Interaction between the nucleon and muon currents in elastic neutrino-nucleon interactions

The spin relations of neutrino-nucleon interaction with the formation of a muonv(V) N N are investigated within the framework of the two-component and four-component theories of two neutrinos under the assumption of a point neutrino. The difference between the predictions of the two theories is identified. It is shown that the four-component theory of two neutrinos, unlike the two-component theory, accommodates the V + A variant of interaction between the muon current (v) and the barion current.The authors are grateful to Prof. A. A. Sokolov and to R. Sh. Yakh'yaev for evaluating the results.     

Gauge Theories: Geometry and Cohomological Invariants

We develop a geometrical structure of themanifolds and associated, respectively, withgauge symmetry and BRST symmetry. Then, we show that , where is the group of BRST transformations, is endowed with the structureof a principal fiber bundle over the base manifold. Furthermore, in this geometricalsetup, due to the nilpotency of the BRST operator, weprove that the effective action of a gauge theory is aBRST-exact term up to the classical action. Then, weconclude that the effective action where only the gaugesymmetry is fixed is cohomologically equivalent to the action where the gauge and the BRSTsymmetries are fixed.     

МОДЕЛИРОВАНИЕ ЭЛЕКТ РОННО-ОПТИЧЕСКИХ СИС ТЕМ С ОСЕВОЙ СИММЕТРИЕЙ П РИ ПОМОЩИ СЕТИ СОПРОТИВЛЕНИЙ

The paper explains the theory of modelling electrostatic fields by a resistance network. The conditions, which the resistance network must satisfy, are derived and the question of modelling electrodes of different shapes is solved. The finished network and the results obtained on it when modelling a jet for a linear h-f accelerator of electrons are described. Particular attention is paid to the influence of a space charge, the modelling of which is an advantage of this method.

---

---

1- , 1964., , .

---

. .     

Nuclear Responses for Neutrinos and Mo Observatory of Neutrinos

Nuclear responses for neutrinos and neutrino studies in Mo nuclei are briefly reported. Nuclear spin-isospin responses for neutrinos are crucial for neutrino studies in nuclei. Spin-isospin responses for solar neutrinos, supernova neutrinos and neutrinos involved in double-beta decays are discussed. It is of great interest to study neutrino masses and low energy solar neutrinos. It is shown that it is possible to carry out with ¹⁰⁰Mo both spectroscopic studies of double-beta decays with the sensitivity of the order of m 0.03eV and real-time exclusive studies of the low energy solar neutrinos.     

Structure of σ model in [1, 1] representation of SU(2) ⊗ SU(2) group

The spontaneous breakdown of symmetry of the-model in the [1, 1] representation of SU(2) SU(2) group is investigated. It is shown that the spontaneous breakdown is realized in all cases of squared mass ² in mass term in the Lagrangian ( ²>0, ²=0, ²<0), unlike the-model in [1/2, 1/2] representation, in which the spontaneous breakdown only for the case ²<0 manifests itself. Further, different but equivalent methods of obtaining the nonlinear realization for pions in the frame of an extended in such a way-model are demonstrated. Finally, it is sketched, that the obtained results can be generalized to all [N/2,N/2] representations of SU(2) SU(2) chiral group.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.On leave of absence from theDept. of Theoretical Physics, Comenius University, Bratislava, Czechoslovakia.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Inertial effects on the escape rate of a particle driven by colored noise: An instanton approach

A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation , where is a Gaussian colored noise with mean zero and correlator (t)(t')=(D/)exp(–|t–t'|/). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D0) limit. This yields an escape rateexp(–S/D), where the actionS is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an instanton of the theory. The extremal actionS is calculated analytically for smallm and for general potentials, and numerical results forS are displayed for various ranges ofm and for the typical case of the quartic potentialV(x)=–x ₂/2+x ₄/4.     

Measurement of charm fragmentation ratios and fractionsin photoproduction at HERA

The production of , D⁰, D ⁺ , D_s ⁺ and charm hadrons and their antiparticles in e p scattering at HERA was measured with the ZEUS detector using an integrated luminosity of . The measurement has been performed in the photoproduction regime with the exchanged-photon virtuality and for photon-proton centre-of-mass energies in the range . The charm hadrons were reconstructed in the range of transverse momentum and pseudorapidity . The production cross sections were used to determine the ratio of neutral and charged D-meson production rates, , the strangeness-suppression factor, , and the fraction of charged D mesons produced in a vector state, . The measured and values agree with those obtained in deep inelastic scattering and in e ⁺ e^- annihilations. The measured value is smaller than, but consistent with, the previous measurements. The fractions of c quarks hadronising as a particular charm hadron, , were derived in the given kinematic range. The measured open-charm fragmentation fractions are consistent with previous results, although the measured is smaller and is larger than those obtained in e ⁺ e^- annihilations. These results generally support the hypothesis that fragmentation proceeds independently of the hard sub-process. Received: 12 August 2005, Revised: 8 September 2005, Published online: 6 October 2005     

Enhancement of activated decay of metastable states by resonant pumping

We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,_E(0)T(0)T/V₀ (0)[_E(0) is the derivative of(E) atE= 0,V ₀ is the barrier height,V ₀ T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v _E (0)T/, and the resonance mismatch, [ —(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ^–1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.     

Chains of twists and induced deformations

Chains of extended twists are composed of factors . The set of Jordanian twists { } can be applied to the initial Hopf algebra . In this case the remaining (transformed) factors of the chain can serve as extensions for such a multijordanian twist. We study the properties of these generalized extensions and the spectra of deformations of the corresponding Heisenberg-like algebras. The results are explicitly demonstrated for the case when .     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

Lorentz-invariant solutions of the classical Yang-Mills equations

A gauge representation of the noncompact group SL(2,C) is defined. All the corresponding invariant (singular) solutions of the classical Yang-Mills equations in Minkowski space are found. It is shown that they are related to a family of real SU(2) x SU(2)-invariant Euclidean solutions containing the self-dual (one-instanton) configurations.     

Evaluation ofS,T, U parameters, triple gauge boson vertices and some oblique corrections in extraU(1) superstring inspired model

Explicit evaluation of the following parameters has been carried out in the extraU (1) superstring inspired model: (i) As Mz₂ varies from 555 GeV to 620 GeV and (m _t) CDF = 175.6 ± 5.7 GeV (Table 1): (a) S^New varies from -0.100 ± 0.089 to -0.130 ± 0.090, (b) T^New varies from -0.098 ± 0.097 to -0.129 ± 0.098, (c) U^New varies from -0.229 ± 0.177 to -0.253 ± 0.206, (d) Τ_z varies from 2.487 ± 0.027 to 2.486 ± 0.027, (e) A_LR varies from 0.0125 ± 0.0003 to 0.0126 ± 0.0003, (f) A _FB ^b remains constant at 0.0080 ± 0.0007. Almost identical values are obtained for (m _t)D0 = 169 GeV (see table 2). (ii) Triple gauge boson vertices (TGV) contributions: AsMz ₂ varies from 555 GeV to 620 GeV and (m _t) CDF = 175.6 ±5.7 GeV. (a)√s = 500 GeV, asymptotic case: varies from -0.301 to -0.179; varies from -0.622 to -0.379; varies from +0.0061 to 0.0056; varies from -3.691 to -2.186. varies from +0.270 to +0.118; varies from +0.552 to 0.238; varies from +0.0004 to +0.0002; remains constant at -0.110. (b)√s = 700 GeV, asymptotic case: varies from -0.297 to -0.176; varies from -0.609 to -0.370; varies from -0.0082 to -0.0078; varies from -3.680 to -2.171.√s = 700 GeV, nonasymptotic case: varies from -0.173 to -0.299; varies from-0.343 to -0.591; varies from -0.005 to -0.011; remains constant at -0.110. The pattern of form factors values for√s = 1000, 1200 GeV is almost identical to that of√s= 700 GeV. Further the values of the form factors for (m _t)D0 (=169 GeV) follow identical pattern as that of (m _t) CDF form factors values (see tables 5, 6, 9, 10). We conclude that the values of all the form factors with the exception of these of , are comparable or larger than theS, T values and therefore the TGV contributions are important while deciding the use of extraU (1) model for doing physics beyond standard model.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

Spinor two-point functions in maximally symmetric spaces

The two-point function for spinors on maximally symmetric four-dimensional spaces is obtained in terms of intrinsic geometric objects. In the massless case, Weyl spinors in anti de Sitter space can not satisfy boundary conditions appropriate to the supersymmetric models. This is because these boundary conditions break chiral symmetry, which is proven by showing that the order parameter for a massless Dirac spinor is nonzero. We also give a coordinate-independent formula for the bispinor introduced by Breitenlohner and Freedman [1], and establish the precise connection between our results and those of Burges, Davis, Freedman and Gibbons [2].     

On General Plane Fronted Waves. Geodesics

A general class of Lorentzian metrics, , , with any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as , as in the classical model of exact gravitational waves.     

Coherent states and partition function

The concept of coherent states for arbitrary Lie group is suggested as a tool for explicitly obtaining an integral representation of the partition function, whenever the Hamiltonian has a dynamical group. Two examples are thoroughly discussed: the case of the nilpotent group of Weyl related to a generic many-body problem with two-body interactions, and the case of SU(1, 1)() relevant for a superfluid system.     

Geometry of gauge fields in a multidimensional universe

Let S be a group of automorphisms of a principal fibre bundle (U, , E, R), both groups S and R being compact. Let I (resp. H) be the isotropy group of S (resp. S x R) acting on E (resp. U), and let N(I) (resp. N(H)) be the normalizer of I (resp. H) in S (resp. S x R). We construct two principal bundles P(M, N(I)|I) E and Q(M, N(H)|H) U, where M=E/S is the space of orbits of S in E, and we prove that, given a connection A in P, there is a one-to-one correspondence between S-invariant connections in U and triples (B, , ), where B is a connection in Q, part of which is a pullback ^* A of A, and , are scalars which are crosssections of certain vector bundles associated with Q. The resulting final gauge group N(H)|H is shown to contain as a normal subgroup the centralizer of I in R, known from earlier works of other authors. A dimensional reduction of the Einstein-Yang-Mills system on E is briefly discussed.Partially supported by the Polish Ministry of Science, Higher Education and Technology under the Project MRI-7.     

Gelation and Cluster Growth with Cluster-Wall Interactions

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c _k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p ₀. We assume that for 01, which encompasses both bond linking kernels (R _jk = j k ) and surface reaction kernels (R _jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on ^–1 in the limiting case R _{= jk} , p ₀=1.