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

Missing Momentum Reconstruction and Spin Measurements at Hadron Colliders

We study methods for reconstructing the momenta of invisible particles in cascade decay chains at hadron colliders. We focus on scenarios, such as SUSY and UED, in which new physics particles are pair produced. Their subsequent decays lead to two decay chains ending with neutral stable particles escaping detection. Assuming that the masses of the decaying particles are already measured, we obtain the momenta by imposing the mass-shell constraints. Using this information, we develop techniques of determining spins of particles in theories beyond the standard model. Unlike the methods relying on Lorentz invariant variables, this method can be used to determine the spin of the particle which initiates the decay chain. We present two complementary ways of applying our method by using more inclusive variables relying on kinematic information from one decay chain, as well as constructing correlation variables based on the kinematics of both decay chains in the same event.Comment: Version to appear in JHE

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

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

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

Minimal Universal Extra Dimensions in CalcHEP/CompHEP

We present an implementation of the model of minimal universal extra dimensions (MUED) in CalcHEP/CompHEP. We include all level-1 and level-2 Kaluza-Klein (KK) particles outside the Higgs sector. The mass spectrum is automatically calculated at one loop in terms of the two input parameters in MUED: the radius of the extra dimension and the cut-off scale of the model. We implement both the KK number conserving and the KK number violating interactions of the KK particles. We also account for the proper running of the gauge coupling constants above the electroweak scale. The implementation has been extensively cross-checked against known analytical results in the literature and numerical results from other programs. Our files are publicly available and can be used to perform various automated calculations within the MUED model.Comment: 32 pages, 4 figures, 6 tables, invited contribution for New Journal of Physics Focus Issue on 'Extra Space Dimensions', the model file can be downloaded from http://home.fnal.gov/~kckong/mued

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