Searches for Prompt RR-Parity-Violating Supersymmetry at the LHC

Searches for supersymmetry (SUSY) at the LHC frequently assume the conservation of $R$-parity in their design, optimization and interpretation. In the case that $R$-parity is not conserved, constraints on SUSY particle masses tend to be weakened with respect to $R$-parity-conserving models. We review the current status of searches for $R$-parity-violating (RPV) supersymmetry models at the ATLAS and CMS experiments, limited to 8 TeV search results published or submitted for publication as of the end of March 2015. All forms of renormalisable RPV terms leading to prompt signatures have been considered in the set of analyses under review. Discussing results for searches for prompt R-parity-violating SUSY signatures summarizes the main constraints for various RPV models from LHC Run I and also defines the basis for promising signal regions to be optimized for Run II. In addition to identifying highly constrained regions from existing searches, also gaps in the coverage of the parameter space of RPV SUSY are outlined

Energy-second-moment map analysis as an approach to quantify the irregularity of Hamiltonian systems

A different approach will be presented that aims to scrutinize the phase-space trajectories of a general class of Hamiltonian systems with regard to their regular or irregular behavior. The approach is based on the `energy-second-moment map' that can be constructed for all Hamiltonian systems of the generic form $H=p^{2}/2+V(q,t)$. With a three-component vector $s$ consisting of the system's energy $H$ and second moments $qp$, $q^{2}$, this map linearly relates the vector $s(t)$ at time $t$ with the vector's initial state $s(0)$ at $t=0$. It will turn out that this map is directly obtained from the solution of a linear third-order equation that establishes an extension of the set of canonical equations. The Lyapunov functions of the energy-second-moment map will be shown to have simple analytical representations in terms of the solutions of this linear third-order equation. Applying Lyapunov's regularity analysis for linear systems, we will show that the Lyapunov functions of the energy-second-moment map yields information on the irregularity of the particular phase-space trajectory. Our results will be illustrated by means of numerical examples.Comment: 9 pages, 7 figure

Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.Comment: 93 pages, no figure

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements