Reconstructing sparticle mass spectra using hadronic decays

Most sparticle decay cascades envisaged at the Large Hadron Collider (LHC) involve hadronic decays of intermediate particles. We use state-of-the art techniques based on the K⊥ jet algorithm to reconstruct the resulting hadronic final states for simulated LHC events in a number of benchmark supersymmetric scenarios. In particular, we show that a general method of selecting preferentially boosted massive particles such as W±, Z0 or Higgs bosons decaying to jets, using sub-jets found by the K⊥ algorithm, suppresses QCD backgrounds and thereby enhances the observability of signals that would otherwise be indistinct. Consequently, measurements of the supersymmetric mass spectrum at the per-cent level can be obtained from cascades including the hadronic decays of such massive intermediate bosons

Asymptotic analysis of the EPRL four-simplex amplitude

The semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a non-degenerate 4-simplex geometry, the asymptotic formula contains the Regge action for general relativity. A canonical choice of phase for the boundary state is introduced and is shown to be necessary to obtain the results.Comment: v2: improved presentation, typos corrected, refs added; results unchange

A new approach to hyperbolic inverse problems

We present a modification of the BC-method in the inverse hyperbolic problems. The main novelty is the study of the restrictions of the solutions to the characteristic surfaces instead of the fixed time hyperplanes. The main result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the self-adjoint hyperbolic operator up to a diffeomorphism and a gauge transformation. In this paper we prove the crucial local step. The global step of the proof will be presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that potentials A(x),V(x) are real value

Axiomatic approach to radiation reaction of scalar point particles in curved spacetime

Several different methods have recently been proposed for calculating the motion of a point particle coupled to a linearized gravitational field on a curved background. These proposals are motivated by the hope that the point particle system will accurately model certain astrophysical systems which are promising candidates for observation by the new generation of gravitational wave detectors. Because of its mathematical simplicity, the analogous system consisting of a point particle coupled to a scalar field provides a useful context in which to investigate these proposed methods. In this paper, we generalize the axiomatic approach of Quinn and Wald in order to produce a general expression for the self force on a point particle coupled to a scalar field following an arbitrary trajectory on a curved background. Our equation includes the leading order effects of the particle's own fields, commonly referred to as ``self force'' or ``radiation reaction'' effects. We then explore the equations of motion which follow from this expression in the absence of non-scalar forces.Comment: 17 pages, 1 figur

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure

Unitarity and Holography in Gravitational Physics

Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and non-perturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the non-perturbative quantum level, we argue that either 1) the S-matrix is unitary or 2) the dynamics in the region near timelike, null, and spacelike infinity is not described by perturbative quantum gravity about flat space. We also consider perturbation theory about a collapsing asymptotically anti-de Sitter (AdS) black hole, where we show that the algebra of boundary observables within any neighborhood of any boundary Cauchy surface is similarly complete. Whether or not this algebra continues to be complete non-perturbatively, the assumption that the Hamiltonian remains a boundary term implies that information available at the AdS boundary at any one time t_1 remains present at this boundary at any other time t_2.Comment: 13 pages; appendix added on controlling failures of the geometric optics approximatio

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.Comment: 30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references adde

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $\mu_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of measures on a space \cG of maps from $\P^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $\mu_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of \fg-valued three-forms on $M.$ We show that these measures are positive, and that the measures \mu_\cG^{s,t} are Borel probability measures. As an application we show that formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $\mu_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$Comment: Minor correction