polarized vector bosons or Higgses diverge quadratically with momenta. This high-energy growth is a genuine signal of models where the top quark is strongly coupled to the sector responsible for electroweak symmetry breaking. We propose to profit from the high energies accessible at the LHC to enhance the sensitivity to non-standard top-$Z$ couplings, which are currently very weakly constrained. To demonstrate the effectiveness of the approach, we perform a detailed analysis of $tW \to tW$ scattering, which can be probed at the LHC via $pp\to t\bar{t}Wj$. By recasting a CMS analysis at 8 TeV, we derive the strongest direct bounds to date on the $Ztt$ couplings. We also design a dedicated search at 13 TeV that exploits the distinctive features of the $t\bar{t}Wj$ signal. Finally, we present other scattering processes in the same class that could provide further tests of the top-Higgs sector.Comment: 37 pages, 10 figures; v2: minor improvements in the discussion, references added. Matches version published in JHE

On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010