Strongly positive semigroups and faithful invariant states

Let (?, τ, ω) denote aW*-algebra ?, a semigroupt>0?τ _t of linear maps of ? into ?, and a faithful τ-invariant normal state ω over ?. We assume that τ is strongly positive in the sense that $$\tau _t (A^ * A) \geqq \tau _t (A)^ * \tau _t (A)$$ for allA∈? andt>0. Therefore one can define a contraction semigroupT on ?= \(\overline {\mathcal{M}\Omega } \) by $$T_t A\Omega = \tau _t (A)\Omega ,{\rm A} \in \mathcal{M},$$ where Ω is the cyclic and separating vector associated with ω. We prove 1. the fixed points ?(τ) of τ are given by ?(τ)=?∩T′=?∩E′, whereE is the orthogonal projection onto the subspace ofT-invariant vectors, 2. the state ω has a unique decomposition into τ-ergodic states if, and only if, ?(τ) or {?υE}′ is abelian or, equivalently, if (?, τ, ω) is ?-abelian, 3. the state ω is τ-ergodic if, and only if, ?υE is irreducible or if $$\mathop {\inf }\limits_{\omega '' \in Co\omega 'o\tau } \left\| {\omega '' - \omega '} \right\| = 0$$ for all normal states ω′ where Coω′°τ denotes the convex hull of {ω′°τ _t } _t>0. Subsequently we assume that τ is 2-positive,T is normal, andT* _t ?₊Ω \( \subseteqq \overline {\mathcal{M}_ + \Omega } \) , and then prove 4. there exists a strongly positive semigroup |τ| which commutes with τ and is determined by $$\left| \tau \right|_t \left( A \right)\Omega = \left| {T_t } \right|A\Omega ,$$ 5. results similar to 1 and 2 apply to |τ| but the τ-invariant state ω is |τ|-ergodic if, and only if, $$\mathop {\lim }\limits_{t \to \infty } \left\| {\omega 'o\tau _t - \omega } \right\| = 0$$ for all normal states ω′.     

Prompt neutrino production in 400 GeV proton-copper interactions

A new beam-dump experiment has been performed at the CERN Super Proton Synchrotron using the CHARM neutrino detector. The instrumentation and the statistics have been significantly improved with respect to earlier experiments. For a neutrino energy above 20 GeV the asymmetry of the prompt muon-neutrino and electron-neutrino fluxes \([(v_\mu + \bar v_\mu ) - (v_e + \bar v_e )]/[(v_\mu + \bar v_\mu ) + (v_e + \bar v_e )]\) is found to be 0.20±0.10 (stat.)±0.05 (syst.), and the asymmetry of prompt antineutrino and neutrino fluxes for muonneutrinos \((v_\mu - \bar v_\mu )/(v_\mu + \bar v_\mu )\) is 0.02±0.16 (stat.)±0.02 (syst.) in agreement with our previous results. For the cross-section times branching ratio for charm production and semileptonic decay we obtain a value of \(\sigma \times BR\left[ {D(\bar D) \to v_e (\bar v_e ) X} \right] = 1.9 \pm 0.2 \pm 0.2\mu b\) per nucleon. We find no evidence forv _τ orv _x interactions. The \((v_\tau + \bar v_\tau )\) flux is less than 21% of the total prompt neutrino flux. We derive an improved limit on the branching ratio \(\pi ^0 \to v\bar v\) of 6.5×10^?6, and as a verification of the universality of the neutral weak coupling we find \(g_{v_e \bar v_e } /g_{v_\mu \bar v_\mu } = 1.05_{ - 0.18}^{ + 0.15} \) .     

Improved limits on the mass of the tau neutrino

Several methods to determine (or set an upper bound on) the mass of the tau neutrino are described. The decay spectrum of \(\tau \to e\bar \nu _e \nu _\tau \) near the high center-of-mass electron-energy end is particularly sensitive to the tau-neutrino mass. It is shown that an upper bound of 20 MeV or lower may be feasible. In addition, improved limits on the mass and mixing angle of a heavy component of the tau-neutrino may be readily obtained. We also discuss the purely leptonic decays of theD andF mesons, and show how measurements of the ratiosB(D→τν_τ/B(D→μν_μ,B(F→τν_τ/B(D→μν_μ can be sensitive to tau-neutrino masses of 30 MeV or greater.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_?)^?1 with the dwell time τ_D through the cavity and the dephasing rate τ _? ^?1 , we find an exponential suppression of weak localization by a factor of ∝ exp[? $\tilde \tau $ /τ_?], where $\tilde \tau $ is the system-dependent parameter. In the dephasing probe model, $\tilde \tau $ coincides with the Ehrenfest time, $\tilde \tau $ ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $\tilde \tau $ ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F.     

Decays τ → (η, η')<Emphasis Type="Italic">K</Emphasis>–ν<Subscript>τ</Subscript> in the extended Nambu–Jona-Lasinio model

The decays τ → (η, η')K–ν_τ are described in the framework of the extended Nambu–Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channel, the subprocesses with the intermediate K*(892) and K*(1410) mesons play the main role. In the scalar channel, the subprocesses with the intermediate and K₀^*(800) and K₀^*(1430) mesons are taken into account. The scalar channel gives an insignificant contribution to the full width of the decay τ → ηK–ν_τ. The obtained results are in satisfactory agreement with the experimental data. The prediction for the width of the process τ → η′K–ν_τ is made.     

Angular correlations and the tau-neutrino mass

Effects of a nonzero mass for the tau neutrinov _τ as well as a right-handed charged-current contribution to the τ?v _τ coupling are discussed. Angular correlations of the decay products of τ⁺τ^? ine ⁺ e ^? annihilation are calculated as functions of \(m_{v_\tau } \) and the relative amount of right-handed τ?v _τ coupling.     

233Pa(2nth, f ) cross-section determination using a fission track technique

The νp process is a primary nucleosynthesis process which occurs in core-collapse supernovae. An essential role in this process is being played by electron antineutrinos. They generate, by absorption on protons, a supply of neutrons which, by (n, p) reactions, allow to overcome waiting point nuclei with rather long beta-decay and proton-capture lifetimes. The synthesis of heavy elements by the νp process depends sensitively on the $\bar \nu _e$ luminosity and spectrum. As has been shown recently, the latter are affected by collective neutrino flavor oscillations which can swap the $\bar \nu _e$ and $\bar \nu _{\mu ,\tau }$ spectra above a certain split energy. Assuming such a swap scenario, we have studied the impact of collective neutrino flavor oscillations on the νp-process nucleosynthesis. Our results show that the production of light p-nuclei up to mass number A = 108 is very sensitive to collective neutrino oscillations.     

Systematization of intermediate-mass fragments

We consider the power law dependence of cross-sections of formation of intermediate-mass fragments on the mass number and atomic number, σ (A _f ) ～ A _f ^?τ and σ (Z _f ) ～ Z _f ^?τ . The values of parameter τ are determined for fragments detected by the ΔE ? E and the induced activity methods. It is shown that in “liquid-gas” phase transition τ varies within the limits of 2–3. A conclusion was drawn that at high beam energies parameter τ does not depend on the detection angle of the fragment. At the increase in the energy τ passes through a minimum at E _i ～ 6–7 GeV which is typical “critical behavior” predicted by models.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.     

The semileptonic decaysB→Mτν as a probe of hadron dynamics

We show how data on \(\bar B \to M\tau \bar v\) can be used to probe models for the hadronic form-factors which describe the \(\bar B \to M\) transition, whereM isD,D ^* etc. Extra form-factors contribute to \(\bar B \to M\tau \bar v\) , as compared to \(\bar B \to Me\bar v\) , and these may be studied by observing the polarisation of the outgoing τ. Model predictions for the decay rate and the τ polarisation are presented.     

The mixing angles in matter for three generations of neutrinos and the MSW mechanism

Mikheyev and Smirnov have recently shown that oscillations between two species of neutrinos may be amplified in matter. We give analytic expressions for the energy eigenvalues, all the mixing angles and the CP-violating phase in matter for three generations of neutrinos using the Fritzsch parametrization for the flavor mixing matrix. For clearly separated neutrino masses Δm ₃₁ ² ?Δm ₂₁ ² we find two MSW resonance effects—one forv _e ?v _µ and one forv _e ?v _τ conversions —which can each be approximated by a separate two neutrino treatment as has been recently shown by Kuo and Pantaleone. Nearly degenerate neutrino masses Δm ₃₁ ² ～Δm ₂₁ ² on the other hand lead to only one resonance region withs _{1 2} ^{m 2} no longer necessarily approaching 1 for very high densities.     

Timelapse

We discuss the existence, in an arbitrary frame, of a finite time for the transformation of an initial quantum state into another, e.g., in a decay. This leads to the introduction of a timelapse $\tau $ , by analogy with the lifetime of a particle. An argument based upon the Heisenberg uncertainty principle suggests the value of $\tau $ =1/M ₀. Consequences for the exponential decay formula and the modifications which $\tau $ introduces into the Breit-Wigner mass formula are described.     

A test of the Lorentz structure of semi-hadronic τ decays

A method is proposed for the determination of the Lorentz structure of the electroweak interaction in semi-hadronic τ decays. Spin correlations in the process $$e^ + e^ - \to \tau ^ + \tau ^ - \to \bar v_\tau \pi ^ + \pi ^0 v_\tau \pi ^ - \pi ^0 $$ are exploited for a measurement of the normalized product, γ_AV = 2Re{g_Ag _V ^* }/(|g_V|² + |g_V|²), of the vector (g _V ) and axial vector (g _A ) coupling of the τ lepton. The contribution of scalar (g _S ) or pseudo-scalar (g _P ) couplings is also investigated. Since in the above process the direction of flight of the τ leptons can be reconstructed up to a twofold ambiguity a likelihood method using the whole kinematic information can be employed. The matrix element entering the likelihood function has been evaluated in terms of the momenta and angles of the observed pions. The sensitivity of the derived method in ane ⁺ e ^? energy region around 10 GeV has been investigated for the ARGUS experiment using Monte Carlo simulations.     

Neutrino production of charmed particles in a hybrid experiment E-564

Cryogenically sensitive nuclear emulsion was placed inside the 15-foot bubble chamber of FNAL and exposed to a wide-band energy (up to 200 GeV) neutrino beam. 194 charged-current neutrino interactions and 13 decays of charmed particles were registered. Using the nuclear emulsion as a vertex detector with the good spectrometric properties of the 15-foot bubble chamber has allowed the decays of charmed particles to be effectively analysed. Attentions is focussed on the new physical results. Λ _c ⁺ baryon andD _s ⁺ meson decay channels, production of charmed ∑ _c baryons and Λ _c ⁺ via ∑ _c . For the first time an event interpreted as production of the excited (c \(\overline s\) )-state with mass ～2790 MeV/c² has been registered.     

Fragmentation production of Ωccc baryons at LHC energies

Within the nonrelativistic quark-diquark model for heavy baryons, the fragmentation functions for the transitions of a c-quark and a doubly charmed vector diquark into an Ω_ccc baryon are calculated in the leading order of perturbative QCD. The cross section for Ω _ccc production in high-energy hadron interactions is estimated. It is assumed that Ω_ccc baryons are formed via the fragmentation of a c quark or a vector (cc) diquark produced in the partonic subprocesses gg → c $\bar c$ , q $\bar q$ → c $\bar c$ , gg → (cc)+ $\bar c$ + $\bar c$ , and q $\bar q$ → (cc)+ $\bar c$ + $\bar c$ .     

Cosmological General Relativity with Scale Factor and Dark Energy

In this paper the four-dimensional (4-D) space-velocity Cosmological General Relativity of Carmeli is developed by a general solution of the Einstein field equations. The Tolman metric is applied in the form 1 $$ ds^2 = g_{\mu \nu} dx^{\mu} dx^{\nu} = \tau^2 dv^2 -e^{\mu} dr^2 - R^2 \left(d{\theta}^2 + \mbox{sin}^2{\theta} d{\phi}^2 \right), $$ where g _μν is the metric tensor. We use comoving coordinates x ^α = (x ⁰, x ¹, x ², x ³) = (τv, r, θ, ?), where τ is the Hubble-Carmeli time constant, v is the universe expansion velocity and r, θ and ? are the spatial coordinates. We assume that μ and R are each functions of the coordinates τv and r. The vacuum mass density ρ _Λ is defined in terms of a cosmological constant Λ, 2 $$ \rho_{\Lambda} \equiv -\frac{ \Lambda } { \kappa \tau^2 }, $$ where the Carmeli gravitational coupling constant κ = 8πG/c ² τ ², where c is the speed of light in vacuum. This allows the definitions of the effective mass density 3 $$ \rho_{eff} \equiv \rho + \rho_{\Lambda} $$ and effective pressure 4 $$ p_{eff} \equiv p - c \tau \rho_{\Lambda}, $$ where ρ is the mass density and p is the pressure. Then the energy-momentum tensor 5 $$ T_{\mu \nu} = \tau^2 \left[ \left(\rho_{eff} + \frac{p_{eff}} {c \tau} \right) u_{\mu} u_{\nu} - \frac{p_{eff}} {c \tau} g_{\mu \nu} \right], $$ where u _μ = (1,0,0,0) is the 4-velocity. The Einstein field equations are taken in the form 6 $$ R_{\mu \nu} = \kappa \left(T_{\mu \nu} - \frac{1} {2} g_{\mu \nu} T \right), $$ where R _μν is the Ricci tensor, κ = 8πG/c ² τ ² is Carmeli’s gravitation constant, where G is Newton’s constant and the trace T = g ^αβ T _αβ . By solving the field equations (6) a space-velocity cosmology is obtained analogous to the Friedmann-Lemaître-Robertson-Walker space-time cosmology. We choose an equation of state such that 7 $$ p = w_e c \tau \rho, $$ with an evolving state parameter 8 $$ w_e \left(R_v \right) = w_0 + \left(1 - R_v \right) w_a, $$ where R _v = R _v (v) is the scale factor and w ₀ and w _a are constants. Carmeli’s 4-D space-velocity cosmology is derived as a special case.     

Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data

We propose a modified procedure for extracting the numerical value for the strong coupling constant α _s from the τ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark–hadron duality specifically, introducing a boundary energy squared s _p > 0, the onset of the perturbative QCD continuum in Minkowski space (Bertlmann et al. in Nucl Phys B 250:61, 1985; de Rafael in An introduction to sum rules in QCD. In: Lectures at the Les Houches Summer School. arXiv: 9802448 [hep-ph], 1997; Peris et al. in JHEP 9805:011, 1998). To approximate the hadronic spectral function in the region s > s _p, we use analytic perturbation theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter ${\Lambda_{\overline{\rm MS}}}$ and the boundary energy squared s _p. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the ${\overline{\rm MS}}$ scheme coupling constant, we obtain ${\alpha_s(m^{2}_{\tau})=0.3204\pm 0.0159_{exp.}}$ . We show that our numerical analysis is much more stable against higher-order corrections than the standard one. Additionally, we recalculate the “experimental” Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.     

New results from the T2K neutrino oscillation experiment

The T2K experiment searches for the appearance of electron neutrinos in a muon neutrino beam. The rate of this process is sensitive to the neutrino mixing parameter θ ₁₃. Recent measurements that $\theta_{13} \ne 0$ imply that ν _μ → ν _e oscillations should be observable. Using all data through May 15, 2012 the T2K experiment has detected 10 candidate ν _e events, with an expected background for θ ₁₃?=?0 of 2.73±0.37 events. This 3.2σ excess of ν _e events is the strongest indication to date for appearance of electron neutrinos in a neutrino oscillation experiment, and for normal mass hierarchy and δ _CP ?=?0 yields $0.059 < \sin^2 2\theta_{13} < 0.164$ at the 68 % C.L.     

W-production viaZ-decay

We calculate the decay rate for the processZ Boson→W Boson+fermion+antifermion. The result is applied to compute the decay rates for \(Z \to W^ + + l + \bar v_l \) ,l=e, μ or τ andZ→W ⁺+anything in the Weinberg-Salam model. At the present experimental value of sin² θ _w=0.23 the branching ratios for the above processes are \(\Gamma (Z \to W^ + l\bar v_l )/\Gamma (Z \to all) \simeq 9 \times 10^{ - 9} \) and Γ(Z→W ⁺+anything)/Γ(Z→all)?8×10^?8.