Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1965"

A dispersion theory of symmetry breaking

Abstract: A new relativistic approach to the problem of broken symmetries is proposed. This is the covariant generalization of the non-relativistic sum rules obtained in previous investigations. The result is in the form of dispersion sum rules where the pole term represents the group-theoretical answer and the cut the breaking correction. The method is applied toSU3 and chiralSU3×SU3 leading to very satisfactory results and predictions.

Reduction of feynman diagrams

Abstract: Formulae expressing the amplitude for a Feynman diagram consisting of a single internal loop withn sides andn external lines as a sum of its reduced diagrams are derived by applying restrictions imposed by the finite dimensionality of space-time on the unparametrized amplitude. In 4-dimensional space-time these formulae express the amplitude for then-sided diagram as i) a sum of all its 5-sided reduced diagrams; this can be further expressed as ii) a sum of all its 4-sided reduced diagrams. The coefficients in each sum depend only on the external invariants and internal masses.

Kinematical form factors in the peripheral model

Abstract: In potential theory the «vertex functions» for resonance formation contain kinematical form factors, which depend on the spin of the resonance and are simply related to penetration factors. Analogous form factors are introduced for the relativistic vertex functions of the one-pion exchange model. The resulting vertex functions behave like the Born term functions near the pion pole, but go to constants as the momentum transfer goes to infinity, for arbitrary resonance spin. For elastic nucleon-nucleon scattering, the total form factor reduces to a simple pole.

Dynamical rearrangement of symmetries: I.—The Nambu-Heisenberg model

Abstract: SummaryThe aim of this article is to examine certain aspects of the so-called theory of dynamical breakdown of symmetries. Since such theories begin with field equations possessing certain invariance properties, one might argue that these invariance properties should not just disappear from the theory without leaving any trace. Pursuing this line of thought, one might expect that some kind of «rearrangement» of invariance properties takes place in the dynamical process of going from the bare particles to the physical particles given by the theory. This conjecture turns out to be verifiable when we formulate the theory in such a manner that all Heisenberg operators are expressed in terms of field operators of physical particles (i.e. incoming particles). Specifically, we find that the original invariance turns itself into the gauge invariance of a massless physical particle called the Goldstone particle. Making use of this formulation, we find several other characteristics which appear when the invariances are dynamically rearranged. Although we make use of the Nambu-Heisenberg model as an illustration, many of our results seem to be generally true.RiassuntoScopo di questo articolo è l'esame di alcuni aspetti della cosiddetta rottura dinamica delle simmetrie. Poichè tali teorie iniziano con equazioni di campo che possiedono alcune proprietà di invarianza, se ne potrebbe dedurre che queste proprietà di invarianza non dovrebbero sparire ad un tratto dalla teoria senza lasciare alcuna traccia. Seguendo questa linea di pensiero, ci si potrebbe attendere che abbia luogo una specie di «riordinamento» delle proprietà di invarianza nel processo dinamico per cui si passa dalle particelle nude alle particelle fisiche date dalla teoria. Risulta che questa congettura può essere verificata se si formula la teoria in modo tale che tutti gli operatori di Heisenberg siano espressi in termini di operatori di campo di particelle fisiche (cioè, particelle entranti). Specificamente, si trova che l'invarianza originale si trasforma nell'invarianza di misura di una particella fisica priva di massa chiamata particella di Goldstone. Facendo uso di questa formulazione si trovano molte altre caratteristiche che compaiono quando le invarianze vengono riordinate dinamicamente. Sebbene si faccia uso del modello di Nambu-Heisenberg come illustrazione, molti dei nostri risultati sembrano veri in generale.

The leptonic annihilation modes of the proton-antiproton system at 6.8 (GeV/c) 2 Timelike four-monentum transfer

Abstract: which wa~ suggested by ZICmCHI et a l . (1). The experiment was carried out at 2.5 GcV/c incident antiproton momentum, which corresponds to a timelike fourmomentum transfer of 6.8 (GeV[e) 2. ~Ihe choice of this q2-value was dictated, by the requirement of the maximum number of observable events predicted, using the knowledge of the p flux as a function of momentum at the CERN PS, together with the behaviour of the cross-section as a function of the ~ momentum for processes (1) and. (2), which was calculated, assuming that the proton-photon interaction is pointlike. The aim of the experiment was twofold.: firstly, to measure the electromagnetic form factors for timclike four-momentum transfers and secondly to check the equivalence of the electromagnetic interactions of the electron and. the muon for timelike four-momentum transfers. In practice the cross-section was shown to be so low that only an upper l imit for annihilation into lepton pairs of

Emission of neutrino-pairs from a stellar plasma

Abstract: The emission of neutrino-pairs by a stellar plasma is calculated. Our expressions for longitudinal and transverse emissivities differ from the corresponding expressions of Adams, Ruderman and Woo by factors of 3/8 and 1/4, respectively.

Theory of corrections to unitary symmetry formulae

Abstract: A systematic analysis of the equal-time commutation relations of the generators of an algebra with certain physical operators is made. A method is then introduced whereby considering matrix elements of such commutators between physical one-particle states and using completeness and invariance under space-time translations, corrections to broken-symmetry group-theoretical formulae are obtained. Several applications to weak, electromagnetic and strong interactions are then made.

Primakoff effect and π0 lifetime

Abstract: The results of an experiment to measure the π0 lifetime via the inverse decay process (“Primakoff effect”) are presented. The coherent photoproduction of neutral pions in the reaction γ+Pb→π0+Pb has been measured with very high angular resolution with a π0 detector containing 10 independent counting channels, at the two mean energies 950 and 1000 MeV, using the bremsstrahlung beam of the Frascati electron synchrotron. The angular distributions show a characteristic bumping around the forward direction, giving conclusive evidence for the existence of the Primakoff effect. The results are interpreted in terms of two amplitudes-the electromagnetic and the nuclear one-adding up coherently to give the over-all coherent cross-section. Such a cross-section is expressed in terms of four unknown parameters: the lifetime τ, the phase δ between the electromagnetic and nuclear amplitude, the strengthC of the nuclear amplitude, and the nuclear radiusR0. Neutral-pion reabsorption inside nuclear matter is taken into account, and a χ2 analysis of the data is done in terms of τ, δ,C, andR. The best fit τ value is (0.73±0.105)·10−16s. Systematic errors, as well as the sensitivity of the results to the model used to interpret the data, are extensively discussed and conservatively taken into account.

Pion-nucleon resonances and the angular distribution in pion electroproduction

Abstract: Using the helicity formalism, we find the contributions from final states of definite spin and parity, together with the interference terms between different final-state contributions, to the angular distributions of pions electro-produced from protons For a single resonant final state the azimuthal terms turn out to be particularly simple, and may well serve as a test for the spin of the resonance We show that the angular distribution may be used to detect the possible presence of ap1/2 resonant state in the energy region of the second resonance

Virtual pion-nucleon scattering

Abstract: We discuss the problem of pion-nucleon scattering when the initial pion is virtual with the aid of one-dimensional dispersion relations, under the usual assumption that the dispersive integrals are dominated by theJ=J=3/2 partial-wave amplitude. We reconsider the problem of obtaining the off-shell behaviour of the latter amplitude by avoiding certain approximations which had been used previously. The improvements are important at high momentum transfer. We calculate furthermore the other partial-wave amplitudes and obtain in particular a largeS1/2 amplitude withI=1/2. The significance of this result in certain production processes is discussed.

The momentum spectrum and charge ratio of μ-mesons at sea-level-II

Abstract: The sea-level momentum spectrum of single cosmic-ray μ-mesons has been measured for near vertical incidence within the range 2.34 GeV/c

Inelastic muon interactions in nuclear emulsion at 2.5 and 5.0 GeV

Abstract: The inelastic scattering of high-energy muons from emulsion nuclei was measured with the use of a monoenergetic beam of 2.5 GeV/c and 5.0 GeV/c muons produced at the Brookhaven Alternating Gradient Synchrotron. Ilford G-5 stacks were exposed perpendicularly to the beam and Ilford K-5 stacks were exposed parallel to the beam. Area scanning resulted in a total of 135 events with four-momentum transfers greater than 26 MeV/c. The observed scattering distribution which extends up to 10 degrees, or a momentum transfer of about 900 MeV/c, is in good agreement with the predictions of the electromagnetic theory assuming single-photon exchange. There were also observed four events with scattering angles greater than 10 degrees which are not inconsistent with the theory. Pion production was observed with the major contribution coming from the 3/2, 3/2 resonance. The cross-sections for this process were found to be (3.6±0.7) and (5.1±0.5) microbarn for muon momenta of 2.5 and 5.0 GeV/c, respectively. Events involving much lower energy exchanges were found to have much larger cross-sections and were consistent with «giant resonance» photodisintegration observations.

Electromagnetic form factors.—II.

Abstract: Une formulation covariante des facteurs de forme electromagnetiques d'une particule de spin 3/2 est etudiee dans le formalisme de Rarita-Schwinger. La relation entre ces facteurs de forme et les facteurs de forme physiques est explicitement donnee. La formulation covariante est ensuite etendue aux particules de spin quelconque.

Irreducible representations of the rotation group in terms of Euler's theorem

Abstract: In all of the previous discussions of the irreducible representations of the rotation group, the matrix elements corresponding to finite rotations are given in terms of the Euler angles of the rotation. In the present paper we describe rotations by means of a vector θ where the direction of θ is the direction of the axis of rotation and |θ| is the angle of rotation. The matrix elements corresponding to the finite rotation given by θ, are matrix elements of exp [i(θ·J)] where the matrixesJi(i=1, 2, 3) are the infinitesimal generators of the representation of the rotation group. Our representation thus takes the form given by Stone's theorem for one-dimensional groups. We express the matrix elements corresponding to the finite rotations in closed form in terms of Jacobi polynomials. Aside from the mathematical elegance of the result, our representation is useful in showing how wave functions transform in a rotated frame of reference when the axis of rotation is prescribed. Although in principle one could obtain the transformation properties of the wave function in terms of the Euler angle parametrization, the expressions are extremely cumbersome for a general axis of rotation. In the present representation, on the other hand, the expressions are simple. As part of the proof we also give the transformation from the basis in whichJ3 is diagonal to that in which θ·J is diagonal. The matrix elements for finite rotation for the cases of spin 1/2, 1 and 3/2 have been computed in the new representation and are given in the Appendix.

Some properties of the radiation recorded by the IGY cosmic-ray neutron monitors in the lower atmosphere

Abstract: In the Autumn of 1964 a survey was carried out near Rome from sea level up to 1800 m altitude with a mobile neutron monitor of the IGY design mounted on a lorry. Both the monitor counting rate and the rates of events with different detected multiplicities were measured as a function of altitude, and the corresponding attenuation coefficients were deduced. The results are discussed together with those obtained in 1963 on the latitude effect of the different detected multiplicities, under the assumption that the muon contribution is a controlling factor of the counting rate of the IGY neutron monitors in the lower atmosphere. The dead-time dependence of the monitor response to variations of atmospheric pressure and primary spectrum is also studied.

The Nottingham cosmic-ray spectrometer-I

Abstract: Measurements of the sea-level μ-meson momentum spectrum made during the last decade utilizing conventional air gap spectrometers have indicated that the differential intensity is approximately proportional to 1/(momentum)3. For a study of the high-momentum region therefore, the instrument concerned not only must have a high angular resolution but also be able to accumulate data at a significant rate. These requirements can only be met with difficulty when conventional air gap magnets are used. This paper is concerned with the characteristics of a μ-meson spectrometer in which the air gap magnet is replaced by a block of lagnetized iron. Methods are given for computing the effects of energy loss and scattering in the material and it is shown that the angular scattering distribution produced by the iron in the unmagnetized state can be accurately predicted. Further since the magnetic material acts as a filter for nuclear active particles this type of instrument has all the advantages of operating underground while retaining the convenience of working at sea-level.

An upper limit to the existence of charges (2/3) e in the cosmic radiation at 500 m above sea level

Abstract: In connection with the proposals of Gell-Mann and Zweig on the possible origin of theSU3 symmetry, an experiment has been designed which is able to detect particles with electric charges 2/3 in the cosmic radiation. The upper limit established by the present experiment is: quark per minimum ionizing incident particle ≤3·10−6 with 90% confidence level.

A study of the production of γ-rays in high-energy nuclear interactions

Abstract: An analysis is given of 46 nuclear interactions occurring in graphite in each of which at least 1300 GeV was radiated as γ-rays. In each event the energies and relative angles of all γ-rays within certain fiducial limits were measured. Data are presented concerning the multiplicity of γ-rays and their energy and transverse-momenta distributions.

A study of 6.1 GeV/c π− interactions in a heavy-liquid bubble chamber

Abstract: A systematic study has been carried out at various multiplicities onH-like andN-like interactions produced by 6.1 GeV/c mesons from the CERN P.S. in the Ecole Polytechnique Heavy-Liquid Bubble Chamber, filled with a mixture of propane and CF3Br. The total multiplicity of events has been obtained by determining the number of neutral pions emitted, from measurements of the γ-rays materializing into the chamber and with the help of kinematics fit. Our results on the population of events in the various categories and on the angular and invariant mass distributions have been compared with the predictions of the existing models of high-energy interactions. While these results were, found to be in excellent agreement with the statistical model for events with six or more emitted pions, a strong contribution by peripheral processes exists at lower multiplicities. In addition to the one-pion exchange mechanism a contribution of ρ exchange, and Drell and Hiida diffraction seem relevant for events with pion multiplicity equal to two. “Nuclear” interactions, where the complex nucleus acts coherently, are present at all multiplicities up to five; this effect is particularly strong in the reactions where three pions are emitted. A bump between 1600 and 1800 MeV appears in the mass distribution of the events with four emitted pions. The values of the average transverse momenta of the secondaries at various multiplicities are reported.

N* production in high-energy π-p and K-p collisions by regge-pole exchange modelproduction in high-energy π-p and K-p collisions by regge-pole exchange model

Abstract: The reactions K+p→K0N*++,π p→π0N*+┴ and π p→ωN*++ are studied using ρ Regge-pole exchange mechanism. The values of the ρ trajectory α (t) are taken from the π− -p charge exchange scattering data and thet-dependence of the residues is neglected. Then the latter are obtained in terms of the field-theoretic coupling constants using the fact that Regge-pole exchange is identical to the corresponding elementary-particle exchange at the pole point. Thus the production cross-sections are obtained in terms of these coupling constants and do not involve any other unknown parameters. The coupling constants are then determined by normalizing the total cross-section for each reaction to the experimental value at a given energy, and are shown to agree with existing estimates. Finally the energy and momentum-transfer dependence of the three production cross-sections are analysed and are found to be in broad agreement with experiment.

Σ−Λ mass difference

Abstract: Λ c (2880) + I (J P) = 0(? ?) Status: * * * A narrow peak seen in Λ + c π + π − and in p D 0. It is not seen in p D + , and therefore it is probably a Λ + c and not a Σ c. ARTUSO 01 guesses, based on the narrow width, that it might be a J P = 1/2 − Λ + c0 , where the subscript 0 indicates that the two light quarks are in a J P = 0 − state.

Electromagnetic corrections to muon and beta decays when mediated by a vector boson.—II

Abstract: The results of a previous paper are generalized to include vector bosons having arbitrary magnetic dipole moment and electric quadrupole moment. The increased divergence inherent in such terms is reflected in our results for the electron energy spectrum from muon decay, and in the muon lifetime, both of which are cut-off dependent. After the inclusion of the corrections to beta decay the conserved vector current hypothesis gives us the prediction for the muon lifetime in terms of theft value for14O. While this predicted value still depends upon the cut-off, the dependence vanishes in the limit of the boson mass becoming infinite. In this limit the boson mass provides an effective cut-off.

V-θ sector of the lee model

Abstract: By a slight extension of Amado's method, the matrix elements of the current operators between physical scattering states in the V-θ sector of the Lee model are determined. Then also the coefficients of the expansion of the scattering states in terms of the noninteracting states and theS-matrix elements are computed. The production amplitude is exhibited as a product of the contribution of pole diagrams times a simple correction factor which contains the effect of initial- and final-state interactions.

On singular potential scattering.—II

Abstract: Asymptotic expansions of tg δ, in weak coupling limit, are derived for scattering by «inverse-power», singular potentials in higher waves, and for scattering by a superposition of two «inversepower» singular potentials. These results are obtained by the same approach followed in Part I.

A study of the production of γ-rays in high-energy nuclear interactions: II.—A study of individual high-energy interactions in graphite

Abstract: SummaryAn analysis is given of 46 nuclear interactions occurring in graphite in each of which at least 1300 GeV was radiated as γ-rays. In each event the energies and relative angles of all γ-rays within certain fiducial limits were measured. Data are presented concerning the multiplicity of γ-rays and their energy and transverse-momenta distributions.RiassuntoSi espone un'analisi di 46 interazioni nucleari avvenute in grafite in ciascuna delle quali almeno 1300 GeV vennero irradiati come raggi γ. In ciascun evento si sono misurate le energie e gli angoli relativi di tutti i raggi γ compresi entro certi limiti fiduciali. Si presentano i dati relativi alla molteplicità dei raggi γ e le loro distribuzioni di energia e di impulsi trasversali.

Peripheral production ofN*(1518)→pπ+π− andN*(1688)→pπ+π− resonances in pp→ppπ+π− reaction at 5.5 Gev/c*(1688)→pπ+π− resonances in pp→ppπ+π− reaction at 5.5 Gev/c

Abstract: The reactions pp→pN*(1518)→ppπ+π− and pp→ →pN*(1688)→pπ+π− at 5.5 GeV/c were studied. Total and differential cross-sections were calculated with the unmodified and modified (absorptive0 one-pion exchange (OPE) models using explicit wave functions for the spin-3/2 and spin-5/2 particles. The agreement between the experimental and calculated angular distributions is imposed with the absorption modification to the OPE model.

Étude de la diffusion π-He entre 500 et 1200 MeV

Abstract: A counter experiment has been made to study the π-He interaction, in the (500÷1200) MeV energy range. Measurements of the integral distribution of charged secondaries for forward angles between 4° and 30° in the laboratory system have been performed. The interpretation has been made in the frame of the optical model, but the results have led to a careful re-examination of the usual approximations of this model. While the validity of the impulse approximation is confirmed, it has been found that both the nonlocality of nucleon forces and the Fermi motion of nucleons have to be reconsidered. The nonlocality of nuclear forces leads to an apparent difference between «electromagnetic» and «nuclear» radii of the nucleus. The difference has been estimated. The Fermi motion of the nucleons gives a displaying of the π-nucleon interaction energies, and, consequently, to a smoothing of the mean π-bound nucleon total cross-section\(\bar \sigma \) (which is related to the optical potential) in the πN resonances region. Using thea) andb) considerations, a good agreement has been got between the experimental results and the theoretical predictions issued from the known π-nucleon interaction. Some estimates concerning the elastic differential π-He cross-sections in the above framework are shown in the last Section.