Negative muon precession in nuclei with spin

Polarized negative muons were stopped in various materials containing nuclei with nonzero spin. The TF-SR precession signal of theF ⁺ hyperfine state (frequencyv ₊ > 0) was pronounced for ^–Li and ^–Be, faint for ^–Cl (in NiCl₂), and undetectable for ^–F (in CaF₂ or NiF₂) and ^–P. TheF ^– signal (frequencyv _– < 0) was observed clearly for ^–Be, ^–Al and ^–Na, marginally for ^–K, ^–V and ^–Nb, and not at all for ^–Ga (at 4 kOe) or ^–Co (ferrromagnetic, zero field). In the heavier elements theF ^– signal is fed by transitions from theF ⁺ to theF ^– state at a rateR, as long asR(v ₊ –v _–). [See separate paper on ^–Al in these Proceedings, p. 879.]I am grateful to Alex Schenck and Bruce Patterson for the loan of equipment and samples, to Fred Gygax for helping set up the apparatus, to Jun Imazato for help with the experiment, and to Toshi Yamazaki and Tak Suzuki for valuable comments. I am also indebted to SIN for several weeks of free ^– beam time and to SIN, BOOM, and the University of Tokyo for free time on their VAX computers, which were kept busy for several months in the analysis.     

Solution of three-dimensional Faddeev equations for three-body Coulomb bound states

A new method of directly solving the three-dimensional Faddeev equations in the total-angular-momentum representation for the pure Coulomb bound-state problem is developed. The method is based on the tri-quintic Hermite spline expansion of the Faddeev components. The ground states of thee ^– e ^– e ⁺ system and thepp ^– mesic molecule are calculated.     

Redox reaction of μ−O in water determined by the chemical shift

The chemical shift of ^–O in water, ice and in aqueous hydrogen peroxide (H₂O₂) was examined using ^–O resonance. Two distinct signals are obtained in water and ice. Using ⁺ resonance signal as a standard, the observed shiftsg are –7.0×10^–4 (signal A) and –12.1×10^–4 (signal B) respectively. The intensity of the two fractions are almost equivalent in water; however, in ice, the intensity of signal B decreases with increase of signal A. After the addition of hydrogen peroxide to the water signal B disappears, A increases, and the total amplitude is increased.     

Radiation effects in lepton decays of neutral vector mesons and μ-e universality

A study has been made of the effects of radiation corrections of order as regards the probability of lepton decay of a moving neutral vector meson V e⁺e^– and V ^+– (V = ⁰, , ); -e universality has been checked by examining the effects of radiation corrections due to exchange of virtual photons between lepton and antilepton, and also to vacuum polarization by e⁺e^– electron and ^+–muon closed loops; in addition, a study has been made of the emission of soft photons as regards the partial width for the electron and muon modes of V-meson decay. Closed expressions (1), (4), and (5) for the corrections imply that the ratio ¦R_v¦ for the probabilities of decay of a V meson to e⁺e^– and ^+–, which are given by (11), agree well with the available evidence on ⁰ e⁺e^{– +–} decays and indicates a possible deviation from -e universality in e⁺e^–+– decays.Read at the meeting on high-energy physics, Nuclear Physics Section Academy of Sciences of the USSR (Moscow, February 11–15, 1974).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 84–89, July 1975.We are indebted to Professor A. A. Sokolov for a discussion.     

Elementary particle states based on the Clifford algebraC 7

The lepton isodoublet (e ^–,v _e ), the bare nucleon isodoublet (n,p), and their antiparticles are shown to constitute a basis of the irreducible representation of the Clifford algebraC ₇. The excited states of these doublets, i.e., ( ^–, ), ( ^–, ),..., and (s ⁰,c ⁺),(b⁰,t⁺) are generated by the products (e ^–,v _e )a and (n,p)a, wherea2^–1/2(e ^– e ⁺+v _e v _e ) has the same quantum numbers as the photon state. The bare baryonss, c, b, t carry the strangeness, charm, bottom, and top quantum numbers. These lepton and bare baryon states are in one-to-one correspondence with the integrally charged colored Han-Nambu quarks, and generate all the observedsu(3) andsu(4) hadron multiplets.     

Branching Fraction Measurements of the SM Higgs with a Mass of 160 GeV at Future Linear e + e − Colliders

Assuming an integrated luminosity of 500 fb^–1 and a center-of-mass energy of 350 GeV, we examine the prospects for measuring branching fractions of a Standard Model-like Higgs boson with a mass of 160 GeV at the future linear e⁺e^–collider TESLA when the Higgs boson is produced via the Higgsstrahlung mechanism, e⁺e^– HZ. The Higgs boson mass chosen close to the W pair threshold covers a mass regime with complicated background structures. We study in detail including some detector responds the precisions achievable for the branching fractions of the Higgs boson into WW^(*), ZZ^* and , whereas the measurement of BF(H ) remains a great challenge. Expectations for the total Higgs width are discussed using either the BF(Z ZZ^*) measurement of this study and the expected error for the inclusive Higgsstrahlung cross section or in addition the precise cross section expected for the weak boson fusion process, e⁺e^– v H, or W,Z-universality.     

Gluon and quark jets in deep-inelastic scattering of electrons by nucleons

The paper considers the formation of gluon and quark jets in the inelastic scattering of electrons by nucleons with large momentum transfers. It is assumed that these jets are created by the processes e^–+qe^–+q+g and e^–+ g e^–+q+q, where q is a quark and g is a gluon. The angular distributions of gluon and quark jets are calculated in the lowest order in the quark-gluon coupling constant. It is shown that after integration the processes e^–+qe^–+q+g and e^–+g e^–+q+¯q lead to violation of the scaling invariance of deep-inelastic scattering of electrons by nucleons.Translated from Izvestiya Vysshkikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 68–73, September, 1981.     

Inverse muon decay in a steady external field

A standard Weinberg-Salam model has been used to calculate the cross section of +e »v _e+ in steady crossed fields (EH=E ²–H ²=0). The asymptotic behavior of the cross section has been examined as a function of the kinematic and dynamic (field) invariant parameters.M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 106–111, December, 1992.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

Analyticity properties of eigenfunctions and scattering matrix

For potentialsV=V(x)=O(|x|^–2–) for |x|,x³ we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+V–z ²)^–1 has an analytic continuation from ⁺ to {kOImk|<b} as an operator from _b ={f=e ^–b|x| g|gL ₂(³)} to _–b . Based on this, we define for potentialsW=o(e ^–2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)     

Towards slow μ− production via muon catalyzed fusion

Slow ^– production via dd-CF using a two-layer arrangement is investigated. To determine its feasibility, experimental measurements are now in progress using the muonic X-ray detection method. The following experimental steps are being considered: (1) measurement of the number of ^– stopped inside a solid H₂/D₂ layer by detecting p K X-rays, (2) hot d emission detection by placing a secondary target at a distance of 10–30 mm from the layer and by detecting specific delayed X-rays, (3) measurement of the disappearance of d emission as the added D₂ layer is increased, (4) dd-CF measurement by detecting fusion protons, and (5) slow ^– emission detection. Results of the initial test experiment are presented.     

Levinson's Theorem for the Schrödinger Equation in One Dimension

Levinson's theorem for the one-dimensional Schrödinger equation with asymmetric potential which decays at infinity faster thanx ^–2 is established by theSturm-Liouville theorem. The critical case where the Schrödinger equation hasa finite zero-energy solution is also analyzed. It is demonstrated that the numberof bound states with even (odd) parityn ₊(n _–) is related to the phase shift ₊ (0)[_– (0)] of the scattering states with the same parity at zero momentum as ₊ (0)+ /2 =n ₊ and _– (0) =n _– for the noncritical case, and ₊ (0) =n ₊ and_– (0) – /2 =n _– for the critical case.     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.     

Decomposition of many-body Schrödinger operators

The complex-dilated many-body Schrödinger operatorH(z) is decomposed on invariant subspaces associated with the cuts {+z ^–2 R ⁺}, where is any threshold, and isolated spectral points. The interactions are dilation-analytic multiplicative two-body potentials, decaying asr ^–1+ atr=0 and asr ^–1+ atr=.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.     

Mixing of toponium and Z° boson in elastic e+ − annihilation

If toponium with a mass close to the mass of a Z meson exists, it could be studied on the basis of the interference pattern which would be produced in the differential cross section for elastic e⁺e^– annihilation with unpolarized initial beams. The energy and angular dependence of the quantity which determines the relative contribution of vector toponium to the differential cross section for the process e⁺e^– e⁺e^– has been studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika,No. 10, pp. 38–42, October, 1988.     

The lanthanideβ″ aluminas

The entire sodium ion content of sodium alumina (Na_1.67Mg_0.67Al_10.33O₁₇) can be replaced with a variety of lanthanide ions by simple diffusion reactions at moderate temperatures (500–700°C). Lanthanide alumina crystals are hard, clear, chemically stable, and have well-defined crystal structures. The fluorescence spectrum of Nd³⁺ in alumina is similar to that in YAG. The lifetime of the⁴ F _3/2 state of Nd³⁺ in completely-exchanged alumina (350s at 10²¹ Nd³⁺ cm^–3) is about 45% longer than in YAG (240s at 10²⁰Nd³⁺ cm^–3). The lanthanide aluminas may be of considerable interest as new phosphor and laser host materials.     

R andRτ ratios at the five-loop level of perturbative QCD

We study perturbative QCD at the five-loop level. In particular we considerR = _tot(e ⁺ e ^– hadrons)/(e ⁺ e ^{– + –}) andR = ( v+hadrons)/( ev). We use our method to estimate the five-loop coefficients. As a result, we obtain _s (M _z ) = 0.1186(11) and _s (34 GeV) = 0.1396(16), which are accurate at the 1% level. We also findR = 3.8350(18), which is consistent withR and is accurate to 0.05%.     

Production of supersymmetric particles ine + e − andep collisions

A review is given of the theoretical predictions for chargino, neutralino and selectron pair production ine ⁺ e ^– annihilation and for slepton and squark production inep collisions. The energy range considered is that of LEP, SLC and HERA. The expectations for the production of SUSY particles at ane ⁺ ev ^– collider in the TeV energy range are also discussed.Invited talk at the International Symposium Hadron Interactions — Theory and Phenomenology, Bechyn, Czechoslovakia, June 26–July 1, 1988.I want to thank H. Baer, H. Fraas, D. Karatas, W. Majerotto and X. Tata for discussions and correspondence. Financial supports of the Czechoslovak Academy of Sciences and the Austrian Academy of Sciences are gratefully acknowledged.