Kinetic growth walk on critical percolation clusters and lattice animals

The statistics of recently proposed kinetic growth walk (KGW) model for linear polymers (or growing self avoiding walk (GSAW)) on two dimensional critical percolation clusters and lattice animals are studied using real-space renormalization group method. The correlation length exponents 's are found to be _KGW ^Pc = 0.68 and _KGW ^LA respectively for the critical percolation clusters and lattice animals. Close agreements are found between these results and a generalized Flory formula for linear polymers at theta point _KGW ^F = 2/ +1),, where is the fractal dimension of the fractal objectF.     

Anyonic realization of the quantum affine Lie algebras

We give a realization of the quantum affine Lie algebras and in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter q being related to the statistical parameter of the anyons by q = eⁱ. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel [1] fermionic construction of undeformed affine Lie algebras.     

Determination of an upper limit for the mass of the τ-neutrino at LEP

An upper limit for the mass is determined through the kinematic reconstruction of the decay5 ^± in the OPAL detector at LEP. The limit is obtained using a new method based on the comparison of the two-dimensional distribution of energy and invariant mass of the five-pion system with expectations from different neutrino mass hypotheses. From a sample of five events surviving the selection criteria we obtain an upper limit of 74 MeV at 95% confidence level. It is the first measurement at LEP energies, where the larger average multiplicity of events makes the suppression of this background more robust compared to lower energies.     

Nuclear structure calculation ofβ + β +,β +/EC and EC/EC decay matrix elements

Nuclear matrix elements for double positron emisson ( ^{+ +}), positron emission/electron capture ( ⁺/ EC) and double electron capture (EC/EC) in the 2 decay mode and for ^{+ +} and ⁺/EC decay in the 0 mode are calculated for the experimentally most promising isotopes⁵⁸Ni,⁷⁸Kr,⁹⁶Ru,¹⁰⁶Cd,¹²⁴Xe,¹³⁰Ba and¹³⁶Ce within pn-QRPA. We point out that the matrix element for the 2 ⁺/EC decay differs from the 2 ^{+ +} matrix element, an effect not considered previously. For the neutrino accompanied decays our calculation predicts for the ⁺/EC and the EC/EC mode half lives which are shorter typically by 4–7 orders of magnitude than those for the double positron emission. However, even for the best candidates typical values for 2 ⁺/EC (2 EC/EC) are still in the range of 10²² ((some) 10²¹) years. For 0 decay we have calculated all matrix elements relevant for both, the mass mechanism and the right-handed currents for the first time complete. A detailed discussion of the differences between the 0 ⁺⁺, the 0 ⁺/EC and 0 ^{– –} decay is given.This work is supported in part by a Grant-in-Aid for Scientific Research (05243204) from the Ministry of Education, Science and Culture. One of us (M.H.) would like to thank the Japanese Ministry of Education, Science and Culture (Monbusho) for financial support. He also acknowledges valuable discussions with S.S.     

A Quantization on Riemann Surfaces with Projective Structure

Let X be a Riemann surface equipped with a projective structure. Let be a square-root of the holomorphic cotangent bundle K _X . Consider the symplectic form on the complement of the zero section of obtained by pulling back the symplectic form on K _X using the map ². We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K _X equipped with the natural symplectic form.     

A Far IR Study of NbN in the Normal and Superconductive State

A thin film of NbN (thickness t = 300 Å), has been deposited on an MgO and a Si wafer. Both samples have been studied by transmission from 10 or 20 to 120 cm^–1, and have exhibited one maximum of transmission at a given frequency like the classical superconductors as Pb, Sn or Hg in the superconductive state. From the Far IR experimental data, the characteristic temperature _c, and the gap frequency (_gap () = 2 (), () being the energy gap) are immediately obtained (for instance for the NbN / MgO sample, _c = 15.5 K; _g (5 K) = 39.7 cm^–1), and it is seen that as expected from the BCS theory for a weak coupling. To fit the data we had to adjust only two additionnal parameters: collision and plasma frequency, _c () and _p (including all carriers). At = 5 K, thebest fit for the NbN / MgO sample is obtained with _c = 371 cm^–1 and _p = 12,600cm^–1.     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

CP-violating effects inZ decays to τ leptons

We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 10⁷ producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Testing the Higgs system at a photon-photon collider

The level of sensitivity of the processes ZZ, W ⁺ W ^– and to the Higgs sector of the Standard Model Lagrangian in the energy region between 200 GeV and 1 TeV is examined. The elementary Higgs boson is taken to have a mass less than 1 TeV. Sizeable effects are found in theZZ and channels if the incoming photons have the same helicity. Also the possibility that the elementary Higgs boson does not exist is examined. Assuming new physics to show up in the TeV energy region the cross sections are evaluated according to the heavy Higgs model. For center of mass energy values close to 1 TeV interesting effects are found in the channel if the photons have the same helicity. The limit of large Higgs mass is not unique. The parametrization of this arbitrariness may be interpreted as a representation of the new physics. The effects for the processes ZZ and are investigated. These effects may be correlated to a possible resonance inWW scattering in the TeV region.     

Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus

TheSU(N) Yang-Mills equations are considered in a four-dimensional Euclidean box with periodic boundary conditions (hypertorus). Gauge-invariant twists can be introduced in these boundary conditions, to be labeled with integersn (= –n ), defined moduloN. The Pontryagin number in this space is often fractional. Whenever this number is zero there are solutions to the equationsG =0 HereG is the covariant curl. When this number is not zero we find a set of solutions to the equations , provided that the periodsa of the box satisfy certain relations.Work supported in part by the US Department of Energy under Contract No. DE-AC-03-76ER 00068 and by the Fairchild FoundationOn leave from the Institute for Theoretical Physics, University of Utrecht, P.O. Box 80.006, NL-3508 TA Utrecht, The Netherlands     

Composite weak bosons inpp(p\bar p) \to W^ \pm Z^0 X

We study the production process , where is a proton (antiproton), allowing an anomalous weak magnetic dipole moment parameter _Z in the ZWW vertex. We compute the pairWZ mass invariant, and total cross section production for various values of _Z .     

N\bar N annihilation at rest into five pions

annihilation at rest into five pions was studied in the ASTERIX spectrometer by stopping antiprotrons from LEAR in a H₂ or D₂ gas target. In annihilations in H₂ leading to the ^+–+–0 final state, the invariant mass spectra of two, three, and four pions show no evidence for any new narrow states. In the difference of the four pion mass spectra recoiling against a ^– and those recoiling against a ⁺ shows a resonance-like structure ( (1480)), confirming a previous analysis with a smaller event sample. The (1480) mass is shown to depend strongly on the momentum of the spectator proton. In H₂, we searched for the (1480) in the reaction (1480), (1480) ^+–+– to clarify whether the (1480) is identical to the 4-mode of thef ₂ (1520). No evidence for this decay mode was found. A prominent resonance in innihilation into five pions is the meson. We find two quasi-two-body intermediate states: and (1235). The mass and width of theb ₁ (1235) are determined to be:

Shell model high-spin states in 67 151 Ho84

In an in-beam study of ₆₇ ¹⁵¹ Ho₈₄ we have established its high-spin states up to 10 MeV and have suggested spin assignments up to (49/2) at 6.2 MeV. The main decay-cascade proceeds through the yrast states of the h³ _11/2f² _7/2 and h³ _11/2f_7/2h_9/2 5-particle configurations, which are predicted with good accuracy in parameter-free shell-model calculations. States with one proton in d_3/2, or involving i_13/2 or f_7/2×3^– excitations were also identified.     

A Generally Covariant Field Equation for Gravitation and Electromagnetism

A generally covariant field equation is developed for gravitation and electromagnetism by considering the metric vector q in curvilinear, non-Euclidean spacetime. The field equation is

Nonlinear superposition for Liouville's equation in three spatial dimensions

We derive in 3+0 dimensions exact solutions of Liouville's equation ²=exp , by applying the Bäcklund transformation technique in conjunction with the principle of nonlinear superposition. The procedure, which is later extended to 3+1 dimensions, yield, as a byproduct, particular solutions of ² and ² =exp (² +² ).     

High-spin states of odd-odd156Ho

High spin states in the nucleus¹⁵⁶Ho have been studied via the fusion-evaporation reaction¹⁴⁰Ce(¹⁹F,3n)¹⁵⁶Ho at the beam energy of 82 MeV.- coincidences, E, I and excitation functions have been measured. With two rotationally-aligned bands identified as [h_11/2] [i_13/2], we found two new bands with a signature splitting, whose structure is believed to arise from either [h_9/2] or [f_7/2] coupled to [h_11/2]. Our placement of rays belonging to these new bands suggests that the previously known level scheme should be corrected. We also found many new low-energy rays in the low excitation energy. As compared to¹⁵⁴Ho, the present nucleus with two more neutrons becomes more collective, and shows well-observed rotationally-aligned bands with a clear signature splitting.Communicated by B. Herskind