Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1969"

A PCAC puzzle: π0→γγ in the σ-model

Abstract: The effective coupling constant for π0→γγ should vanish for zero pion mass in theories with PCAC and gauge invariance. It does not so vanish in an explicit perturbation calculation in the σ-model. The resolution of the puzzle is effected by a modification of Pauli-Villars-Gupta regularization which respects both PCAC and gauge invariance.

Level structure of dual-resonance models

Abstract: In this paper the level structure of narrow-resonance models with duality is considered We shall use to this purpose the multiparticle dual amplitudes recently proposed by several authors and shall study the structure of the residue of each pole in what concerns its factorizability We find that for each energy eigenvalueE n =√s n the residue does indeed factorize in a finite number of terms (number of degenerate levels) and that this number increases withn like exp [cEn] The physical interpretation of this wild increase is found in the essential many body nature of models consistent with duality The appearence of states with imaginary coupling follows easily from the covariant, four-dimentional approach that we have taken and that insures absence of kinematical singularities It is nevertheless found that a cancellation mechanism analogous to the one existing in QED (Ward identities) occurs here too Although the problem of a systematic cancellation of all ghosts in a realistic case has not been solved, we see that the leading and most troublesome ghosts are indeed eliminated in this way

A remark on bound states in potential-scattering theory

Abstract: Let ℋ = ℋB + ℋC be the Hilbert space of ann-particle quantum system, where ℋB is spanned by the bound states and ℋC corresponds to the continuous spectrum of the Hamiltonian. It is shown that the wave functions which are in some sense localized in space and energy form a compact set in ℋ. This is used to prove that a wave packet ψ remains localized at finite distance for all time if ψ∈ℋB, and that it disappears at infinity if ψ∈ℋC.

A stable and convergent extrapolation procedure for the scattering amplitude.—I

Abstract: The extrapolation of the amplitude out of its physical region being mathematically an «improper problem», it is not sufficient to have convergent expansions, one has to be also sure that the results are stable against small perturbations (experimental errors). In the present paper, this problem is solved by means of semi-convergent expansions in terms of conformal mappings of double connected domains. An optimization problem leads to an optimal mapping function, whose explicit form is then derived. Although a good deal of the paper is devoted to the mathematical side of this problem, the results can be used directly in the analysis of experimental data.

Classical and quantum fields in de Sitter space

Abstract: In the (1+4) de Sitter space the equations for free fields of spin 0, spin 1/2 and spin 1 are derived as eigenvalue equations of the Casimir operators. Completeness relations for the solutions are given in the case of spin 0 and spin 1/2, and with these the different Green functions and commutation functions are obtained. It is possible to construct causal commutation functions only for a certain part of the spectrum. This gives rise to a spectrum condition, by which,e.g., the solution satisfying the conformal invariant equation for spin 0 is excluded from the physical state space. All functions are shown to permit an expansion in powers of the de Sitter curvature 1/R, where the first term is in each case the corresponding invariant function of Minkowski space.

Revision of the relativistic dynamics with variable rest mass and application to relativistic thermodynamics

Abstract: For point bodies with variable rest mass it is shown that the definition of forcem 0dU i /dτ=F i is better than the usual d(m 0 U i))/dτ=F i and the explicit equation of motion is given bym 0dU i/dτ=F ext +(z −1 U i B −U i)dm 0/dτ, where the external forceF ext has been separated from the reaction force due to the ejected mass,U i B is the four-velocity of the mass centre of the ejected mass andz=U s B U2c−2. For extended bodies it is shown that the von Laue mechanical-energy flux (in the usual «synchronous» formulation) is not plausible. Moreover a new formulation, called «asynchronous» is given. By this formulation many problems receive an immediate solution. The resultant «asynchronous» force density is always orthogonal to the four-velocity, and the equations of motion for continuous media turn out to be formally equal to the classical equations. Expanding the new equations to the first order when the pressure is a regular function of space and time, one obtains the usual «synchronous» equations. In the asynchronous formulation, all quantities relevant to extended bodies transform in a covariant way. In particular, momentum and energy turn out to have the expression proposed by Rohrlich. The above concepts are applied to relativistic thermodynamics. It is shown that, for point bodies, heat transforms as in the recent Ott formulation. For extended bodies, in the usual «synchronous» formulation, heat transforms as pointed out by von Laue. In the «asynchronous» formulation we always haveQ=γQ 0. TemperatureT is considered invariant and the relation dQ=TdS valid in the rest system only.

Construction of the scattering amplitude from the differential cross-sections

Abstract: We establish rigorously a sufficient condition for the existence of a scattering amplitude corresponding to a given angular distribution for scalar particles in the elastic region. The condition is max [(1/4π) · e|F(13)||F(23)|dΩ3/|F (12)|]=sinµ<1. We show that if |sinµ|<0.79 the amplitude is unique, except for one obvious ambiguity. Further, by examining the case of a finite, but arbitrarily large number of partial waves, we show that it is very likely that the solution is still unique for 0.79

Fourth-order vacuum polarization contribution to the sixth-order electron magnetic moment

Abstract: The contribution of fourth-order vacuum polarization to sixth-order radiative correction to the electron magnetic moment is analytically evaluated and found to be 0,055(α/π)3.

A stable and convergent extrapolation procedure for the scattering amplitude. ii. least squares and interpolation in roots of unity.

Abstract: SummaryThe extrapolation of the experimental data on scattering amplitude out of the physical region being a typical mathematical example of an «improperly posed problem», one has first to provide rapidlyconvergent expansions for the amplitude, and then make sure that the results arestable against small perturbations (experimental errors). In a recent paper of Cutkosky and Deo, and in paper I, we found a powerful extrapolation method in the form of an optimal conformal mapping, in terms of which this problem was then solved by means of a limited-term (semi-convergent) expansion, whose coefficients were found by minimizing the maximum of the deviations in the physical region (Tchebycheff case). In the present paper, this analysis is extended to the physically important least squares and discrete-point interpolation cases.RiassuntoPoichè l’estrapolazione dei dati sperimentali sull’ampiezza di scattering oltre la 2 regione fisica è un tipico esempio matematico di «problema improprio», bisogna prima fornire sviluppi in serie dell'ampiezza rapidamenteconvergenti, e poi assicurarsi che i risultati sianostabili per le piccole perturbazioni (errori sperimentali). In un recente articolo di Cutkosky e Deo e nell’articolo I si è trovato un potente metodo di estrapolazione sotto forma di rappresentazione conforme ottimale, in base al quale si è poi risolt questo problema per mezzo di uno sviluppo a termini limitati (semiconvergente), i cui coefficienti sono stati trovati rendendo minimo il massimo delle deviazioni nella regione fisica (caso di Tchebycheff). In questo articolo si estende questa analisi ai casi, fisicamente importanti, dell’interpolazione con il metodo dei minimi quadrati e con quello dei punti discreti.РезюмеПри экстраполяции экспериментальных данных по амплитуде рассеяния за пределы физической области, что представляет типичный математический пример «некорректно поставленной проблемы», сначала необходимо обеспечить быструю сходимость разложений для амплитуды, а затем можно быть уверенным, что результаты будут устойчивыми относительно малых возмущений (экспериментальных ошибок). В недавней статье Кутковского и Део и в статье I мы получили мощный метод экстраполяции в форме оптимального конформного отображения, на основе которого эта проблема решается посредством (полу-сходящегося) разложения с ограниченным числом членов, коэффициенты которого находились путем минимизации максимума отклонений в физической области (случай Чебышева). В настоящей статье этот анализ расширяется на физически важные наименьшие квадраты и случаи интерполяции дискретных точек.

A group-theoretic approach to chiral transformations

Abstract: Nonlinear transformations of meson fields under any chiral group are derived in which the fields appear as a local co-ordinate system on a differentiable manifold. The techniques are extended to include any multiplet of nucleon fields.

On the low--burnett--kroll theorem for soft-photon emission.

Abstract: SummaryBurnett and Kroll’s extension of Low’s theorem is proved for particles of arbitrary spin.RiassuntoSi prova l’estensione di Burnett e Kroll del teorema di Low per particelle di spin arbitrario.РезюмеДля частиц с произвольным спином доказывается расширение Бурнэ и Кролля для теоремы Лоу.

Nonstrong amplitudes in a veneziano-type model.

Abstract: We propose a general procedure for constructing the scattering amplitudes of hadrons with external currents. These are obtained from a representation of theN-point function for hadrons and leptons, in the lowest order of the weak constant. We consider a model with external scalar mesons and vector currents only. Current conservation is not required. We study the form factor, electroproduction and Compton scattering finding good analytic properties for the amplitudes.

Padé approximants in strong interactions. Two-body pion and kaon systems

Abstract: We construct the Pade approximants to theS-matrix starting from a formal perturbation series. Starting with a first-order «germ» we calculate the higher-order terms by repeatedly applying unitarity and crossing in the Mandelstam representation. The germ is chosen to be compatible with crossing and analyticity requirements, and to lead to a nonincreasing number of subtraction constants. We consider meson-meson scattering in which case the germs are simply constants. We have studied systems involving pions and kaons. In that case, there are only three parameters. Resonances and Regge trajectories have been computed. The seven lowest-lying two-body resonances (ρ, K*(890), ϕ, K*(1420), f0, f 0 ′ , A2) are obtained within a few percent of their actual masses. Also, the intercepts of the ρ and f0 trajectories agree very well with present estimates. Some degeneracies between channels with different quantum numbers appear and are discussed. The comparison with a pure π-π calculation shows promising improvement. We explain the further extensions of the model to compute meson states, and also baryon-meson and baryon-baryon amplitudes. In the course of this work, we have studied many mathematical and practical aspects of Pade approximants and their application to various fields.

On a new instability in electron-positron storage rings (The head-tail effect)

Abstract: It is shown that a bunched electron or positron beam of a storage ring can become unstable because of an effect not previously considered; the instability is due to the regenerative effect introduced by synchrotron oscillations, which enhances the action on the beam of rapidly decaying electromagnetic signals excited by the beam itself on its surrounding media. The results obtained show that the effect can produce instabilities for small beam currents (in the milliampere range), and that it can be influenced and reduced by properly choosing some parameters of the storage ring.

Algebra of currents on the light cone

Abstract: On the basis of observation that the fixed-mass sum rules are Fourier transforms of the commutators of currents on a lightlike hyperplane a new treatment of the algebra of currents is proposed. It consists in use of the currents integrated over the lightlike hyperplane (« lightlike » charges) and thus includes the commutators of currents on the whole light cone. An algebra of the lightlike charges is a sufficient assumption for the derivation of the fixed-mass sum rules and may be represented in the one-particle space with any momenta. Hence this extension of the usual equal-time current algebra allows us to abandon the methods likep→∞ without losing any of its advanteges.

Coherent elastic scattering of π-mesons from deuterium: Theory and applications

Abstract: The Glauber theory is extended to include spin variables for πD scattering. The results are compared with existing experiments and rather good fits are obtained. Predictions for forthcoming (experiments are given. The possibility of extracting the phase of πN amplitude from polarization experiments is briefly discussed.

Double-resonance production by 5 GeV/c K+ mesons on protons

Abstract: Among the interactions of K+p at 5 GeV/c produced in the CERN 2 m and Saclay 81 cm hydrogen bubble chambers we have studied the four-body reactions K+p→ Kππ. The cross-sections for the various final states contributing to these reactions have been determined. A detailed analysis has been performed on the double-resonance production K+p→ K*(892)*(1236). Decay angular distributions for both resonances have been studied and single and joint spin-density matrix elements calculated as a function of four-momentum transfer. The results have been compared to the absorption-model predictions assuming pion exchange. Various quark-model predictions for the decay angular distributions have been tested. The quark-model relations derived on the basis of the additivity assumption only, are experimentally well satisfied. If additional conditions about the quark-quark scattering amplitudes are imposed, only some of the quark-model predictions agree with experiment.

Probabilistic interpretation of relativistic scattering

Abstract: We present a detailed diseussion of the interpretation of a seattering process within the framework of relativistic quantum mechanics. This argument is particularly well suited to the seattering of charged scalar particles in an external electromagnetic field, but it breaks down for spin-1/2 particles. In the latter case, we can improve certain features if we use the Klein-Gordon equation instead of the Dirae equation.

Crossing conditions for the pion-pion amplitude

Abstract: We obtain a denumerable set of rigorous inequalities on the π0π0-π0π0 partial-wave amplitudes which guarantee that the amplitude is crossing symmetric. The numerical inequalities presented for the case of S and D waves indicate that one has very little freedom in the choice of the D-waves once the .S-waves are given.

The hybrid model: Further results

Abstract: In a previous paper we proposed a « hybrid » model for the large-energy, small-angle elastic scattering of hadrons, and used it to understand the structure in the angular distributions of proton-proton and proton-antiproton differential cross-sections. This model describes the scattering amplitude as the sum of an optical diffractive piece and a piece arising from the exchange of « absorbed » Regge poles; alternatively, it can be viewed as a specific prescription for calculating the effects of Regge cuts. In the present paper, we present some further results obtained from this hybrid model: we extrapolate our solutions for the pp amplitude to higher energies. We show how our model may be extended to deal with inelastic (or backward elastic) scattering, and consider processes which cannot be described by the single exchange of any known Regge trajectory, such as K−p backward elastic scattering. We explain why Regge cuts do not affect the presence or location of the dip in the π+p near-backward differential cross-section which is thought to arise from a nonsense zero of the nucleon trajectory. We predict that the differential cross-sections of elastic and of inelastic reactions should have the samet-dependence at large |t|, whether or not they do at small |t|.

A new large-acceptance and high-efficiency neutron detector for missing-mass studies

Abstract: A large-acceptance and high-efficiency neutron detector is described. The sensitive surface and volume of the detector are 2.16 m2 and 0.78 m3, respectively. The detector consists of twenty-four elements of plastic scintillator, each having dimensions (100×18×18) cm3. The large volume of scintillator, in the particular geometrical arrangement chosen, allows a mean detection efficiency of about 25% in the range (70÷390) MeV neutron kinetic energy for a laboratory solid angle of 0.14 sr at 4 m radial distance. With the techniques adopted, calibrations with charged particles can be easily performed in a few hours using a low beam intensity. An interesting features of this instrument is the accuracy achieved in locating incident particles, which is ±1.4 cm for charged particles, and ±2.5 cm for neutrons. The accuracies achieved for the time-of-flight measurement are ±0.35 ns for charged particles and ±0.7 ns for neutrons. With these resolutions in the neutron time of flight and angle, the uncertainty in the missing mass is ±4 MeV for η, ±10 MeV for ω, and ±15 MeV for ϕ mesons.

Physical photo- and electroproduction at threshold by current-algebra sum rules.

Abstract: By saturation of equal-time commutators of current algebra and field algebra, expressions for physical electroproduction amplitudes are deduced. They contain electromagnetic and axial form factors plus terms of orderμ2 (pion mass). A detailed evaluation of those corrections 3 is discussed together with the comparison with experiments.

About collision-process lifetimes and causality

Abstract: The authors generalize their previous results, by defining and calculating reaction and partial-process lifetimes, to the case of two-wave-packet collisions with an arbitrary number of final packets. Besides, they express the principle of causality and the new one of « anticausality » in terms of interaction time shifts. Some notes about tachyons are added.

High-energy proton--proton scattering in the eikonal model.

Abstract: The eikonal model for high-energy pp scattering is extended to include spin effects. The single scattering corresponds to the exchange of a flat Pomeranchukon and two (degenerate) secondary trajectories. A very simple parametrization with five arbitrary parameters is chosen. We obtain a good description of the pp data on total and differential cross-sections. the ratio of real to imaginary part of the amplitude at t = 0 and polarizations. for incident momenta between 5 and 20 GeV/c. Predictions for the\(p\bar p\) high-energy scattering, are made. They are in reasonable agreement with the experimental data and exhibit the cross over effect near the right value of the momentum transfer. Some general features of the cikonal model are also discussed.

The annihilation at rest → K\overline K \pi π

Abstract: We have analysed the three-body annihilations at rest \(\overline p n \to K\overline K \pi \), from a total sample of 2.22·105 annihilations. The annihilation at rest \(\overline p n \to K\overline K \pi \) has been studied by Conforto et al. The « multiple final-state interaction model » developed by them has been used to analyse the Open image in new window annihilation; an overall consistent picture is obtained in this way.

Superconvergent sum rules for pion--pion scattering.

Abstract: Sum rules for pion-pion scattering amplitudes are derived using analyticity, crossing symmetry and rigorous or ad hoc asymptotic bounds. They are superconvergent in the sense that they involve only integrals over physical quantities. They differ from the simplest superconvergent relations because absorptive parts as well as derivatives of absorptive parts with respect to the momentum transfer appear in the integrals. The fact that one of the sum rules is likely to be violated provides an experimental evidence for the necessity of subtractions. Our present information on pion-pion scattering (known resonances and high-energy behaviour as predicted by the Regge-pole model) is in qualitative agreement with the sum rules. They are used for setting the orders of magnitude of Borne pion-pion parameters.

Properties of legendre expansions related to series of stieltjes and applications to π-π scattering

Abstract: Legendre expansions whose coefficients are those of a series of Stieltjes are considered. It is shown that the analyticity domain of a function defined by such an expansion is the cut plane and that sequences of approximants may be defined which converge to the function in this domain, with each approximant determined from a finite number of coefficients in the expansion. These approximants are related to the Pade approximants of the corresponding series of Stieltjes. It is shown that if the coefficients satisfy a « Froissart-Gribov »-type representation with positive weight, then they are also coefficients of series of Stieltjes. It follows that the above results may be applied to the π-π scattering amplitudeA(s, t) for certain states when 0⩽s<4. In particular the approximation ofA(s, t) is the complext-plane, when only the first few partial wavesal(s) are known, is discussed and the interpolation of theal(s) for nonintegerl is also considered. Another consequence is that theal(s) satisfy an infinite set of determinantal inequalities when 0⩽s<4.

Metric structures and chiral symmetries

Abstract: Various aspects of nonlinear-group realizations are discussed and it is shown that the nonlinearSU3×SU3 chiral-invariant meson Lagrangian, and hence the meson-meson low-energy processes, can be expressed completely in terms of the canonical metric on the group space ofSU3.

Direct measurement of the transfer rates of muons from μp muonic atoms to argon, krypton and xenon atoms

Abstract: We have measured the rates of the muon transfer reaction μp+zY→μzY+p in a target of ultra-pure gaseous hydrogen at 10 atmospheres contaminated by a small proportion of thezY element (zY stands here for argon, krypton and xenon). The results are compared with preceding experimental data and discussed in connection with those obtained for the reaction μd+zY→μzY+p.

Crossing-symmetry constraints on partial-wave amplitudes and their physical content

Abstract: A very simple derivation of a complete set of sum rules implied by crossing symmetry on partial-wave amplitudes is given This set is shown to be equivalent to the Balachandran-Nuyts crossing relations for partial-wave amplitudes Many applications to dynamical models are proposed and discussed, and it is shown in particular that the Pade treatment of theλϕ4 theory for ππ scattering yields extremely good agreement with crossing symmetry