Showing papers in "Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields in 1970"

Field and particle equations for the classical Yang-Mills field and particles with isotopic spin

Abstract: A complete system of equations describing the interaction between the Yang-Mills field and isotopic-spin-carrying particles in the classical limit is extracted from the equations of motion for the quantum fields. Some simple consequences are derived. The consistency of the equations is investigated.

Dual-symmetric theory of hadrons.—I

Abstract: A theory of mesons is based on the experimentally observed linear level spacing of hadron excitations. The theory uses a model for the internal structure of mesons consisting of a system of harmonic vibrations. Roughly speaking, a meson is described by the degrees of freedom of a four-dimensional rubber band with a quark pair embedded in it. The theory satisfies relativistic invariance, crossing symmetry and a generalization of duality which we call dual-symmetry. In the approximation of retaining only tree graphs, the scattering amplitudes are given by then-point dual amplitudes recently proposed by Virasoro, Bardakci and Ruegg, Chan and Goebel and Sakita. In the special case,n=4, we reproduce Veneziano’s formula.

Transformation coefficients in the hyperspherical approach to the three-body problem

Abstract: The transformation from one set of Jacobi co-ordinates to another for hyperspherical functions is closely related to the Talmi-Moshinsky transformation for two particles in an oscillator well. The corresponding coefficients are calculated analytically.

Group-theoretical analysis of elementary particles in an external electromagnetic field II.—The nonrelativistic particle in a constant and uniform field

Abstract: Two subgroups of the Galilei group are shown to play a particular role in the case of charged systems in an external electro-magnetic field which is constant and uniform. Projective representations of these subgroups involve the electric charge and mass as generators of phase factors. Additivity and superselection rules for charge and mass appear as direct consequences. A comparison is made with the relativistic case investigated in the first part of this article.

Duality in operator formalism

Abstract: We propose a form for a dual resonant amplitude in which both duality and factorization are explicitly exhibited. This result is achieved by considering in detail the transformation properties of the operators appearing in the model under the fundamental projective transformation of Koba and Nielsen.

Quantum field theory on lightlike slabs

Abstract: Restricting the support of relativistic quantum fields to lightlike hyperplanes (e.g. x0+x3)=const) we find examples of such fields to exist as well-defined self-adjoint operators with properties however that differ vastly from those of fields on the usual spacelike surfaces. We show that on a lightlike hyperplane 1) the free-field algebra is irreducible (instead of Abelian, and in contrast to what one would expect of data on a characteristic surface) and 2) fields with different masses become unitarily equivalent (whereas they are inequivalent on spacelike planes). Furthermore the field algebra restricted to the space-time slab between two parallel lightlike planes is always irreducible (while there are counterexamples for spacelike slabs). We establish this directly for generalized free fields and rederive it for Wightman fields in gereral.

Symmetry properties of dual tree-graphN-point amplitudes

Abstract: The dual tree-graphN-point functions are investigated from the point of view of symmetry properties. Using a cyclic symmetric-contour integral forBN, we deduce a set of simple relations betweenN—1BN-functions and give rules for writing down more complicated relations. Secondly, we establish a new relationship between the cyclic symmetric integral and the conventional “multiperipheral” integral forBN. Finally, both approaches are used to investigate the signature properties ofBN.

A mixing operator for the SU 3 × SU 3 chiral algebra

Abstract: A saturation scheme within an infinite set of states is proposed for the chiral algebra. Mesons are classified in the (35, anyL) representations ofSU6×O3, while the (56,L=even) and (70,L=odd) representations are chosen for baryons. A mixing operator exp [−iθZ] is proposed which transforms the axial charges of theSU6 solution into the physical ones. The specific form we choose forZ gives rise to many predictions. All the axial couplings of the lower positive-parity meson states to π, ϱ and ω are obtained in terms of only one parameter and the results are in fair agreement with experiment. In particular, the B-meson is predicted to decay transversely, whileg1/g0 ratio for the A1 is found to be −1/2. For the 1/2+ baryon octet, we getD/F=3/2 andG*=4/5GA (which impliesΓΔ→Nπ=125 MeV) up to second order in the mixing angle θ. For eachSU6×O3 multiplet all the decays intoN+π are given in terms of only one parameter (at lowest possible order in the mixing angle) in general agreement with experiment. Finally, we are able to obtain strong restrictions on the chiral content of the 1/2+ octet, which are perfectly compatible with nature.

Gauge-invariant spinor theories

Abstract: It is demonstrated that in spinor theories with nonlinear quadratic self-interaction, gauge symmetries connected withx-dependent internal symmetry transformations can be established without the introduction of additional vector fields if the spinor field operator has the noncanonical length dimension −1/2. In this case the theory is scale invariant at small distances and hence formally renormalizable. Operator products can be defined according to prescriptions given by Zimmermann and Wilson. The usual role of the gauge fields in these spinor theories is taken over by the formally constructed vector and axial vector «currents» of the noncanonical spinor fields which have the correct length dimension of boson operators. Physical fermion fields are related to deverivatives of these spinor fields or to 3-products of these fields. The noncanonical spinor field hence may be regarded as a «spinor potential» in the sense that its relation to a physical spinor field is similar to the relation of the vector potential to the physical electromagnetic field. The unobservable «spinor potential» acts in a state space with indefinite metric. Examples forSU n ⊗SU n gauge-invariant theories are given. The Heisenberg nonlinear spinor theory is shown to beSU 2 gauge-invariant, and hence the parity symmetry version of Durr to beSU 2⊗SU 2 gauge-invariant. This formal invariance, however, does not necessarily imply that the summetry holds in Hilbert space.

Crossing restrictions on ππ partial waves

Abstract: We find a parametrization for the most general ππ partial-wave amplitudes consistent with crossing symmetry and isospin invariance. This enables us to write all the constraints on the partial-wave amplitudes which follow from, and which ensure, crossing symmetry. We then discuss how these relations might be useful, and apply them in particular to Brown and Goble's model for ππ scattering

Magnetic moment of the relativistic composite system

Abstract: The relativistic corrections to the magnetic moment of the loosely bound composite system of particles are considered within the framework of the three-dimensional quasi-potential method. Particular attention is paid to the corrections connected with recoil of the system as a whole.

Covariant equations of motion for a charged particle with a magnetic dipole moment.

Abstract: The Hamiltonian for a Dirac particle with anomalous magnetic moment in an electromagnetic field is transformed to even form up to terms linear in the coupling constant and without derivatives of the field. The even parts of the position and spin operators are derived by imposing conditions of covariance. Covariant equations of motion and of spin are then deduced; they turn out to have the same form as the classical equations for a composite particle with magnetic dipole moment. (The magnetodynamic effect for a particle in a time-dependent field is shown to contain the vector product of the electric field and the anomalous magnetic moment only.)

Characterization of the physical states in dual-resonance models

Abstract: In the framework of dual-resonance models we derive the necessary conditions that the physical states on the mass shell have to satisfy. The orthogonality with the spurious states is required. By using these conditions we show that the first «daughter» is empty, while the second daughter contains at least three particles for each level (N>4). The first three excited levels are analysed in some detail.

A new measurement of the π0 lifetime through the Primakoff effect in nuclei

Abstract: A new measurement of the π0 lifetime through the Primakoff effect on nuclei was performed at DESY. The π0 photoproduction at small angles was measured on four elements (C, Zn, Ag, Pb) at two energies (1.5 GeV and 2.0 GeV). The final result for the lifetime is τ=(0.56±0.06)·10−16 s.

On pion electroproduction at 5 fm −2 near threshold

Abstract: A preliminary coincidence experiment designed for determining the electroproduction cross-section at threshold is described. At a four-momentum transfer −k 2=0.2 (GeV/c)2 and a polarization of the exchanged virtual photon e=0.74, one finds for π+ % MathType!MTEF!2!1!+-% feaafiart1ev1aaatuuDJXwAK1uy0Hwmaerbfv3ySLgzG0uy0Hgip5% wzamXvP5wqonvsaeHbfv3ySLgzaeXatLxBI9gBamXvP5wqSXMqHnxA% Jn0BKvguHDwzZbqehqvATv2CG4uz3bIuV1wyUbqehm0B1jxALjhiov% 2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qq% aqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8% qqQ8frFve9Fve9Ff0dmeaaciGacmaadaWabiqaeaqbaqaagaaakeaa% daWfqaqaaiGbcYgaSjabcMgaPjabc2gaTbWcbaGaemyCae3aaWbaaW% qabeaaiqaacaWFQaaaaSGaeyOKH4QaaGimaaqabaGcdaqadaqaamaa% laaabaGaaGymaaqaaiabdghaXnaaCaaaleqabaGaa8NkaaaaaaGcfa% qabeGabaaabaGaa8hzaiabeo8aZbqaaiaa-rgacqaHjpWDdaWgaaWc% baaceiGaa4xzaaqabaGccaWFKbGaa4NCamaaBaaaleaacaWFWaGaa8% NmaaqabaaaaaGccaGLOaGaayzkaaWaaSbaaSqaaiabec8aWnaaCaaa% meqabaGaey4kaScaaaWcbeaakiabg2da9iaaisdacqGGUaGlcaaI5a% GaeyyXICTaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodacaaI% XaaaaGGaaOGae03yamMae0xBa02aaWbaaSqabeaacqqFYaGmaaGccq% GGVaWldaqadaqaaiab9nhaZjab9jhaYjabgwSixpaabmaabaGae03r% aCKae0xzauMae0NvayfacaGLOaGaayzkaaWaaSWaaSqaaiaaikdaae% aacqqFJbWyaaaakiaawIcacaGLPaaadaqadaqaaiabgglaXkaaigda% caaI0aqehWuDJLgzHbYqV52CVXwzaGWbaiaa8vcaaiaawIcacaGLPa% aaaaa!86A9! $$\mathop {\lim }\limits_{q^* \to 0} \left( {\frac{1}{{q^* }}\begin{array}{*{20}c} {d\sigma } \\ {d\omega _e dr_{02} } \\ \end{array} } \right)_{\pi ^ + } = 4.9 \cdot 10^{ - 31} cm^2 /\left( {sr \cdot \left( {GeV} \right){\raise0.5ex\hbox{$\scriptstyle 2$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle c$}}} \right)\left( { \pm 14\% } \right)$$ whereq * is the three-momentum of the pion in the frame of the c.m. of the (pion+nucleon) system observed in the final state. This value of the cross-section agrees with the theoretical value obtained in Born approximation. Two different approaches can be adopted for interpreting this result. The first one, based on a formula derived by De Tollis and Nicolo by considering only Born terms in a double dispersion theory, allows a determination of the pion form factorsF π. By this method one obtainsF π(0.2)=0.80+0.20 −0.25 if one takes (G E n (0.2)=0. The second approach, based on current algebra and PCAC assumption, allows a determination of the axial vector form factorG A of the nucleon, which, however, depends on the procedure followed to correct for the finite mass of the pion. For example, by using the Gleesonet al. formula andG E n =0, one obtainsG A /g A =0.760±0.055. Assuming forG A the dipole approximation, one derivesM A =(1.17±0.07) GeV. From the measurements of the π0 electroproduction only a very low upper limit of the cross-section at threshold can be derived. The cross-section, however, increases rapidly withq * reaching a value equal to about 30% of the π+ cross-section already atq * around 50 MeV/c.

On the inversion of Noether’s theorem in the Lagrangian formalism

Abstract: Both the «direct» and the «inverse» Noether's theorems are generalized to allow for infinitesimal transformations that add to the action functional an integral over a 4-divergence and an integral over a function vanishing «on the orbit» (Noether transformations) It is then shown that: i) to every Noether transformation there corresponds a«weak» continuity equation and a family of Nother transformations (Noether family) defining the same continuity equation; ii) every Noether family contains an invariance transformation; iii) to every «weak» continuity equation there corresponds a Noether family; iv) every Noether family contains a subset of Noether transformations equivalent to a 4-divergence translation of the Lagrangian density

Rigorous inequalities onS andP waves for π-π scattering

Abstract: Inequalities on theS andP pion-pion partial-wave amplitudes are obtained by combining crossing symmetry with positivity properties for general isospin mixtures. This set of inequalities can be used in particular to rule out models. For instance in the Iliopoulos model we exclude all solutions except the one of the type proposed by Weinberg.

Low-energy electroproduction and equal-time commutators.

Abstract: We estimate low-energy photoproduction and electro-production of pions by using equal-time commutators between current densities and divergences and by including low-lying intermediate states. Predictions are presented for charged photoproductions- andp-wave multipoles, in agreement with experiments and dispersion theory, and for transversal and longitudinal electroproduction cross-sections near threshold. The dependence of the results on the axial vector form factorGA(t) is discussed.

The hyperspherical-expansion approach to nuclear bound states

Abstract: The first approximation of the hyperspherical-expansion approach to nuclear bound states is discussed in the limit of largeA. For velocity-independent potentials, the results given in a previous paper are rederived in a more explicit and straightforward fashion, and a more complete discussion of the next-to-leading terms in the asymptotic formula for the binding energy is given. For velocity-dependent potentials similar results are obtained. The density distribution that obtains in this treatment is exhibited and discussed. A comparison with the analogous formula for the binding energy per nucleon that obtains in the Fermi-gas treatment of nuclear matter is made, including the presentation of numerical results for the potential of Nestor, Davies, Krieger and Baranger.

Rigorous inequalities on the derivatives ofS- andP-wave amplitudes for π-π scattering

Abstract: Inequalities involving theS- andP-wave pion-pion amplitudes and their first derivatives are obtained from crossing symmetry and positivity properties for some isospin combinations. They can be used to test low-energy models.

General analysis of the vector-meson dominance model predictions for meson decays.

Abstract: Using the vector-meson dominance model,SU3 symmetry and the ω-ϕ and η-X0 mixing hypotheses (recent results seem to contradict the possibility of a mixing between the η and the E (1420)-meson) the decays of the pseudoscalar and the vector mesons are systematically investigated. The explicit expressions for phase-space evaluations are listed. The predictions of the model concerning the branching ratios and decay rates are discussed in detail, classifying those which are independent of some coupling constants, mixing angles and (or) experimental inputs. A consistent picture is obtained for the π0→γγ and the ω→π0γ decay modes and the ω and ϕ branching ratios and a resonable agreement is generally found with the experimental situation, which is sometimes rather unclear. Our results seem to disagree with a recent determination of the branching ratios of the ω→хγ and ω→π0π0γ decay modes.

Relativistic quantum mechanics of identical bosons.

Abstract: We extend the probabilistic interpretation of the relativistic scattering of a charged scalar particle by an external electromagnetic field to a system of several such particles. We find that the use of causal Green functions again demands the specification of boundary conditions for particles at the initial time, and for antiparticles at the final time. The resulting theory is essentially one for a fixed number of particles, which can be found in two states, customarily described as «going forward in time» (particles) and «going backward in time» (antiparticles). This feature allows, and strongly recommends, the use of Dirac's many-time formalism, with one time parameter for each particle. The probabilistic interpretation includes the possibilities of pair creation and annihilation.

The twisting operator in multi-Veneziano theory

Abstract: Using the operatorial expression for the gauge conditions, we derive an explicit form for the twisting operator and the semi-twisting operator which takes theP states intoV states. The expression for the last operator facilitates the proof of theV states factorization previously found by us. We show that the twisting operator proposed in the literature is inconsistent with multiple factorization,i.e. factorization of amplitudes with extermal spinning particles. The correct twisting operator depends on the integration variables of the twisted line, and automatically satisfies double-twist invariance.

Multiple particle production from e + e − interactions at C.M. energies between 1.6 and 2 GeV

Abstract: Multiple particle production in electron-positron interactions has been observed in an experiment performed at Adone, the Frascati 2×1.5 GeV e+e− storage ring. A total number of 239 events collected at several energies of the incident electron and positron beams between 0.8 and 1.0 GeV were analysed. The distribution of the multiplicity of charged particles produced in the final state is discussed and some upper limits on these multiplicities are reported. The observed lower limit to the total cross-section for multiple particle production in e+e− interactions, averaged over the energy range explored, is 3·10−32 cm2 with a statistical error of ±10% and a systematic uncertainty of ±25%.

One- and three-quasi-particle projected states for odd-mass nuclei with a major closed shell

Abstract: The formalism of the «projected states» is generalized to the odd-mass nuclei which can be treated as identical nucleon systems. The idea consists in picking out from the one-and three-quasi-particle states the components with a fixed particle number. The nuclear Hamiltonian is then diagonalized in the Hilbert space spanned by these components. Using this model we are able to reproduce the correct level sequence of117Sn. The force and the parameters are the same as those we used in a previous paper to fit the experimental data of the even isotopes starting from the appropriate projeeted model.

Calculation on nuclear three- and four-body systems with Jastrow-type correlated wave functions

Abstract: The nuclear three- and four-body systems are investigated with a variational method and various nucleon-nucleon potentials. The trial wave functions used are products of a central-field wave function and a correlation factor symmetric in the interparticle distances. The results show that i) the use of a fixed-centre reference frame or the centre-of-mass reference frame yield very nearly the same values for the binding energies and r.m.s. radii of3H and4He and ii) the trial functions, although containing few variational parameters, allowed for accurate evaluations. Moreover it is shown that the correlations between more than three particles give a disregardable contribution to the various calculated quantities.

Dynamical calculation of Regge trajectories

Abstract: The possibility of dynamical constructing a Regge trajectory α(s) is investigated under the assumption that it satisfies a oncesubtracted dispersion relation. This implies a departure of α(s) from a pure straight line behavior at sufficiently large |s|. This departure is shown to be connected t e rate of growth of the resonance-width function (which interpolates a long the experimental width of the resonances lying on the Regge trajectory) and turns out to be very small, in agreement with the present data on resonant states.

Application of a Reggeized multiperipheral model to π − p interactions at 11 GeV/c

Abstract: We use the modified multi-Regge model by Chan, Łoskiewiez and Allison (CLA) to calculate one-particle distributions of transverse and longitudinal momenta,pt andpl*, and invariant-mass distributions of the reactions\(\pi ^ - p \to {\mathcal{N}} + (n - 1)\pi \) with multiplicitiesn ranging from 3 to 7 and an incident momentum of 11 GeV/c. We apply the model in a way that allows us to distinguish between differently charged pions. In order to account for the experimentally observed neutral pions in the forward direction, we have to take for the trajectory withG-parity +1 the ρ and not the Pomeron used by CLA. A comparison between the multi-Regge calculations and the experiment shows a good overall agreement. A remarkable feature of the reaction π−p→pπ+π−π−π0 is that almost no Δ++ production can be observed, when the prediction of the multi-Regge model is taken as a representation of the background in the pπ+ mass plot. However, this does not necessarily mean that no Δ++ production is present, but it might be an indication of the local duality now under discussion.