Instantons and condensates in supersymmetric CPN−1 models

The partition function in the multi-instanton background for the supersymmetric CP^N?1 model is calculated and is shown to be supersymmetry invariant. This is used to calculate Green's function involving N pairs of $\text{ψ}\text{ψ(x}{}_{\mathrm{i}}\text{)}$, and this turns out to be independent of the positions. A possible interpretation is that the composite field $\text{ψ}\text{ψ}$ acquires a vacuum expectation value. The results are in agreement with those obtained in the 1/N expansion.     

Isospin analysis of the reactions pp→N(Nπ) at 12 and 24 GeV/c

The reaction pp → nucleon + nucleon + pion at 12 and 24 GeV/c is analyzed in terms of the isospin amplitudes for the production of the (Nπ) system. The energy dependence of the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ amplitude is weak, while the $\text{I(}\text{N}\text{π) =}\text{3}\text{2}$ contribution shows the strong energy dependence known from meson exchange reactions. The slope parameter B of the dσ/dt′ distributions of the $\text{I(}\text{N}\text{π)=}\text{1}\text{2}$ contribution is a strong function of the (Nπ) mass, decreasing sharply from about 12 GeV^?2 at threshold to about 4 GeV^?2 above 1700 MeV. Comparing our results for the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ cross section with those of similar investigations in πp and Kp reactions, we find that factorisation is valid within experimental errors. The results support the conclusion that the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ contribution is dominated by diffraction dissociation of the proton.     

Off-shell NN annihilation studied in π+p interactions at 8 and 16 GeV/c

Interactions in which the baryon is emitted forwards in the c.m.s. are studied in 8 and 16 GeV/cπ⁺p collisions. These interactions are interpreted as representing baryon exchange. The properties of such off-shell $\text{N}$N annihilation events are studied. It is found that the multiplicity distribution of the multi-pion system as a function of the effective mass for events with |u_pp| < 1 GeV² is the same as for real $\text{N}\text{N}$ annihilations.     

Features of diffractive scattering and the nature of the N1(1400) observed in NN→N(Nπ) reactions at 5.7 GeV/c

The results for the diffractive scattering contribution ($\text{F}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^0$) obtained in a cross channel isospin analysis of the $\text{N}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}$ reactions at 5.7 GeV/c are compared with those obtained for other ZN → Z′(Nπ) reactions where Z stands for N, π and the carbon nucleus. The dependence of the diffractive scattering on the mass M_πN and the momentum transfer t seems very weakly related to the nature of Z and the incident momentum.A comparison between amplitudes of the isospin exchange I_ex = 0 and I_ex = 1 leading to $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ production shows that $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1492)}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1670)}$ are produced essentialy through I_ex = 1.     

A t-channel isospin analysis of the chew-low plot for NN → N(Nπ) interactions at 5.7 GeV/c

A new approach to the t-channel isospin analysis of ZN → Z′(Nπ) reactions is presented. This approach, useful for $\text{Z = N,}\text{N}\text{, K}{}^{\mathrm{?}}$ when only five independent sets of data are availables, is used to analyse data of $\text{N}\text{N →}\text{N}\text{(Nπ)}$ reactions obtained in a $\text{p}\text{p →}\text{N}\text{N}\text{π}$ experiment at $\text{5.7}\text{GeV}\text{/c}\text{and a}\text{p}\text{d →}\text{N}\text{Nπp}{}_{\mathrm{s}}$ experiment at 5.5 GeV/c. the t behaviour of the different isospin exchange amplitudes, suggests their exchange mechanism production. The mass spectrum, M_πN, of the contributions produced by exchanged isospin I_ex = 1, shows enhancements corresponding to N(1490) N(1670) and Δ(1230) isobars, while the mass spectrum for I_ex = 0 presents only a large bump at ～1350 MeV commonly identified as N¹(1400).     

Consistency requirements for 1N expandable field theories

It is demonstrated that $\text{1}\text{N}$ expansion in a class of field theories with an internal O(N) symmetry leads to pathologies. Therefore, these models are either not internally consistent, or their perturbation expansions (ordinary as well as $\text{1}\text{N}$ are unreliable.     

Isospin analysis of NN → NNπ reactions at 5.7 GeV/c

A cross-channel isospin analysis has been performed on the channels $\text{p}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}\text{and}\text{p}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}$ in terms of three isospin amplitudes $\text{M}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^0\text{, M}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$, and $\text{M}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^1$ where the upper index is the isospin of the exchanged “object” in the t-channel and the lower index is the isospin of the $\text{(}\text{N}\text{π)}\text{or}\text{(}\text{N}\text{π)}$ system. Enhancements are observed in the low Nπ) invariant mass region for an $\text{I =}\text{1}\text{2}$ final state when the isospin of the exchanged object in cross channel is I_E = 0 and 1.     

Continuum limit of QED2 on a lattice

A path integral is defined for the vacuum expectation values of Euclidean QED₂ on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).     

Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

1N-expanded ϕ2X model. I. Phase transition

We consider the ?²X model in a $\text{1}\text{N}$ expansion in six-dimensional Euclidean spacetime. Using the path-integral formalism and the method of stationary phase we show the existence of two phases in the model: with broken O(N) symmetry and with O(N) maintained. In both phases the massless ? fields acquire masses. -Expressions for the masses including $\text{1}\text{N}$ order are given.     

Planar limit of the singlet spectrum for SU(N)-invariant quantum hamiltonians by the quantum collective field method

We calculate the quantum fluctuations around the classical vacuum of the quantum collective field in the case of SU(N)-invariant quantum mechanical systems. We obtain in this way the singlet spectrum up to corrections of order $\text{1}\text{N}$. Difficulties in the calculation of higher order terms in $\text{1}\text{N}$ are pointed out.     

Integral equations for the scattering of N identical particles

Integral equations are obtained for the scattering of N identical particles using a form of the N-particle scattering equations derived previously. The equations couple together only transition operators between physical two cluster channels, the breakup amplitudes being expressed in terms of quadratures over two-cluster amplitudes. The kernel of the equations becomes connected after a single iteration. The number of coupled equations for identical particles is $\text{1}\text{2}\text{N}\text{or}\text{1}\text{2}\text{(N?1)}$ when N is even or odd respectively.     

A nucleon-nucleon potential that includes the effect of the N1(1236)

The transition potentials for the reaction $\text{N}\text{+}\text{N}\text{?}\text{N}\text{+}\text{N}{}^1\text{(1236)}$ and $\text{N}\text{+}\text{N}\text{?}\text{N}{}^1\text{(1236) +}\text{N}{}^1\text{(1236)+}\text{N}{}^1\text{(1236)}$ are derived in the case of the π and ? exchange using the quark model. The nucleon-nucleon scattering in the T=1, ¹S₀ state is treated as a coupled channel $\text{N}\text{+}\text{N}\text{?}\text{N}\text{+}\text{N}{}^1$ system.     

Mass and energy characteristics of the 241Pu(nth, f) fragments

Fission-fragment mass and kinetic energy distributions and their correlations have been studied for the thermal neutron induced fission of ²⁴¹Pu. The global mass distribution is smooth, apart from a small shoulder at μ_H ≈ 144 probably due to the deformed shells N ≈ 88 and N ? 60 in the heavy and the light fragment respectively. When low excitation events are selected, these structures become more pronounced. Furthermore, there is a sudden increase of 1–2 MeV in $\text{E}\text{?}\text{(μ)}$ for masses around 85 and above 155 which is probably associated with a spherical shell N = 50 in the light fragment. Finally, the prompt neutron emission curve $\text{v(m}{}^1\text{)}$ is calculated.     

Some information from nucleon-antinucleon annihilation at rest: e+e− annihilation,hadronic fragmentation and deep inelastic structure functions

The experimental spectra of charged pions in $\text{N}\text{N}$ annihilation at rest are described in a model of quasi-two-body decays. The same model predicts the π⁰, ? and ω spectra. We apply a previous calculation to determine in the vector-dominance model, the pions spectra in e⁺e^? annihilation at the same energy. The $\text{N}\text{N}$ system is then used as a heavy hadron in order to describe, in a model-independent way: (i) the projectile fragmentation part in inclusive reactions; (ii) the valence part of the deep inelastic structure function.     

The non-linear sigma model in the 1N expansion and the inverse scattering transformation in the angular momentum

We develop an inverse scattering transformation in the angular momentum to deal with rotationally invariant problems in higher dimensions. We consider the two-dimensional non-linear σ-model in the $\text{1}\text{N}$ expansion. We succeed in expressing the action (a renormalized determinant) in terms of spectral data and we show that no real saddle points exist. This relates to an instability under dilatations connected with the asymptotic freedom of the model. This result together with Zamolodchikov's S-matrix lead us to conjecture that the $\text{1}\text{N}$ series may be convergent for this model.     

Proton 1h112 excitations in odd-mass N = 82 nuclei

The structure of negative-parity states in odd-mass N= 82 isotones (135 ≦ A ≦ 145) is investigated in the framework of a model which is based on coupling one $\text{1h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ proton to π = + 1 states of the appropriate doubly-even isotonic core. It is shown that an effective model-space truncation can be achieved if only core states in the vicinity of the yrast line are taken into account. These have been selected from the several hundreds or even thousands of states obtained from shell-model calculations, where the $\text{1g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{3s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ single- are assumed to be occupied. Spectroscopic data are calculated and predictions on the structure of low-lying π = ? 1 states are discussed and compared as far as possible to experimental findings. Thereby, the particle-core coupling approach is shown to be capable of describing essential properties of negative-parity levels in the N = 82 nuclei considered.     

1N2 corrections in two-dimensional lattice gauge system with mixed action

A form of the $\text{1}\text{N}{}^2$ correction for a two-dimensional system described by the mixed fundamental-adjoint action is discussed. An exact result for the U(N) gauge group is derived. The form of correction in SU(N) is also discussed and the difference between the two groups is pointed out. The form of correction in two dimensions can be generalized for any number of dimensions if corrections to the plaquette free energy are to be calculated.