Predictions for inclusive reactions based on a parton structure of hadrons

It is proposed that the asymptotic single-particle distributions f(x)=x(dσ/dx) in inclusive reactions should reflect the limiting longitudinal momentum distribution, ∼νW₂(x), of the hypothetical partons constituting a hadron. It is further argued that f(x) becomes, proportional to νW₂(x) as x → 1. Predictions are then made for a large class of inclusive reactions based on our knowledge of νW₂(x) from electroproduction data. For some of these (such as pp → π^±X), in which the predictions differ markedly from the Regge ones, present experiments distinctly favor ours.     

An approach to radially symmetrical solutions of the sine-Gordon equation

The solution φ(r, t) of the radially symmetric sine-Gordon equation is considered in three and two spatial dimensions for initial curves, analogous to a 2π-kink, in the expanding and in the shrinking phase, for R(t)j? R(0). It is shown that the parameterization φ(r, t) = 4 arcian exp[γ(r?R(0)] + x(r, t), where R(t) describes the exact propagation of the maximum of φ,(r, t), is suitable. Using an appoximate differential equation, recently given for the propagation of the solitary ring wave, a rough analytic approximation for the correction function x(r = R(t), t) is found and tested numerically. A relationship between the fluctuations in x(r = R(t), t) and those in $\text{R}\text{?}\text{(t), t)}\text{and}\text{R(t)}$ explains why the solitary wave is almost stable. From x(r = R(t), t) and the supposition x(1, t) ≈ x(∞, t) ≈ 0 an assymetry in φ_r(r, t) with respect to r = R(t) is predicted. It also exhibits fluctuations corresponding to those in x(r = R(t), t). The condition for validity of this approximation apparently is also a limit for the stability of the solitary ring wave.     

Probing the mesonic structure of the nucleon by means of exclusive quasielastic pion knockout in (e, e′π) reactions at high energies

By including the Z diagram in an analysis performed in the laboratory frame (instantaneous form of dynamics), the notion of quasielastic pion knockout by protons and electrons [(p, 2p) and (e, e′p) reactions treated in terms of the relevant pole diagrams] is generalized to the relativistic case where a meson is quasielastically knocked out of a nucleon by an electron having an energy of a few GeV. The concept of the wave function is introduced for the pion (and for other mesons), and its relation to the vertex constant G _πNN and the vertex function g _πNN(k ²) is indicated. The spectroscopic factor S _N ^B? is defined as the normalization of the wave function for the meson ?. It is shown by two methods that, under the kinematical conditions of quasielastic knockout that include the condition E _π?m _π (E _π is the energy of the knock-on pion) and the condition that the square Q ² of the virtual pion mass is large, the competing tree diagram is suppressed in relation to the pole diagram (this is not so in the case of pion photoproduction). From data of a p(e, e′π ⁺)n experiment involving longitudinal virtual photons γ _L ^* , the momentum distribution |Ψ _p ^nπ (k)|² of pions in the nucleon is extracted for the first time over the entire range of significant momenta k, and this result is used to determine the cutoff constant Λ_π and the value of S _p ^nπ ≈0.2. The momentum distribution of positive rho mesons in the soft section of the spectrum is determined from experimental data on the process p(e, e′π ⁺)n proceeding through the mechanism ρ ⁺+γ _T ^* → π ⁺ involving transverse photons. A way to determine the momentum distribution of omega mesons through data on the process p(e, e′π ⁰)p is indicated. Two forms of dynamics—instantaneous form and that of light-front dynamics (the latter does not involve the Z diagram)—are compared for the example where the calculations are performed for the spectroscopic factor S _N ^B? .     

Branching ratios for the decays of Ψ(3770) and ϒ(10580) mesons to a pair of light hadrons

The branching ratios for the exclusive decays of the heavy quarkonia Ψ(3770) and ?(10580) to a pair of light mesons [π ⁺ π ^-, $K\bar K$ , ρ(ω)π, ρ(ω)η, ρ(ω)η’, $K^* \bar K$ +c.c, ρ ⁺ ρ ^-, and $K^* \bar K^* $ ] and the branching ratios for the decays Ψ(3770) → J/Ψ + P(P = π ⁰, η) and ?(10580) → ?(1S) + P(P = π ⁰,η,η′), which involve a heavy quarkonium in the final state, are calculated with allowance for new data on the width of the D*^±(2010) meson and the mass differences between the charged and neutral beauty mesons (B ^±, on one hand, and B ⁰ and $\bar B^0 $ , on the other hand). The calculations are based on the model where the Okubo-Zweig-Iizuka rule is dynamically violated owing to the intermediate state $D\bar D (B\bar B)$ in the case of the Ψ(3770) [?(10580)] meson. The inclusive annihilation of Ψ(3770) and ?(10580) mesons to light hadrons is discussed.     

Effects of cross correlations between inhomogeneities of the parameters of an isotropic medium on the spectrum and damping of elastic waves

The dispersion and damping laws have been investigated for elastic waves in an isotropic medium with one- and three-dimensional inhomogeneities of the density p(x) of the material and the elastic force constants μ(x) and λ(x) with allowance for the cross correlations between these inhomogeneities. It has been demonstrated that the positive cross correlations between μ(x) and λ(x), as well as the negative cross correlations between p(x) and μ(x) or p(x) and λ(x), lead to an enhancement of the modification of the dispersion law and an increase in the damping of waves. The positive cross correlations between p(x) and μ(x) or p(x) and λ(x), as well as the negative cross correlations between μ(x) and λ(x), result in the opposite effects: a weakening of the modification of the dispersion law and a decrease in the damping. An analysis of the results obtained in this paper and in our recent work [15] has made it possible to formulate the general regularity of the effects of cross correlations, irrespective of the physical nature of the waves: the effects of cross correlations between inhomogeneities of any two parameters of the material on the wave spectrum depend on whether both parameters related by the cross correlations belong to the same part of the Hamiltonian (i.e., if they both belong to either the kinetic part or the potential part of the Hamiltonian) or they belong to different parts of the Hamiltonian. The positive cross correlations lead to a greater modification of the dispersion law and to an increase in the damping of waves in the former case and to a decrease in these characteristics in the latter case. Correspondingly, the negative cross correlations in each of these cases result in the opposite effects. This regularity has been explained qualitatively.     

Diffraction dissociation of neutrons in the reaction dp → pppπ− at 25 GeV/c

We observe the reaction dp → p_spec (pπ^?)p in a bubble chamber exposure at 25 GeV/c incident deuteron momentum. The (pπ^?) system with invariant mass below 2.0 GeV is interpreted as neutron diffraction dissociation. The (pπ^?) mass spectra show little if any direct evidence of N¹ production. The decay angular distributions and the momentum transfer distributions of the (pπ^?) system suggest a smooth increase in contributions from higher partial waves $\text{(J ?}\text{3}\text{2}\text{)}$ with increased mass or momentum transfer. A simple partial-wave analysis shows a P₁₁ contribution below 1.3 GeV for small ?t′ and a dominant D₁₃ contribution elsewhere. Both the P₁₁ and D₁₃ amplitudes peak far below the N¹(1470) and N¹(1520) resonances. We also find evidence for the charge-exchange reaction np → p(pπ^?). In this process the (pπ^?) system shows evidence for Δ^o(1236) and N¹(1520) production.     

Nuclear structure of 18F: (IV). Negative-parity states

Studies via the ¹⁶O(³He, pγ)¹⁸F, ¹⁴N(α,γ)¹⁸F and ¹⁷O(p, γ)¹⁸F reactions have resulted in new J^π assignments for 11 states or negative parity: E_x(keV) (J^π) = 3791(3^?), 4226(2^(?)), 4398(4^?), 4860(1^(?)), 5502(3^(?)), 5785(2^?), 6097(4^?), 6108(1^(?), 2^(?), 3^(?)), 6241(3^?, T = 1), 6643(2^?, T = 1) and 6878(3^(t-), 4^?). The 6241 keV state is probably isospin mixed. New information for 5 states of positive parity has also been obtained: E_x(keV) (J^π) = 3838(2⁺), 4115(3⁺), 4652(4⁺, T = 1), 4753((0⁺), T = 1) and 4964(2⁺, T = 1). Mean lives, branching and mixing ratios are reported for all states. The results for the negative-parity states are discussed in the framework of the various models available. The states at E_x = 1080(0^?), 2100(2^?) and 4398(4^?) keV are interpreted as the first three members of a K^π = 0^? rotational band.     

Interferometry for Ellipso-Height-Topometry part 3: Correction of the aspect errors and reduction of the dispersion of the ellipsometric parameters

Ellipso-Height-Topometry, EHT, is an extended optical topometry, where both the topographies of the surface height H(x,y) and the ellipsometric local parameters Ψ(x,y) and Δ(x,y) of surfaces with locally changing materials are measured on the same pixel raster with high resolution and using the same data sets. Further quantities can be calculated from these measurements on the base of locally confined surface models: the local refractive index, the thickness t(x,y) of overlayers or films, or other parameters of layered systems.     

Radiative decays as tests of the symmetries of the Ψ particles

The success of the Okubo-Iizuka-Zweig rule for decays of Ψ and Ψ′ suggests that the radiative decays Ψ → γ + hadrons should be dominated by intermediates like Ψ → Ψ′ hadrons. This mechanism is consistent with experimental data which show Γ(Ψ → ?⁰π⁰) and Γ(Ψ → ηγ) to be comparable. if all Ψ-like particles are isoscalar, $\text{Γ(Ψ →}{}^0\text{γ)}$ should be very small. If all Ψ-like particles are SU(3) singlets, Γ(Ψ → η′γ)/Γ(Ψ → ηγ) should be large. Substantial violation of our predictions would be circumstantial evidence for the existence of non-singlet new quarks.     

Laser-induced predissociation spectrum of O2 + in an ion beam

Physical observables associated with interactions between electromagnetic radiation and charged particles are required to be gauge invariant, i.e. independent of the gauge of the field potentials. Gauge invariance implies the involvement of the electric polarization field, P(x), in electrodynamics, but leaves undetermined the transverse component P(x)^⊥ which occurs in the interaction terms coupling charges to radiation. We put the Hamiltonian for non-relativistic electrodynamics into a completely general form displaying the arbitrary polarization field. The well-known Coulomb gauge and ‘multipolar’ Hamiltonian formalisms then arise as special cases corresponding to particular choices of P(x)^⊥. For practical calculations some choice of P(x)^⊥ has to be made, and we present a particularly useful form for neutral collection of charges, not necessarily bound, but typically appropriate to atoms and molecules. Some results concerning the independence from the arbitrary quantities of physical observables are described.     

Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

Interferometry for ellipso-height-topometry: Part 2: Measurement of the ellipsometric data, material identification, and correction of the measured height

Ellipso-height-topometry, EHT, as introduced by Leonhardt, et al. [Interferometry for ellipso-height-topometry, part 1, Optik 113 (2003) 513-519; Topometry for locally changing materials, Opt. Lett. 23 (1998) 1772-1774]; [Ellipso-height topometry, Optik 112 (2001) 413-420] is an extended topometry where topographies of the surface height H(x,y), the ellipsometric parameters Ψ(x,y) and Δ(x,y) (and optionally the intensity distribution I(x,y)) of the surface are measured on the same pixel raster and with high resolution. Thus, we can dispose over a set of (mutually coherent) topographies, and further topographies of quantities of interest can be calculated from this set: the local change in the complex refractive index N(x,y)=n(x,y)−k(x,y)i of bulk surfaces, the thickness distribution t(x,y) of locally changing (discontinuous) films and overlayers, and a correction of the optically measured local height H(x,y). The height error ΔH(x,y) can be calculated from the ellipsometric data and the true height h(x,y)=H(x,y)−ΔH(x,y) is thus obtained. ΔH(x,y) can assume large values when overlayers of oxidations or residues from lubrication oil or from processing are present. Much more information about the surface is gained with this concept.In part 1 of this work a z-scanning interferometric scheme with oblique incidence over the entire object field has been introduced, with the advantages of white-light interferometry, but with the additional capability of measuring material information to supply a complete set of topographies for extended topometry. In addition, very useful coherence properties for interferometry with oblique incidence were presented and discussed which allow to shape the interferogram in a simple way without any additional devices. In this part we derive the theory of the ellipsometric measurement and present first results by complete sets of two different samples.     

Kinetic Limit of N-Body Description of Wave–Particle Self-Consistent Interaction

A system of N particles $\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z ^(N)(0), ξ ^N (0)), it evolves according to Hamiltonian dynamics to (Z ^(N)(t), ξ ^N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z ^(∞)(0), f(0)) evolve to (Z ^(∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution f ^N(0) → f(0) weakly and with Z ^(N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z ^(N)(t), f ^N(t)) converges weakly to (Z ^(∞)(t), f(t)).     

Multiplicity distributions in the generalized Feynman gas model

Multiplicity distributions Ψ_n^(k) in the generalized Feynman gas model of order k (defined by saying that all integrated correlation functions f_n except f₁,…,f_k are zero) are derived and expressed in terms of Poisson distributions with different ”average multiplicities”, which are related to the integrated correlation functions. The relations between Ψ_n^(k) and Ψ_n^(j) for arbitrary positive integers k,j are found. An intuitive picture to gain a better feeling for these relations is developed.On the basis of our formulae we show that the experimentally observed multiplicity distributions (between 50 GeV/c and 303 GeV/c incoming momentum) can be well reproduced by those of a Feynman gas model of order two. Other applications of our formulae are suggested.     

On rational functions of first-class complexity

It is proved that, for every rational function of two variables P(x, y) of analytic complexity one, there is either a representation of the form f(a(x) + b(y)) or a representation of the form f(a(x)b(y)), where f(x), a(x), b(x) are nonconstant rational functions of a single variable. Here, if P(x, y) is a polynomial, then f(x), a(x), and b(x) are nonconstant polynomials of a single variable.     

Asymptocic Freedom of Gluons in Hamiltonian Dynamics

We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang–Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang–Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian \({\beta}\) -function coincides with the one obtained in an earlier calculation using a different generator.     

SU(6) symmetry breaking effects in deep inelastic scattering

The fact that the N and Δ states of the $\text{56}$ baryons are not degenerate in mass is shown to imply that the deep inelastic scattering ratio F_2n(x)/F_2p(x) should approach $\text{1}\text{4}$ as x → 1. The rate of approach is predicted to be approximatel linear in x. The possibility of observing analogous effects in other large momentum transfer processes is also discussed.     

Von Neumann entropy-preserving quantum operations

For a given quantum state ρ and two quantum operations Φ and Ψ, the information encoded in the quantum state ρ is quantified by its von Neumann entropy S(ρ). By the famous Choi-Jamio?kowski isomorphism, the quantum operation Φ can be transformed into a bipartite state, the von Neumann entropy Smap(Φ) of the bipartite state describes the decoherence induced by Φ. In this Letter, we characterize not only the pairs (Φ,ρ) which satisfy S(Φ(ρ))=S(ρ), but also the pairs (Φ,Ψ) which satisfy Smap(Φ°Ψ)=Smap(Ψ).     

Die Stromdichte eines quadratisch integrierbaren Klein-Gordon-Feldes mit Wechselwirkung

A four vector is constructed for the statistical interpretation of a relativistic scalar wave function which is not a solution of an interaction-free Klein-Gordon equation. The zero component of the four vector is positive definite, whereas the four components satisfy the equation of continuity. It is proved that these components, which are bilinear forms inΨ(x)=∫d ⁴pa(p)e^?ipxsatisfying the normalization condition(2π) ⁴(2m)^?1∫ d⁴pθ(p⁰)θ6(p²)¦a(p)¦²=1 reduce to the four-vector ofPetzold and co-workers if the transition fromΨ(x) to the free-particle wave functionΦ(x)=∫d ³¯pa(¯p)e^?ipxsatisfying(2π) ³ (2m)^?1∫(2p₀)^?1¦a (¯p)¦²d³¯p=1 is made in the proper way. The nonrelativistic limit in the case of relativistic interactions is also discussed.