Probing signals of the littlest Higgs model via the WW fusion processes at the high energy e + e- collider

In the framework of the littlest Higgs (LH) model, we consider the processes and , and we calculate the contributions of new particles to the cross sections of these processes in the future high energy e ⁺ e^- collider (ILC) with TeV. We find that, with reasonable values of the free parameters, the deviations of the cross sections for the processes from their SM values might be comparable to the future ILC measurement precision. The contributions of the light Higgs boson H⁰ to the process are significantly large in all of the parameter space preferred by the electroweak precision data, which might be detected in the future ILC experiments. However, the contributions of the new gauge bosons B_H and Z_H to this process are very small.Received: 22 February 2005, Revised: 27 April 2005, Published online: 6 July 2005PACS: 12.60.Cn, 14.70.Pw, 14.80.Cp     

CP-violation in B → π+π- and the unitarity triangle

We analyze the extraction of weak phases from CP-violation in B → π⁺π^- decays. We propose to determine the unitarity triangle by combining the information on mixing-induced CP-violation in B → π⁺π^-, S, with the precision observable sin2β obtained from the CP-asymmetry in B → ψK_S. It is then possible to write down exact analytical expressions for and as simple functions of the observables S and sin2β and of the penguin parameters r and ϕ. As an application clean lower bounds on and can be derived as functions of S and sin2β, essentially without hadronic uncertainty. Computing r and ϕ within QCD factorization yields precise determinations of and since the dependence on r and ϕ is rather weak. It is emphasized that the sensitivity to the phase ϕ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter C of direct CP-violation in B → π⁺π^-. Predictions and uncertainties for r and ϕ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in 1/m_b and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed. Received: 16 April 2005, Revised: 6 August 2005, Published online: 21 November 2005 PACS: 11.30.Er, 12.15.Hh, 13.25.Hw     

Pair-produced heavy particle topologies: MSSM neutralino properties at the LHC from gluino/squark cascade decays

Processes of the form pp → anything → X_iX_j → + + notE are studied via a technique that may be viewed as an adaptation of time-honoured Dalitz plot analyses. X_i and X_j are new heavy states (with i, j =1, . . .,n), which may be identical or distinct; and and are necessarily distinct standard model (SM) fermion pairs whose invariant masses can be measured. A Dalitz-like plot of said invariant masses, versus , exhibits a topology connected to the masses and specific decay chains of X_i and X_j. Aside from relatively minor details, observed patterns consist of a collection of box and wedge shapes. This collection is model-dependent: comparison of the observed pattern to the possibilities for a specific model yields information on which new particle pair combinations are actually being produced, information beyond that extractable from conventional one-dimensional invariant mass distributions. The technique is illustrated via application to the minimal supersymmetric standard model (MSSM) process pp → → e⁺e^- + μ⁺μ^- notE. Here the heavy states are neutralinos (i = 2,3,4) - note that is excluded - which are produced in gluino/squark ( / ) cascade decay chains. Even with fairly modest expectations for the LHC performance during the first few years, this method still provides substantial insight into the neutralino mass spectrum and couplings if gluino/squark masses are relatively low (≃ 400 GeV). Arrival of the final proofs: 29 November 2005     

Measurement of the mass and width of the W boson

The mass and width of the W boson are measured using e⁺e^– → W⁺W^– events from the data sample collected by the OPAL experiment at LEP at centre-of-mass energies between 170 GeV and 209 GeV. The mass (m_W) and width (Γ_W) are determined using direct reconstruction of the kinematics of W⁺W^– → and W⁺W^– → events. When combined with previous OPAL measurements using W⁺W^– → events and the dependence on of the WW production cross-section at threshold, the results are determined to be

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

Condensation of the Roots of Real Random Polynomials on the Real Axis

We introduce a family of real random polynomials of degree n whose coefficients a _k are symmetric independent Gaussian variables with variance , indexed by a real α≥0. We compute exactly the mean number of real roots 〈N _n 〉 for large n. As α is varied, one finds three different phases. First, for 0≤α<1, one finds that . For 1<α<2, there is an intermediate phase where 〈N _n 〉 grows algebraically with a continuously varying exponent, . And finally for α>2, one finds a third phase where 〈N _n 〉∼n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots 〈N _n 〉/n are real. This condensation occurs via a localization of the real roots around the values , 1≪k≤n.     

Complete description of polarization effects in e + e- pair productionby a photon in the field of a strong laser wave

We consider production of a e ⁺ e ^- pair by a high-energy photon in the field of a strong laser wave. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects in the kinematics relevant to the problem of conversion at and colliders.Received: 13 December 2004, Published online: 4 February 2005     

Variable-range hopping in 2D quasi-1D electronic systems

A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states, g(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), i.e. σ(T) ∼exp [-(T_L/T)^γL], and current in the non-linear (NL), i.e. , response regimes ( is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, i.e. with respect to the disorder-dependence of T_L and and the values of γ_L and γ_NL.     

Seesaw induced electroweak scale, the hierarchy problemand sub-eV neutrino masses

We describe a model for the scalar sector where all interactions occur either at an ultra-high scale, Λ_U~10¹⁶-10¹⁹ GeV, or at an intermediate scale, Λ_I = 10⁹-10¹¹ GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, Λ_EW, through a seesaw-like Higgs mechanism, , while the breaking of the SM SU(2) x U(1) gauge symmetry occurs at the intermediate scale Λ_I . The EW scale is, therefore, not fundamental but is naturally generated in terms of ultra-high energy phenomena and so the hierarchy problem is alleviated. We show that the class of such "seesaw Higgs" models predict the existence of sub-eV neutrino masses which are generated through a "two-step" seesaw mechanism in terms of the same two ultra-high scales: . The neutrinos can be either Dirac or Majorana, depending on the structure of the scalar potential. We also show that our seesaw Higgs model can be naturally embedded in theories with tiny extra dimensions of size fm, where the seesaw induced EW scale arises from a violation of a symmetry at a distant brane; in particular, in the scenario presented there are seven tiny extra dimensions. Received: 19 August 2004, Revised: 27 July 2005, Published online: 14 October 2005