Dimension of the Torelli group for Out(F_n)

Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T_3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure

Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ coincides with the closure of the set of saddle points. The methods used combine the pluripotential theory with the theory of non-uniformly hyperbolic dynamical systems

Initial determination of the spins of the gluino and squarks at LHC

In principle particle spins can be measured from their production cross sections once their mass is approximately known. The method works in practice because spins are quantized and cross sections depend strongly on spins. It can be used to determine, for example, the spin of the top quark. Direct application of this method to supersymmetric theories will have to overcome the challenge of measuring mass at the LHC, which could require high statistics. In this article, we propose a method of measuring the spins of the colored superpatners by combining rate information for several channels and a set of kinematical variables, without directly measuring their masses. We argue that such a method could lead to an early determination of the spin of gluino and squarks. This method can be applied to the measurement of spin of other new physics particles and more general scenarios.Comment: 23 pages, 8 figures, minor change

SUSY parameter determination at the LHC using cross sections and kinematic edges

We study the determination of supersymmetric parameters at the LHC from a global fit including cross sections and edges of kinematic distributions. For illustration, we focus on a minimal supergravity scenario and discuss how well it can be constrained at the LHC operating at 7 and 14 TeV collision energy, respectively. We find that the inclusion of cross sections greatly improves the accuracy of the SUSY parameter determination, and allows to reliably extract model parameters even in the initial phase of LHC data taking with 7 TeV collision energy and 1/fb integrated luminosity. Moreover, cross section information may be essential to study more general scenarios, such as those with non-universal gaugino masses, and distinguish them from minimal, universal, models.Comment: 22 pages, 8 figure

Spin Analysis of Supersymmetric Particles

The spin of supersymmetric particles can be determined at $e^+e^-$ colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles -- smuons, selectrons, and charginos/neutralinos. The analysis is based on the threshold behavior of the excitation curves for pair production in $e^+e^-$ collisions, the angular distribution in the production process and decay angular distributions. In the first step we present the observables in the helicity formalism for the supersymmetric particles. Subsequently we confront the results with corresponding analyses of Kaluza-Klein particles in theories of universal extra space dimensions which behave distinctly different from supersymmetric theories. It is shown in the third step that a set of observables can be designed which signal the spin of supersymmetric particles unambiguously without any model assumptions. Finally in the fourth step it is demonstrated that the determination of the spin of supersymmetric particles can be performed experimentally in practice at an $e^+e^-$ collider.Comment: 39 pages, 14 figure

Measuring Invisible Particle Masses Using a Single Short Decay Chain

We consider the mass measurement at hadron colliders for a decay chain of two steps, which ends with a missing particle. Such a topology appears as a subprocess of signal events of many new physics models which contain a dark matter candidate. From the two visible particles coming from the decay chain, only one invariant mass combination can be formed and hence it is na\"ively expected that the masses of the three invisible particles in the decay chain cannot be determined from a single end point of the invariant mass distribution. We show that the event distribution in the $\log(E_{1T}/E_{2T})$ vs. invariant mass-squared plane, where $E_{1T}$, $E_{2T}$ are the transverse energies of the two visible particles, contains the information of all three invisible particle masses and allows them to be extracted individually. The experimental smearing and combinatorial issues pose challenges to the mass measurements. However, in many cases the three invisible particle masses in the decay chain can be determined with reasonable accuracies.Comment: 45 pages, 32 figure

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Dark Matter Candidates: A Ten-Point Test

An extraordinarily rich zoo of non-baryonic Dark Matter candidates has been proposed over the last three decades. Here we present a 10-point test that a new particle has to pass, in order to be considered a viable DM candidate: I.) Does it match the appropriate relic density? II.) Is it {\it cold}? III.) Is it neutral? IV.) Is it consistent with BBN? V.) Does it leave stellar evolution unchanged? VI.) Is it compatible with constraints on self-interactions? VII.) Is it consistent with {\it direct} DM searches? VIII.) Is it compatible with gamma-ray constraints? IX.) Is it compatible with other astrophysical bounds? X.) Can it be probed experimentally?Comment: 29 pages, 12 figure

Les Houches 2013: Physics at TeV Colliders: Standard Model Working Group Report

This Report summarizes the proceedings of the 2013 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt primarily with (1) the techniques for calculating standard model multi-leg NLO and NNLO QCD and NLO EW cross sections and (2) the comparison of those cross sections with LHC data from Run 1, and projections for future measurements in Run 2.Comment: Proceedings of the Standard Model Working Group of the 2013 Les Houches Workshop, Physics at TeV Colliders, Les houches 3-21 June 2013. 200 page