Approach to a theory for the masses of the electron,muon, and heavier charged leptons

The electron mass valuem=9.093 × 10^–28 g is shown to be obtainable from the QED self-energy formula amended to include gravitational selfenergy and restricted by the space-time equipartition lawm/n ₀=4/3. Held together by gravity, the electron has a radiusr _e =8Gm/9e ² c=2.588 × 10^–53 cm. An extension of the analysis yields the theoretical muon-electron mass ratio of 206.241 and predicts heavier charged leptons with mass values of 1.915 GeV, 15.67 GeV, and above.     

Fermion masses

In this paper, we show that 2m _e m /(m _e ² +m ² = (g _V/g _A) _e ² . From this expression, the Weinberg mixing parameter is shown to be 0·2254 or 0·2746. Assuming that the electron and muon neutrino masses are degenerate, we find thatm _v = (g _V/g _A) _e ² . (m _e m )/M _WL, where M_WL is the mass of the standard W^± boson. The neutrino mass turns out to be 6·5 eV. The -neutrino mass is found to be about 81 MeV. The masses of c, t, s and b quarks are found to be respectively 1·7 GeV, 21·2 GeV, 0·57 GeV and 2·18 GeV by assumingm _d=m _u= 0·3 GeV. All these masses agree with other estimates except the b quark which has about half of its expected value.     

A study of the ϱ0 meson polarization in π− p reaction at 5 GeV/c

Experimental data on ⁰ meson polarization in ^– p reaction at 5 GeV/c are presented. Change in ⁰ meson polarization for mesons produced at smallP ² and atP ² 0·3 or produced in backward direction in CMS is demonstrated. Natural explanation of these phenomena is one pion exchange mechanism and mechanism of quark-antiquark annihilation as observed for ⁰ meson production in¯pp reactions.The authors are indebted to Ján Piút, Richard Lednický, V. S. Rumiancev and N. K. Koutsidi for discussions and critical comments.     

Empirical lepton-quark mass formula: Four dimensional state space for fermion structure?

It is observed that a simple mass formula of the formm =¯mQ ²(exp) is wholly consistent with experimental measurements and quark model estimates for all 12 fundamental fermions. Here¯m = 433.3 MeV is an input (mean fermion mass) constant,Q is the charge number of the lepton or quark, and is a real root of a quartic equation that brings in a principal quantum numbern (= 0, 1, 2, 3). The charged lepton masses are given accurately to within 0.3 of 1%, all neutrino masses are zero, and the top mass is predicted by the formula to be close tom _t = 163.6 GeV.     

Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Quantum groupSU(1, 1) ⋊ Z2 and “super-tensor” products

A quantum analogue of the groupSU(1,1)Z ₂—the normalizer ofSU(1, 1) inSL ₂(C)—is introduced and studied. Although there isno correctly defined tensor product in the category of *-representations of the quantum algebraC[SU(1, 1)] _q of regular functions, some categories of *-representations ofC[SU(1, 1)Z ₂] _q turn out to be endowed with a certainZ ₂-graded structure which can be considered as a super-generalization of the monoidal category structure. This quantum effect may be considered as a step to understanding the concept of quantum topological locally compact group.In fact, there seems to be afamily of quantum groupsSU(1, 1)Z ₂ parameterized by unitary characters T ¹ of the fundamental group of the two-dimensional symplectic leaf ofSU(1, 1)/T, whereT is the subgroup of diagonal matrices.It is shown that thequasi-classical analogues of the results of the paper are connected with the decomposition of Schubert cells of the flag manifoldSL ₂(C)_R/B (whereB is the Borel subgroup of upper-triangular matrices) into symplectic leaves.Supported by the Rosenbaum Fellowship.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Inclusive K+-meson production in proton-nucleus interactions

The production of K⁺-mesons in pA (A = D, C, Cu, Ag, Au) collisions has been investigated at the COoler SYnchrotron COSY-Jülich for beam energies T_p = 1.0-2.3 GeV. Double differential inclusive pC cross-sections at forward angles _{K^+} < 12^° as well as the target mass dependence of the K⁺ momentum spectra have been measured with the ANKE spectrometer. Far below the free NN threshold at T_NN = 1.58 GeV the spectra reveal a high degree of collectivity in the target nucleus. From the target mass dependence of the cross-sections at higher energies, the repulsive in-medium potential of the K⁺-mesons can be deduced. Using pN cross-section parameterisations from the literature and our measured pD data we derive a cross-section ratio (pnK⁺X)/(ppK⁺X) (3-4).     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

μSR studies in the heavy fermion systems UNi2Al3, UPd2Al3 and U2PtC2

We have performed Muon Spin Relaxation (SR) measurements of several heavy fermion systems: UNi₂Al₃ (single crystal), UPd₂Al₃ (single crystal) and U₂PtC₂ (polycrystal). ZF -SR measurements of UNi₂Al₃ show magnetic order below the Néel temperatureT _N=4.6K, with the muon precession frequency(T 0)=2.5MHz at low temperatures. The local field distribution obtained at low temperatures in UNi₂Al₃ resembles that of the incommensurate spin density wave (SDW) system (TMTSF)₂PF₆, suggesting an incommensurate spin arrangement in UNi₂Al₃. TF -SR measurements give the penetration depth(T 0)=6100Å for UPd₂Al₃ and(T 0)=7000Å for U₂PtC₂ respectively. Since UPd₂Al₃ and U₂PtC₂ are clean superconductors (/l-0), we can combine n _s/m^* with the Sommerfeld constant n _s ^1/3 m^* to calculate the Fermi temperatureT _F ^3/4–1/4, which represents the characteristic energy scale of the superconducting carriers. We obtainT _C/T_F 0.01 for both UPd₂Al₃ and U₂PtC₂, comparable to other exotic superconductors, but quite different from simple metal BCS superconductors, whereT _C/T_F 0.01.     

Quantum Ergodicity of Boundary Values of Eigenfunctions

Suppose that ⁿ is a bounded, piecewise smooth domain. We prove that the boundary values (Cauchy data) of eigenfunctions of the Laplacian on with various boundary conditions are quantum ergodic if the classical billiard map on the ball bundle B^*() is ergodic. Our proof is based on the classical observation that the boundary values of an interior eigenfunction , =² is an eigenfunction of an operator F_h on the boundary of with h=^–1. In the case of the Neumann boundary condition, F_h is the boundary integral operator induced by the double layer potential. We show that F_h is a semiclassical Fourier integral operator quantizing the billiard map plus a small remainder; the quantum dynamics defined by F_h can be exploited on the boundary much as the quantum dynamics generated by the wave group were exploited in the interior of domains with corners and ergodic billiards in the work of Zelditch-Zworski (1996). Novelties include the facts that F_h is not unitary and (consequently) the boundary values are equidistributed by measures which are not invariant under and which depend on the boundary conditions. Ergodicity of boundary values of eigenfunctions on domains with ergodic billiards was conjectured by S. Ozawa (1993), and was almost simultaneously proved by Gerard-Leichtnam (1993) in the case of convex C^1,1 domains (with continuous tangent planes) and with Dirichlet boundary conditions. Our methods seem to be quite different. Motivation to study piecewise smooth domains comes from the fact that almost all known ergodic domains are of this form.The first author was partially supported by an Australian Research Council Fellowship.The second author was partially supported by NSF grant #DMS-0071358 and DMS-0302518.     

Equations for the Magnetization Modes in a System Having a Quadruple Nucleus with the Spin S = 1

Within the framework of the method of a density matrix, differential equations are obtained that describe the evolution of the modes of magnetization <Î₊>, <Î_{+ z} >, and <Î_{+ z} ²> for a spin system containing a nucleus with a 1/2 spin connected scalarly with the quadruple nucleus of the spin S = 1 in the presence of crosscorrelation between the dipole ISinteractions, anisotropy of the chemical shift of the I and S nuclei, and quadruple interaction of the S nucleus. The equations are used for analysis of the evolution of the intensities of each line in the triplet of the Raman spectrum of the 1/2 spin. Expressions for the times of crossrelaxation and the times of transverse relaxation of each of the lines of the triplet are obtained.     

Radiative decays of the Z boson

We calculate the Stokes parameters of the photons produced in the decays of neutral vector bosons Z, Z 1+¯1+ and Z q+¯q+, wherel=e, , or , and q is a quark. In the decays of unpolarized Z bosons (with the production of unpolarized leptons or quarks) the nonzero Stokes parameters for ₂ (circularly polarized photons) and ₃ (linearly polarized photons). The magnitude of ₃ does not depend on the parameters of the netural weak current of the leptons and the quarks (if their mass is neglected). The anomalous magnetic moment of the Z boson is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 38–43, February, 1986.     

Formation of F-centers in Kcl-Rbcl solid solutions with Sr2+ and OH− impurities

The kinetics of F-center formation are studied in crystals of KCl-RbCl. solid solutions, both in the pure state and with Sr²⁺ and OH^– impurities. The crystals were irradiated by electrons at 1.2 MeV at room temperature. The initial stage of coloration in crystals that have been purified of divalent cation impurities is the same as that of pure crystals; only when Sr²⁺ is introduced is this stage sharply accelerated. The efficiency of F-center formation in the second stage of coloration is significantly smaller in purified crystals than in pure crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 38–41, July, 1971.     

Degenerate four-wave-mixing spectroscopy in NaH

We performed DFWM spectroscopy on X ^–1+–A ¹⁺ transitions in NaH produced in an indirect photochemical reaction between Na(3p) and H₂ and detected v=1, 2 and 3 ground state vibrational levels of NaH molecules, whereas with resonance enhanced CARS, we observed v=0 levels only. This different sensitivity can be explained by considering the Franck-Condon-factors and the relevant damping coefficients for the corresponding transitions in the NaH molecule. Time resolved DFWM spectroscopy showed that NaH(v=1) molecules effectively live much longer than Na(3p) atoms which merely follow the laser excitation pulse.     

P-polarized nonlinear surface polaritons near the surface of a saturable self-defocusing medium: Threshold case

We have obtained the solution of the stationary problem for P-polarized nonlinear surface polaritons (NLSP) near the interface of two media, one of which is optically linear and the other having an optical nonlinearity with saturation and a dielectric function of the form: =_xx=_zz=₀+a|E|²/(1+b|E|²), where E is the amplitude of the electric field. On this basis the NLSP energy and propagation properties, the polarization structure and the localization depth of the NLSP field as well as the physically allowed region in the parameter space have been investigated for the case in which the parameter ₀ is positive, b is non-negative, and a and ₁ are negative (₁ is the dielectric function of the linear medium); ₀>|₁|.     

Theoretical estimate of the Higgs boson mass

It is assumed that the Higgs particle distorts space-time in its own neighborhood and generates a self-referential nonlinear field. Its almost flat space-time metric form gives a nonlinear equation of motion admitting soliton-like solutions. This in turn gives rise to a new type of wave—space-time (mass-transmitting) interactions allowing particles to acquire mass. The curvature of the (pseudo-) Riemannian manifold of a Higgs space-time yields the mass formulam ₂ ^WZ =d ³ x detGR _H (x)=1/4m ₂ ^H orm _H =182 GeV.     

Continuous-wave frequency mixing and UV generation in sodium vapor

Resonant nonlinear four-wave mixing processes have been studied in sodium vapor. The generation of cw uv radiation and the upconversion of =10.8 m light is reported. The coefficientC=P ₄/P₁P₂P₃ obtained was on the order of 10^–2 W^–2, the pump spectral width being 12GHz. Resonant atomic nonlinearities are shown to be used for effective cw frequency conversion.