Showing papers on "Elementary particle published in 2006"

Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos

Abstract: IN THE BEGINNING WAS THE BIT...The universe is made of bits of information and it has been known for more than a century that every piece of the the universe - every electron, atom and molecule - registers these bits and that information. It is only in the last years, however, with the discovery and development of quantum computers, that scientists have gained a fundamental understanding of just how that information is registered and processed. Building on recent breakthroughs in quantum computation, Seth Lloyd shows how the universe itself is a giant computer. Every atom and elementary particle stores these bits, and every collision between those atoms and particles flips the bits into a new arrangement and effortlessly spins out beautiful and complex systems, including galaxies, planets and life itself. But every computer needs a program, the set of instructions that tell it what patterns to create. Where did the bits come from that tell the universe to create its magnificent complexity? Who - or what - is programming the universe?

Tests of the standard electroweak model in nuclear beta decay

Abstract: The current status of precision measurements in allowed nuclear beta decay is reviewed, including neutron decay, with emphasis on their potential to look for new physics beyond the standard electroweak model. Experimental results are interpreted in the framework of phenomenological model-independent descriptions of nuclear beta decay as well as in some specific extensions of the standard model. The values of the standard couplings and the constraints on the exotic couplings of the general beta decay Hamiltonian are updated. The ratio between the axial and vector couplings obtained is ${C}_{A}∕{C}_{V}=\ensuremath{-}1.269\phantom{\rule{0.2em}{0ex}}92(69)$ under standard model assumptions. Particular attention is devoted to the discussion of the sensitivity and complementarity of different precision experiments in direct beta decay. The prospects and impact of recent developments of precision tools and of high intensity low-energy beams are also addressed.

Supersymmetry parameter analysis : SPA convention and project

Abstract: High-precision analyses of supersymmetry parameters aim at reconstructing the fundamental supersymmetric theory and its breaking mechanism. A well defined theoretical framework is needed when higher-order corrections are included. We propose such a scheme, Supersymmetry Parameter Analysis SPA, based on a consistent set of conventions and input parameters. A repository for computer programs is provided which connect parameters in different schemes and relate the Lagrangian parameters to physical observables at LHC and high energy e(+)e(-) linear collider experiments, i.e., masses, mixings, decay widths and production cross sections for supersymmetric particles. In addition, programs for calculating high-precision low energy observables, the density of cold dark matter (CDM) in the universe as well as the cross sections for CDM search experiments are included. The SPA scheme still requires extended efforts on both the theoretical and experimental side before data can be evaluated in the future at the level of the desired precision. We take here an initial step of testing the SPA scheme by applying the techniques involved to a specific supersymmetry reference point.

Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model

Abstract: We show that the energy density spectrum of the primordial gravitational waves has characteristic features due to the successive changes in the relativistic degrees of freedom during the radiation era. These changes make the evolution of radiation energy density deviate from the conventional adiabatic evolution, {rho}{sub r}{proportional_to}a{sup -4}, and thus cause the expansion rate of the universe to change suddenly at each transition which, in turn, modifies the spectrum of primordial gravitational waves. We take into account all the particles in the standard model of elementary particles. In addition, free-streaming of neutrinos damps the amplitude of gravitational waves, leaving characteristic features in the energy density spectrum. Our calculations are solely based on the standard model of cosmology and particle physics, and therefore these features must exist. Our calculations significantly improve the previous ones which ignored these effects and predicted a smooth, featureless spectrum.

Stability and symmetry breaking in the general two-Higgs-doublet model

Abstract: A method is presented for the analysis of the scalar potential in the general two-Higgs-doublet model. This allows us to give the conditions for the stability of the potential and for electroweak symmetry breaking in this model in a very concise way. These results are then applied to two different Higgs potentials in the literature, namely the MSSM and the two-Higgs-doublet potential proposed by Gunion et al. The known results for these models follow easily as special cases from the general results. In particular, for the potential of Gunion et al. we can clarify the stability and symmetry-breaking properties of the model with our method.

Polarized light propagating in a magnetic field as a probe for millicharged fermions.

Abstract: Possible extensions of the standard model of particle physics suggest the existence of particles with small, unquantized electric charge Photon-initiated pair production of millicharged fermions in a magnetic field would manifest itself as a vacuum magnetic (VM) dichroism We show that laser polarization experiments searching for this effect yield, in the mass range below 01 eV, much stronger constraints on millicharged fermions than previous laboratory searches VM birefringence due to virtual pair production gives a slightly better constraint for masses between 01 and a few eV We comment on the possibility that the VM dichroism observed by PVLAS arises from pair production of such millicharged fermions rather than from single production of axionlike particles Such a scenario can be confirmed or firmly excluded by a search for invisible decays of orthopositronium with a branching-fraction sensitivity of about ${10}^{\ensuremath{-}9}$

LHC Signals from Warped Extra Dimensions

Abstract: We study production of Kaluza-Klein gluons (KKG) at the Large Hadron Collider (LHC) in the framework of a warped extra dimension with the Standard Model (SM) fields propagating in the bulk. We show that the detection of KK gluon is challenging since its production is suppressed by small couplings to the proton's constituents. Moreover, the KK gluon decaysmostly to top pairs due to an enhanced coupling and hence is broad. Nevertheless, we demonstrate that for MKKG<~;; 4 TeV, 100 fb-1 of data at the LHC can provide discovery of the KK gluon. We utilize a sizeable left-right polarization asymmetry from the KK gluon resonance to maximize the signal significance, and we explore the novel feature of extremely highly energetic"top-jets." We briefly discuss how the detection of electroweak gauge KK states (Z/W) faces a similar challenge since their leptonic decays ("golden" modes) are suppressed. Our analysis suggests that other frameworks, for example little Higgs, which rely on UV completion via strong dynamics might face similar challenges, namely (1) Suppressed production rates for the new particles (such as Z'), due to their"lightfermion-phobic" nature, and (2) Difficulties in detection since the new particles are broad and decay predominantly to third generation quarks andmore » longitudinal gauge bosons.« less

Recursion relations for gauge theory amplitudes with massive vector bosons and fermions

Abstract: We apply the on-shell tree-level recursion relations of Britto, Cachazo, Feng and Witten to a variety of processes involving internal and external massive particles with spin. We show how to construct multi-vector boson currents where one or more off-shell vector bosons couples to a quark pair and number of gluons. We give compact results for single vector boson currents with up to six partons and double vector boson currents with up to four partons for all helicity combinations. We also provide expressions for single vector boson currents with a quark pair and an arbitrary number of gluons for some specific helicity configurations. Finally, we show how to generalise the recursion relations to handle massive particles with spin on internal lines using gg→t as an example.

MSSM Higgs Boson Searches at the Tevatron and the LHC: Impact of Different Benchmark Scenarios

Abstract: The Higgs boson search has shifted from LEP2 to the Tevatron and will subse- quently move to the LHC. The current limits from the Tevatron and the prospective sensitivities at the LHC are often interpreted in specific MSSM scenarios. For heavy Higgs boson production and subsequent decay into bb or � + � − , the present Tevatron data allow to set limits in the MA-tanplane for small MA and large tanvalues. Similar channels have been explored for the LHC, where the discovery reach extends to higher values of MA and smaller tan�. Searches for MSSM charged Higgs bosons, produced in top decays or in association with top quarks, have also been investigated at the Tevatron and the LHC. We analyze the current Tevatron limits and prospective LHC sensitivities. We discuss how robust they are with respect to variations of the other MSSM parameters and possible improvements of the theoretical predictions for Higgs boson production and decay. It is shown that the inclusion of supersymmetric radiative corrections to the production cross sections and decay widths leads to impor- tant modifications of the present limits on the MSSM parameter space. The impact on the region where only the lightest MSSM Higgs boson can be detected at the LHC is also analyzed. We propose to extend the existing benchmark scenarios by including additional values of the higgsino mass parameter µ. This affects only slightly the search channels for a SM-like Higgs boson, while having a major impact on the searches for non-standard MSSM Higgs bosons.

Dark matter with invisible light from heavy double charged leptons of almost-commutative geometry?

Abstract: A new candidate for cold dark matter arises from a novel elementary particle model: the almost-commutative AC-geometrical framework. Two heavy leptons are added to the standard model, each one sharing a double opposite electric charge and an own lepton flavour number. The novel mathematical theory of almost-commutative geometry (Connes 1994 Noncommutative Geometry (London: Academic)) wishes to unify gauge models with gravity. In this scenario two new heavy (mL ≥ 100 GeV), oppositely double charged leptons (A,C), (A with charge −2 and C with charge +2), are born with no twin quark companions. The model naturally involves a new U(1) gauge interaction, possessed only by the AC-leptons and providing a Coulomb-like attraction between them. AC-leptons posses electro-magnetic as well as Z-boson interaction and, according to the charge chosen for the new U(1) gauge interaction, a new 'invisible light' interaction. Their final cosmic relics are bounded into 'neutral' stable atoms (AC) forming the mysterious cold dark matter, in the spirit of the Glashow's Sinister model. An (AC) state is reached in the early Universe along a tail of a few secondary frozen exotic components. They should be here now somehow hidden in the surrounding matter. The two main secondary manifest relics are C2+ (mostly hidden in a neutral (C2+e−e−) 'anomalous helium' atom, at a 10−8 ratio) and a corresponding 'ion' A2− bounded with an ordinary helium ion (4He)2+; indeed the positive helium ions are able to attract and capture the free A2− fixing them into a neutral relic cage that has nuclear interaction (4He2+A2−). The cage preserves the leptons to later recombine with neutral (C2+e−e−) into (AC) evanescent states. In early and late cosmic stages (AC) gas is leading to cold dark matter gravity seeds. It can form dense cores inside dense matter bodies (stars and planets). Binding (C2+e−e−) + (4He2+A2−) into (AC) atoms results in a steady decrease of the anomalous isotopes and a growing concentration of AC-gas. However the (AHe) influence on big bang nucleo-synthesis and catalysis of nuclear transformations in terrestrial matter appears to be a serious problem for the model. Moreover the zero lepton OLe-helium (AHe), (C2+e−e−) pollution and its on-going (AHe) catalysis in terrestrial waters may release frequent tens MeV gamma photons whose pair production leads to nearly aligned electron pairs; their consequent expected presence by twin Cherenkov rings poses a crucial test to the model. Their total absence in Super-Kamiokande or SNO records might point to the failure of the model, while their eventual discovery (above the background) may hint to the double charge AC-model to solve the cold dark matter puzzle. The new invisible light attraction allows us to stimulate the effective A–C recombination into (AC) atoms inside dense matter bodies (stars and planets), resulting in a decrease of anomalous isotopes below the experimental upper limits. OLe-helium pollution of terrestrial matter and (OHe) catalysis of nuclear reactions in it is one of the dramatic problems (or exciting advantages?) of the present model.

Distinguishing Spins in Decay Chains at the Large Hadron Collider

Abstract: If new particles are discovered at the LHC, it will be important to determine their spins in as model-independent a way as possible. We consider the case, commonly encountered in models of physics beyond the Standard Model, of a new scalar or fermion D decaying sequentially into other new particles C,B,A via the decay chain D→Cq, C→Blnear, B→Alfar, lnear and lfar being opposite-sign same-flavour charged leptons and A being invisible. We compute the observable 2- and 3-particle invariant mass distributions for all possible spin assignments of the new particles, and discuss their distinguishability using a quantitative measure known as the Kullback-Leibler distance.

Smoking-gun signatures of little Higgs models

Abstract: Little Higgs models predict new gauge bosons, fermions and scalars at the TeV scale that stabilize the Higgs mass against quadratically divergent one-loop radiative corrections. We categorize the many little Higgs models into two classes based on the structure of the extended electroweak gauge group and examine the experimental signatures that identify the little Higgs mechanism in addition to those that identify the particular little Higgs model. We find that by examining the properties of the new heavy fermion(s) at the LHC, one can distinguish the structure of the top quark mass generation mechanism and test the little Higgs mechanism in the top sector. Similarly, by studying the couplings of the new gauge bosons to the light Higgs boson and to the Standard Model fermions, one can confirm the little Higgs mechanism and determine the structure of the extended electroweak gauge group.

Lattice simulations of the thermodynamics of strongly interacting elementary particles and the exploration of new phases of matter in relativistic heavy ion collisions

Abstract: At high temperatures or densities matter formed by strongly interacting elementary particles (hadronic matter) is expected to undergo a transition to a new form of matter - the quark gluon plasma - in which elementary particles (quarks and gluons) are no longer confined inside hadrons but are free to propagate in a thermal medium much larger in extent than the typical size of a hadron. The transition to this new form of matter as well as properties of the plasma phase are studied in large scale numerical calculations based on the theory of strong interactions - Quantum Chromo Dynamics (QCD). Experimentally properties of hot and dense elementary particle matter are studied in relativistic heavy ion collisions such as those currently performed at the relativistic heavy ion collider (RHIC) at BNL. We review here recent results from studies of thermodynamic properties of strongly interacting elementary particle matter performed on Teraflops-Computer. We present results on the QCD equation of state and discuss the status of studies of the phase diagram at non-vanishing baryon number density.

Probing the QCD equation of state with thermal photons in nucleus-nucleus collisions at RHIC

Abstract: Thermal photon production at mid-rapidity in Au+Au reactions at \(\sqrt{s_{NN}}=200 GeV\) is studied in the framework of a hydrodynamical model that describes efficiently the bulk identified hadron spectra at RHIC. The combined thermal plus NLO pQCD photon spectrum is in good agreement with the yields measured by the PHENIX experiment for all Au+Au centralities. Within our model, we demonstrate that the correlation of the thermal photon slopes with the charged hadron multiplicity in each centrality provides direct empirical information on the underlying degrees of freedom and on the form of the equation of state, s(T)/T3, of the strongly interacting matter produced in the course of the reaction.

Pion condensation in electrically neutral cold matter with finite baryon density

Abstract: The possibility of the pion condensation phenomenon in cold and electrically neutral dense baryonic matter is investigated in β-equilibrium. For simplicity, the consideration is performed in the framework of a Nambu–Jona-Lasinio model with two quark flavors at zero current quark mass and for rather small values of the baryon chemical potential, where the diquark condensation might be ignored. Two sets of model parameters are used. For the first, the pion condensed phase with finite baryon density is realized. In this phase both electrons and the pion condensate take part in the neutralization of the quark electric charge. For the second set of model parameters, the pion condensation is impossible if the neutrality condition is imposed. The behavior of meson masses vs. quark chemical potential has been studied in electrically neutral matter.

Quasiparticle breakdown in a quantum spin liquid

Abstract: Much of modern condensed matter physics is understood in terms of elementary excitations, or quasiparticles—fundamental quanta of energy and momentum1,2. Various strongly interacting atomic systems are successfully treated as a collection of quasiparticles with weak or no interactions. However, there are interesting limitations to this description: in some systems the very existence of quasiparticles cannot be taken for granted. Like unstable elementary particles, quasiparticles cannot survive beyond a threshold where certain decay channels become allowed by conservation laws; their spectrum terminates at this threshold. Such quasiparticle breakdown was first predicted for an exotic state of matter—super-fluid 4He at temperatures close to absolute zero, a quantum Bose liquid where zero-point atomic motion precludes crystallization1,2,3,4. Here we show, using neutron scattering, that quasiparticle breakdown can also occur in a quantum magnet and, by implication, in other systems with Bose quasiparticles. We have measured spin excitations in a two-dimensional quantum magnet, piperazinium hexachlorodicuprate (PHCC)5, in which spin-1/2 copper ions form a non-magnetic quantum spin liquid, and find remarkable similarities with excitations in superfluid 4He. We observe a threshold momentum beyond which the quasiparticle peak merges with the two-quasiparticle continuum. It then acquires a finite energy width and becomes indistinguishable from a leading-edge singularity, so that excited states are no longer quasiparticles but occupy a wide band of energy. Our findings have important ramifications for understanding excitations with gapped spectra in many condensed matter systems, ranging from band insulators to high-transition-temperature superconductors6.

Yukawa and triscalar processes in electroweak baryogenesis

Abstract: We derive the contributions to the quantum transport equations for electroweak baryogenesis due to decays and inverse decays induced by triscalar and Yukawa interactions. In the minimal supersymmetric standard model (MSSM), these contributions give rise to couplings between Higgs and fermion supermultiplet densities, thereby communicating the effects of CP-violation in the Higgs sector to the baryon sector. We show that the decay and inverse decay-induced contributions that arise at zeroth order in the strong coupling, alphas, can be substantially larger than the [script O](alphas) terms that are generated by scattering processes and that are usually assumed to dominate. We revisit the often-used approximation of fast Yukawa-induced processes and show that for realistic parameter choices it is not justified. We solve the resulting quantum transport equations numerically with special attention to the impact of Yukawa rates and study the dependence of the baryon-to-entropy ratio YB on MSSM parameters.

Very narrow shadow extra Z boson at colliders

Abstract: We consider the phenomenological consequences of a hidden Higgs sector extending the standard model (SM), in which the 'shadow Higgs' are uncharged under the SM gauge groups. We consider a simple U(1) model with one Higgs singlet. One mechanism which sheds light on the shadow sector is the mixing between the neutral gauge boson of the SM and the additional U(1) gauge group. The mixing happens through the usual mass mixing and also kinetic mixing, and is the only way the 'shadow Z' couples to the SM. We study in detail modifications that the presence of such shadow sector would bring to the electroweak precision tests, which in turn provide constraints on the kinetic-mixing parameter, s{sub {epsilon}}, left free in our model. The shadow Z production rate at the CERN LHC and the International Linear Collider depends on s{sub {epsilon}}. We find that the observable event rate at both facilities is possible for a reasonable range of s{sub {epsilon}} allowed by electroweak precision tests.

Quantum ether: photons and electrons from a rotor model

Abstract: We give an example of a purely bosonic model---a rotor model on the 3D cubic lattice---whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac fermions. This model can be viewed as a ``quantum ether;'' a medium that gives rise to both photons and electrons. It illustrates a general mechanism for the emergence of gauge bosons and fermions known as ``string-net condensation.'' Other, more complex, string-net condensed models can have excitations that behave like gluons, quarks and other particles in the standard model. This suggests that photons, electrons and other elementary particles may have a unified origin: string-net condensation in our vacuum.

Sigma Terms of Light-Quark Hadrons

Abstract: A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σπ = mπ/2. This truncation also provides a decent estimate of σρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σω by ≲25%. A Poincare-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σ N and σΔ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σ N ≃ 60 MeV and σΔ ≃ 50 MeV.

Fast hadron freeze-out generator

Abstract: We have developed a fast Monte Carlo procedure of hadron generation that allows one to study and analyze various observables for stable hadrons and hadron resonances produced in ultrarelativistic heavy ion collisions. Particle multiplicities are determined based on the concept of chemical freeze-out. Particles can be generated on the chemical or thermal freeze-out hypersurface represented by a parametrization or a numerical solution of relativistic hydrodynamics with given initial conditions and equation of state. Besides standard spacelike sectors associated with the volume decay, the hypersurface may also include nonspacelike sectors related to the emission from the surface of expanding system. For comparison with other models and experimental data, we demonstrate the results based on the standard parametrizations of the hadron freeze-out hypersurface and flow velocity profile under the assumption of a common chemical and thermal freeze-out. The C++ generator code is written under the ROOT framework and is available for public use at http://uhkm.jinr.ru/.

Prospects for the search for a doubly charged Higgs in the left–right symmetric model with ATLAS

Abstract: We estimate the potential for observation at the LHC of a doubly charged Higgs boson, as predicted in left?right symmetric models. Single production by vector boson fusion, W+W+ ? ?++L,R and pair production by the Drell?Yan process are considered. Various decay channels are investigated: dileptons, including pairs of ?, as well as WW.

Phenomenology of mirror fermions in the littlest Higgs model with T-parity

Abstract: Little Higgs models are an interesting alternative to explain electroweak symmetry breaking without fine-tuning. Supplemented with a discrete symmetry (T-parity) constraints from electroweak precision data are naturally evaded and also a viable dark matter candidate is obtained. T-parity implies the existence of new (mirror) fermions in addition to the heavy gauge bosons of the little Higgs models. In this paper we consider the effects of the mirror fermions on the phenomenology of the littlest Higgs model with T-parity at the LHC. We study the most promising production channels and decay chains for the new particles. We find that the mirror fermions have a large impact on the magnitude of signal rates and on the new physics signatures. Realistic background estimates are given.

Superstrings, entropy and the elementary particles content of the standard model

Abstract: A number of interconnected issues involving superstring theory, entropy and the particle content of the standard model of high energy physics are discussed in the present work. It is found that within a non-transfinite approximation, the number of elementary particles is given by Dim SU(8) in full agreement with the prediction gained from dividing the total number of the massless level of Heterotic string theory (256)(16) = 8064 by the spin representation 27 = 128 which gives Dim SU(8) = (8)2 − 1 = (8064)/(128) = 63 particles. For the exact transfinite case however, one finds our previously established E-infinity result: N = ( 336 + 16 k ) ( 3 / 2 + k ) ( 16 + k ) / ( 128 + 8 k ) = α ¯ o / 2 , where k = ϕ3(1 − ϕ3), ϕ = ( 5 - 1 ) / 2 and α ¯ o / 2 = 68.54101965 . Setting k = 0 one finds that n = 63 exactly as in the non-transfinite case.

Search for neutral Higgs Bosons of the minimal supersymmetric standard model decaying to τ pairs in pp̄ collisions at s=1.96TeV

Abstract: We present a search for neutral supersymmetric Higgs bosons decaying to tau pairs produced in pp collisions at square root of s = 1.96 TeV. The data, corresponding to 310 pb(-1) integrated luminosity, were collected with the Collider Detector at Fermilab in run II of the Tevatron. No significant excess above the standard model backgrounds is observed. We set exclusion limits on the production cross section times branching fraction to tau pairs for Higgs boson masses in the range from 90 to 250 GeV/c2.

The Dalitz decay π0 → e+e– γ revisited

Abstract: The amplitude of the Dalitz decay π0 → e+e– γ is studied and its model-independent properties are discussed in detail. A calculation of radiative corrections is performed within the framework of two-flavor chiral perturbation theory, enlarged by virtual photons and leptons. The lowest meson dominance approximation, motivated by large NC considerations, is used for the description of the π0 –γ*–γ* transition form factor and for the estimate of the NLO low energy constants involved in the analysis. The two photon reducible contributions are included and discussed. Previous calculations are extended to the whole kinematical range of the soft photon approximation, thus allowing for the possibility to consider various experimental situations and observables.

Detecting the standard model Higgs boson in the WW decay channel using forward proton tagging at the LHC

Abstract: We present a detailed study of the central exclusive production of the standard model Higgs boson in the WW decay channel at the LHC. We include estimates of the experimental acceptance, including that of the proposed proton tagging detectors at 220 m and 420 m around either ATLAS and/or CMS, and the level 1 trigger acceptances. We give first estimates of the photon-photon and glue-glue background processes in the semi-leptonic and fully leptonic decay channels. We find that there will be a detectable signal for Higgs masses between 140 GeV and 200 GeV, and that the backgrounds should be controllable.

Analysis of the neutralino system in three-body leptonic decays of neutralinos

Abstract: Neutralinos \(\tilde{\chi}^0\) in supersymmetric theories, the spin–1/2 Majorana–type superpartners of the U(1) and SU(2) neutral electroweak gauge bosons and SU(2) neutral Higgs bosons, are expected to be among light supersymmetric particles so that they can be produced copiously via direct pair production and/or from cascade decays of other sparticles such as sleptons at the planned Large Hadron Collider and the prospective International Linear Collider. Considering the prospects of having both highly polarized neutralinos and possibility of reconstructing their decay rest frames, we provide a systematic investigation of the three–body leptonic decays of the neutralinos in the minimal supersymmetric standard model and demonstrate alternative ways for probing the Majorana nature of the neutralinos and CP violation in the neutralino system.