Points In Parameter Space Research Articles

Trilepton production at the CERN LHC: Standard model sources and beyond

Events with three or more isolated leptons in the final state are known to be signatures of new physics phenomena at high energy collider physics facilities. Standard model sources of isolated trilepton final states include gauge boson pair production such as $WZ$ and $W{\ensuremath{\gamma}}^{*}$, and $t\overline{t}$ production. We demonstrate that leptons from heavy flavor decays, such as $b\ensuremath{\rightarrow}lX$ and $c\ensuremath{\rightarrow}lX$, provide sources of trileptons that can be orders of magnitude larger after cuts than other standard model backgrounds to new physics processes. We explain the physical reason heavy flavor backgrounds survive isolation cuts. We propose new cuts to control the backgrounds in the specific case of chargino plus neutralino pair production in supersymmetric models. After these cuts are imposed, we show that it should be possible to find at least a $4\ensuremath{\sigma}$ excess for supersymmetry parameter space point LM9 with $30\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity.

Supergravity on an Atiyah-Hitchin base

We construct solutions to five dimensional minimal supergravity using an Atiyah-Hitchin base space. In examining the structure of solutions we show that they generically contain a singularity either on the Atiyah-Hitchin bolt or at larger radius where there is a singular solitonic boundary. However for most points in parameter space the solution exhibits a velocity of light surface (analogous to what appears in a Goedel space-time) that shields the singularity. For these solutions, all closed time-like curves are causally disconnected from the rest of the space-time in that they exist within the velocity of light surface, which null geodesics are unable to cross. The singularities in these solutions are thus found to be hidden behind the velocity of light surface and so are not naked despite the lack of an event horizon. Outside of this surface the space-time is geodesically complete, asymptotically flat and can be arranged so as not to contain closed time-like curves at infinity. The rest of parameter space simply yields solutions with naked singularities.

Collider signals and neutralino dark matter detection in relic-density-consistent models without universality

We present brief synopses of supersymmetric models where either the neutralino composition or its mass is adjusted so that thermal relic neutralinos from the Big Bang saturate the measured abundance of cold dark matter in the universe. We first review minimal supergravity (mSUGRA), and then examine its various one-parameter extensions where we relax the assumed universality of the soft supersymmetry breaking parameters. Our goal is to correlate relic-density-allowed parameter choices with expected phenomena in direct, indirect and collider dark matter search experiments. For every non-universal model, we first provide plots to facilitate the selection of ``dark-matter allowed'' parameter space points, and then present salient features of each model with respect to searches at Tevatron, LHC and ILC and also direct and indirect dark matter searches. We present benchmark scenarios that allow one to compare and contrast the non-universal models with one another and with the paradigm mSUGRA framework. We show that many implications about sparticle properties and collider signals drawn from the analysis of the relic density constraint within mSUGRA do not carry over to simple one-parameter extensions of the mSUGRA framework. We find that in many relic-density-consistent models, there is one (or more) detectable edge in the invariant mass distribution of same-flavour, opposite sign dileptons in SUSY cascade decay events at the LHC. Finally, we scan the parameter space of these various models, requiring consistency with the LEP2 constraint on the chargino mass, and with the observed relic density, and examine prospects for direct and indirect dark matter detection. We find that in a large number of cases the mechanism that causes the early universe neutralino annihilation rate to be large (so as to produce the measured relic density) also enhances the direct detection rate, and often also the rates for indirect detection of neutralino dark matter.

A dynamic objective function technique for generating multiple solution models in seismic tomography

SUMMARY A new technique designed for generating multiple solutions to seismic tomography problems using gradient based inversion is presented. The basic principle is to exploit information gained from previous solutions to help drive the search for new models. This is achieved by adding a feedback or evolution term to the objective function that creates a local maximum at each point in parameter space occupied by the previously computed models. The advantage of this approach is that it only needs to produce a relatively small ensemble of solutions, since each model will substantially differ from all others to the extent permitted by the data. Common features present across the ensemble are, therefore, likely to be well constrained. A synthetic test using surface wave traveltimes and a highly irregular distribution of sources and receivers shows that a range of different velocity models are produced by the new technique. These models tend to be similar in regions of good path coverage, but can differ substantially elsewhere. A simple measure of the variation across the solution ensemble, given by one standard deviation of the velocity at each point, accurately reflects the robustness of the average solution model. Comparison with a standard bootstrap inversion method unequivocally shows that the new approach is superior in the presence of inhomogeneous data coverage that gives rise to under or mixed-determined inverse problems. Estimates of posterior covariance from linear theory correlate more closely with the dynamic objective function results, but require accurate knowledge of a priori model uncertainty. Application of the new method to traveltimes derived from long-term cross-correlations of ambient noise contained in passive seismic data recorded in the Australian region demonstrates its effectiveness in practice, with results well corroborated by prior information. The dynamic objective function scheme has several drawbacks, including a somewhat arbitrary choice for the shape of the evolution term, and no guarantee of a thorough exploration of parameter space. On the other hand, it is tolerant of non-linearity in the inverse problem, is relatively straightforward to implement, and appears to work well in practice. For many applications, it may be a useful addition to the suite of synthetic resolution tests that are commonly used.

Sampling using a ‘bank’ of clues

An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments typical of investigations into current constraints on Beyond-the-Standard-Model physics. The sampling technique makes use of pre-existing information (which can safely be of low or uncertain quality) relating to the distribution from which it is desired to sample. This information should come in the form of a “bank” or “cache” of parameter space points of which at least some may be expected to be near regions of interest in the desired distribution. In practical circumstances such “banks of clues” are easy to assemble from earlier work, aborted runs, discarded burn-in samples from failed sampling attempts, or from prior scouting investigations. The technique equilibrates between disconnected parts of the distribution without user input. The algorithm is not lead astray by “bad” clues, but there is no free lunch: performance gains will only be seen where clues are helpful.

Topological quantization by controlled paths: Application to Cooper pairs pumps

When physical systems are tunable by three classical parameters, level degeneracies may occur at isolated points in parameter space. A topological singularity in the phase of the degenerate eigenvectors exists at these points. When a path encloses such point, the accumulated geometrical phase is sensitive to its presence. Furthermore, surfaces in parameter space enclosing such point can be used to characterize the eigenvector singularities through their Chern indices, which are integers. They can be used to quantize a physical quantity of interest. This quantity changes continuously during an adiabatic evolution along a path in parameter space. Quantization requires to turn this path into a surface with a well defined Chern index. We analyze the conditions necessary to a topological quantization by controlled paths. It is applied to Cooper pair pumps. For more general problems, a set of four criteria is proposed to check if topological quantization is possible.

Sensitivity of nonrenormalizable trajectories to the bare scale

Working in scalar field theory, we consider renormalization group trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Λ, changes as the bare scale (and hence the duration of the flow down to Λ) is changed. When the effective action satisfies Polchinski's version of the exact renormalization group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Λ = 0. This does not seem to hold for more elaborate generalizations.

Compound windows of the Hénon-map

For the two-parameter second-order Hénon map, the shapes and locations of the periodic windows–continua of parameter values for which solutions x 0 , x 1 , … can be stably periodic, embedded in larger regions where chaotic solutions or solutions of other periods prevail–are found by a random searching procedure and displayed graphically. Many windows have a typical shape, consisting of a central “body” from which four narrow “antennae” extend. Such windows, to be called compound windows, are often arranged in bands, to be called window streets, that are made up largely of small detected but poorly resolved compound windows. For each fundamental subwindow–the portion of a window where a fundamental period prevails–a stability measure U is introduced; where the solution is stable, | U | < 1 . Curves of constant U are found by numerical integration. Along one line in parameter space the Hénon-map reduces to the one-parameter first-order logistic map, and two antennae from each compound window intersect this line. The curves where U = 1 and U = − 1 that bound either antenna are close together within these intersections, but, as either curve with U = − 1 leaves the line, it diverges from the curve where U = 1 , crosses the other curve where U = − 1 , and nears the other curve where U = 1 , forming another antenna. The region bounded by the numerically determined curves coincides with the subwindow as found by random searching. A fourth-degree equation for an idealized curve of constant U is established. Points in parameter space producing periodic solutions where x 0 = x m = 0 , for given values of m , are found to lie on Cantor sets of curves that closely fit the window streets. Points producing solutions where x 0 = x m = 0 and satisfying a third condition, approximating the condition that x n be bounded as n → − ∞ , lie on curves, to be called street curves of order m , that approximate individual members of the Cantor set and individual window streets. Compound windows of period m + m ′ tend to occur near the intersections of street curves of orders m and m ′ . Some exceptions to what appear to be fairly general results are noted. The exceptions render it difficult to establish general theorems.

Transport through a multiply connected interacting mesoscopic system using the Keldysh formalism

We apply the Keldysh formalism in order to derive a current formula easy to use for a system with many sites, one of which is interacting. The main technical challenge is to deal with the lesser Green's function. It turns out that, in the case of the left-right symmetry, the knowledge of the lesser Green's function is not necessary and an exact current formula can be expressed in terms of retarded Green's functions only. The application is done for a triangular interferometer which gives a good account of the Fano-Kondo effect. It is found that the interference effects, in the context of Kondo correlations, give rise to a point in the parameter space where the conductance is temperature independent. We include a comparison with the results from Ng's ansatz [Phys. Rev. Lett. 70, 3635 (1993)], which are less accurate, but can be used also in the absence of the above mentioned symmetry.

NMSPEC: A Fortran code for the sparticle and Higgs masses in the NMSSM with GUT scale boundary conditions

NMSPEC is a Fortran code that computes the sparticle and Higgs masses, as well as Higgs decay widths and couplings in the NMSSM, with soft susy breaking terms specified at M GUT . Exceptions are the soft singlet mass m s 2 and the singlet self-coupling κ, that are both determined in terms of the other parameters through the minimization equations of the Higgs potential. We present a first analysis of the NMSSM parameter space with universal susy breaking terms at M GUT —except for m s and A κ —that passes present experimental constraints on sparticle and Higgs masses. We discuss in some detail a region in parameter space where a SM-like Higgs boson decays dominantly into two CP odd singlet-like Higgs states. Program summary Manuscript title: NMSPEC: A Fortran code for the sparticle and Higgs masses in the NMSSM with GUT scale boundary conditions Authors: Ulrich Ellwanger, Cyril Hugonie Program title: NMSPEC Catalogue identifier: ADZD_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 121 539 No. of bytes in distributed program, including test data, etc.: 1 560 340 Distribution format: tar.gz Programming language: FORTRAN Computer: Mac, PC, Sun, Dec, Alpha Operating system: Mac OSC, Linux, Unix, Windows RAM: 2M bytes Keywords: Supersymmetry, Higgs masses, sparticle masses, NMSSM PACS: 12.60.Jv, 14.80.Cp, 14.80.Ly Classification: 11.6 Nature of problem: Computation of the Higgs and Sparticle spectrum in the NMSSM with GUT scale boundary conditions, check of theoretical and experimental constraints. Solution method: Integration of the RGEs for all couplings and mass terms from the GUT scale to the Susy scale using a modified Runge–Kutta method; computation and diagonalization of all mass matrices including up to two loop radiative corrections; computation of Higgs decay widths and branching ratios; comparison with exp. bounds from LEPII and the Tevatron. Running time: Less than 1 s per point in parameter space.

Collider signatures of singlet extended Higgs sectors

We explore the collider signatures of the Higgs sectors in singlet extended minimal supersymmetric standard models. We find that even with reduced couplings due to singlet mixing, a significant portion of the parameter spaces have a discoverable Higgs via traditional decay modes or via invisible decays (directly to neutralinos or through cascade decays to neutralinos and neutrinos). For illustrative points in parameter space we give the likelihood of Higgs discovery. In cases where neither traditional nor invisible modes can discover the Higgs, the neutralino sector may provide evidence for the extended models.

A method to calculate coverage probability from uncertainties in radiotherapy via a statistical shape model

In this paper we describe a technique that may be used to model the geometric uncertainties that accrue during the radiotherapy process. Using data from in-treatment cone beam CT scans, we simultaneously analyse non-uniform observer delineation variability and organ motion together with patient set-up errors via the creation of a point distribution model (PDM). We introduce a novel method of generating a coverage probability matrix, that may be used to determine treatment margins and calculate uncertainties in dose, from this statistical shape model. The technique does not assume rigid body motion and can extrapolate shape variability in a statistically meaningful manner. In order to construct the PDM, we generate corresponding surface points over a set of delineations. Correspondences are established at a set of points in parameter space on spherically parameterized and canonical aligned outlines. The method is demonstrated using rectal delineations from serially acquired in-treatment cone beam CT image volumes of a prostate patient (44 image volumes total), each delineated by a minimum of two observers (maximum six). Two PDMs are constructed, one with set-up errors included and one without. We test the normality assumptions of the PDMs and find the distributions to be Gaussian in nature. The rectal PDM variability is in general agreement with data in the literature. The two resultant coverage probability matrices show differences as expected.

Degeneracy of Resonances: Branch Point and Branch Cuts in Parameter Space

The rich phenomenology of crossings and anticrossings of energies and widths, observed in an isolated doublet of resonances when one control parameter is varied, is fully explained in terms of the topological properties of the energy hypersurfaces close to the degeneracy point. The hypersurface representing the complex resonance eigenvalues, as functions of the control parameters, has an algebraic branch point of rank one, and branch cuts in its real and imaginary parts, in parameter space. Associated with this singularity in parameter space, the scattering matrix, Sl(E), and the Green’s function, Gl(+)(k; r,r'), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of any degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.

Numerical simulation of the Vlasov–Maxwell system for the nonlinear Berk–Breizman phenomenology

A fusion plasma is modeled by a one-dimensional Vlasov–Maxwell system of equations. Particle annihilation is considered by a dedicated factor in the Vlasov equation. A term describing background damping mechanisms is considered in the equation relating the electric field to the current (Berk–Breizman model). Results are presented for simulations in a one-dimensional velocity space, the extension by a further velocity dimension is sketched. As an initial condition, a bump-on-tail distribution is assumed. The time evolution of the system is studied and characterized with respect to different points in parameter space. A fractional steps method using cubic splines interpolation is applied for time-integrating this system.

On the stability of the reduced basis method for Stokes equations in parametrized domains

We present an application of reduced basis method for Stokes equations in domains with affine parametric dependence. The essential components of the method are (i) the rapid convergence of global reduced basis approximations – Galerkin projection onto a space W N spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) the off-line/on-line computational procedures decoupling the generation and projection stages of the approximation process. The operation count for the on-line stage – in which, given a new parameter value, we calculate an output of interest – depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. Particular attention is given (i) to the pressure treatment of incompressible Stokes problem; (ii) to find an equivalent inf–sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem; (iii) to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions; (iv) to reduce computational costs in order to allow real-time solution of parametrized problem.

Dark matter from gaugino mediation

We study dark matter (DM) for gaugino-mediated supersymmetry breaking and compactdimensions of order of the grand unification scale. Higgs fields are bulk fields and ingeneral their masses differ from those of squarks and sleptons at the unificationscale. As a consequence, at different points in parameter space, the gravitino, aneutralino or a scalar lepton can be the lightest (LSP) or next-to-lightest (NLSP)superparticle. We investigate the constraints from primordial nucleosynthesis on thedifferent scenarios. While neutralino DM and gravitino DM with a NLSP are consistent for a wide range of parameters, gravitino DM with a NLSP is strongly constrained. Gravitino DM with aχ0 NLSP is excluded.

Structural kinetic modeling of metabolic networks.

To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.

NMHDECAY 2.1: An updated program for sparticle masses, Higgs masses, couplings and decay widths in the NMSSM

We describe the improved properties of the NMHDECAY program, that is designed to compute Higgs and sparticle masses and Higgs decay widths in the NMSSM. In the version 2.0, Higgs decays into squarks and sleptons are included, accompanied by a calculation of the squark, gluino and slepton spectrum and tests against constraints from LEP and the Tevatron. Further radiative corrections are included in the Higgs mass calculation. A link to MicrOMEGAs allows to compute the dark matter relic density, and a rough (lowest order) calculation of BR ( b → s γ ) is performed. Finally, version 2.1 allows to integrate the RGEs for the soft terms up to the GUT scale. Program summary Title of program:NMHDECAY_SCAN, NMHDECAY_SLHA Catalogue identifier:ADXW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXW_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Programming language used:Fortran Computer:Mac, PC, Sun, Dec, Alpha Operating system:Mac OSX, Linux, Unix, Windows No. of lines in distributed program, including test data, etc.:20 060 No. of bytes in distributed program, including test data, etc.:133 644 RAM:2M bytes Distribution format:tar.gz Number of processors used:1 Classification:11.6 Journal reference of previous version:JHEP 0502:066, 2005 Does the new version supersede the previous version?:Yes Nature of problem:Computation of the Higgs and sparticle spectrum in the NMSSM and check of theoretical and experimental constraints. Solution method:Mass matrices including up to 2 loop radiative corrections for the Higgs bosons and all sparticles are computed and diagonalized. All Higgs decay widths are computed and branching ratios are compared to experimental bounds. Renormalisation group equations are integrated up to the GUT scale using a modified Runge–Kutta method, in order to check for the absence of a Landau pole. A modified version of MicrOmegas_1.3 can be called in order to compute the relic density of the lightest sparticle. Reasons for the new version:Higgs to sparticle decays added, computation of dark matter relic density added. Summary of revisions:Treatment of RGEs and radiative corrections improved, Higgs to sparticle decays added, new link to MicrOmegas_1.3. Restrictions:none Unusual features:none Running time:<1 s per point in parameter space

A Method for Stability and Bifurcation Control

In this note, we use the Ro/spl uml/ssler system as an illustrative example to present a method for controlling stability and bifurcations of nonlinear dynamical systems. This approach employs the idea used in computing the transition variety sets of constrained bifurcations to find the stability boundaries of equilibrium points in parameter space. With this method and feedback control, one can obtain appropriate parameter values to delay either static, dynamic, or both bifurcations. A feedback controller is designed to stabilize the Ro/spl uml/ssler system using all feasible control parameters. A numerical example is given to demonstrate the theoretical results.

Statistical Evaluation of Ion-Channel Gating Models Based on Distributions of Log-Likelihood Ratios

The distributions of log-likelihood ratios (ΔLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Ξ, full model; ΞR, submodel) were studied both theoretically and using simulated data. When Ξ is true, ΔLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When ΞR is true and corresponds to a distinct point in full parameter space, ΔLL is Γ-distributed (2ΔLL is χ-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, ΞR corresponds to an infinite set of points in parameter space. The distribution of ΔLL is a mixture of two components, one identically zero, the other approximated by a Γ-distribution. This empirical distribution of ΔLL, assuming ΞR, allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Ξ, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and ΔLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of ΔLL when Ξ or ΞR is true.