Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

The ground state energy of Sdhrödinger operators

We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc ²e()–d ² for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

μ+SR in magnetically ordered BCC metals: Local fields, μ+ sites,quantum diffusion,and strain effects

The paper gives a critical discussion of the procedures for extracting from the ⁺SR signals obtainable on magnetically ordered metals information on ⁺ sites, on local lattice distortions induced by the ⁺, on the local magnetic fields felt by the ⁺, and on quantum diffusion. Results for-Fe are: ⁺ occupy O sites, the tetragonality of the elastic double-force tensor isA–B 2eV, the dipolar magnetic field acting on the ⁺ isB _dip=(0.66±0.02)T. Using this information ⁺ hopping rates and diffusivities in Fe are deduced and compared with diffusivities obtained for hydrogen and deuterium. From this it is concluded that hydrogen in Fe diffuses via the adiabatic mechanism. In addition, the paper contains a brief summary of the theoretical background required for taking advantage of the rather large ¦A– B¦ values expected for ⁺ at O sites in bcc metals in order to gain information on the effects of energy asymmetries between neighbouring ⁺ sites on the ⁺ hopping rates.     

Radiation effects in the production and decay of ψ mesons by leptons

A new expression _e is obtained for resonance in the reaction e⁺e^– ar ^+– with allowance for the radiative corrections, which also contain the emission of hard photons by the final leptons and the final value of the energy resolution E. An expression is obtained for the total probability of radiative lepton decay. A numerical analysis of the experimental data is made for the reaction ^+–, and the parameters e⁺e^– (3, 1) e⁺e^–, and _e ² /, _e, and are determined for (3, 1) resonance-with allowance for the radiative corrections.This paper was read (November 17–21, 1975) at a session on high-energy physics of the Department of Nuclear Physics of the Academy of Sciences of the USSR.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–34, March, 1977.     

Three-dimensional spatial diffusion in optical molasses

We have studied the expansion of a small cloud of⁸⁵Rb atoms in three-dimensional optical molasses (lin lin and ⁺ – ^– configurations) and observed diffusive motion. We determined the spatial-diffusion coefficients for various laser intensities and detunings, and compared them (in the case of lin lin molasses) to values calculated from friction and momentum-diffusion coefficients of a one-dimensional (1D) theory of laser cooling. The predicted variations of the spatial-diffusion coefficient with laser intensity and detuning are in good qualitative agreement with the experimental data. We found that the minimal value observed experimentally, 6 × 10^–4 cm²/s, lies within a factor of 3 of the 1D theoretical minimum, , 26/M, whereM is the atomic mass.Dedicated to H. Walther on the occassion of his 60th birthday     

Zero-Dimensional Spectral Measures for Quasi-Periodic Operators with Analytic Potential

We prove that for quasiperiodic operators with potential V(n)=f(+n), f analytic, the spectral measures are zero-dimensional for large, any irrational . It extends a result of Jitomirskaya and Last to the case of any analytic f.     

The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Polarization of strangeness Arizona muon

The longitudinal polarization of strangeness Arizona muon, namely, the 236 MeV/c ⁺ from the K^{+ +} v decay, has been measured to search for right-handed weak current in the strangeness changing process. The polarization has been determined to be –0.967±0.047.We are grateful to Professors T. Nishikawa, S. Ozaki, A. Kusumegi, and H. Sugawara of KEK for their encouragement and support during the course of this experiment. We are grateful to the operating crew of the KEK proton synchrotron and its experimental facilities for their cooperation during the experiment. This work is partially supported by the Grant-in-Aid of the Ministry of Education, Science and Culture.     

Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

Adjoint solutions of the Brans-Dicke equations

It is shown that if the Brans-Dicke equations have the solution,g _ij generated by the trace free sourceT _n (T-O) then there exists an adjoint solution ^–1, ²g_ij of these equations generated by the source ^-2 T _u. An example is considered.     

Norm inequalities for fractional powers of positive operators

It is shown that ifA, B andX are operators on a Hilbert space such thatA andB are positive andX belongs to a norm ideal associated with some unitarily invariant norm |·|, then for 0 r 1 we have |A ^r XB ^r | |X|^1-r |AXB| ^r . This is an extension of the classical Heinz-Kato inequality which was originally proved for the usual operator norm. Other related inequalities are also discussed.     

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.     

The vacuum and lightcone quantization of interaction Hamiltonians

Let denote the conformally invariant neutral free scalar field on ×S ⁿ. The naive lightcone Hamiltonian for a ^p interaction is given by c^p, where C denotes a lightcone in ×S ⁿ, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.     

Weak four-fermion interaction in terms of SU(3) invariants. II

A lepton octet is constructed by analogy with the baryon octet by the substitution p⁺N ₁e⁺,⁺₁ é⁺,^-₂^-, ^- N ₂^-, where ₁, ₂,N ₁,N ₂ are arbitrary constants. The neutral components are replaced by a linear sum of the electron and muon neutrinos with arbitrary coefficients. The constants are determined from the system of general conditions (normalization, absence of crossed terms of the type ( etc.). As a result, the lepton octet is determined to within a single constant, and this is shown to be identical with the Cabibbo angle. Calculations are also made of the weak decays of baryons of the octet in the case of both charged and neutral currents. In the case of charged currents, the results agree with Cabibbo's theory. Calculations are also made of the lepton-lepton weak interactions and the ratios of the corresponding constants are determined. The ratios are in qualitative agreement with the existing experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–56, January, 1976.     

Quantitative universality for a class of nonlinear transformations

A large class of recursion relationsx _{n + 1} = f(x_n) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum . With sufficiently small),z > 1, the universal details depend only uponz. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio ( = 2.5029078750957... forz = 2). This structure is determined by a universal functiong ^*(x), where the 2ⁿth iterate off,f ⁽ⁿ⁾, converges locally to ^–n g ^*( ⁿ x) for largen. For the class off's considered, there exists a _n such that a 2ⁿ-point stable limit cycle including exists; – _n R~ ^–n ( = 4.669201609103... forz = 2). The numbers and have been computationally determined for a range ofz through their definitions, for a variety off's for eachz. We present a recursive mechanism that explains these results by determiningg ^* as the fixed-point (function) of a transformation on the class off's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.Research performed under the auspices of the U.S. Energy Research and Development Administration.     

Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models

Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ _x,y const/¦x–y¦². For translation-invariant systems with well-defined lim _x x ² J _x =J ⁺ (possibly 0 or ) we establish: (1) There is no long-range order at inverse temperatures withJ ⁺1. (2) IfJ ⁺>q, then by sufficiently increasingJ ₁ the spontaneous magnetizationM is made positive. (3) In models with 0<J ⁺< the magnetization is discontinuous at the transition point (as originally predicted by Thouless), and obeysM( _c )1/( _c J ⁺)^1/2. (4) For Ising (q=2) models withJ ⁺<, it is noted that the correlation function decays as xy()c()/|x–y|² whenever< _c . Points 1–3 are deduced from previous percolation results by utilizing the Fortuin-Kasteleyn representation, which also yields other results of independent interest relating Potts models with different values ofq.