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.     

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.     

Phase transition in the three-dimensional chiral field

The essentially nonlinear chiral field in three dimensional space time non-renormalizable in the usual perturbation expansion is studied. We consider systematic $\text{1}\text{N}$ expansion for this model. In the framework of the latter a phase transition takes place: above the critical point the theory is in the O(N) symmetric phase, below it the O(N) symmetry breaks. The $\text{1}\text{N}$ renormalized expansion for both phases is described and the connection between the non-renormalizability of the conventional perturbation theory and the non-analytic dependence on the coupling constant is established.     

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.     

Vacuum decay by inverse scattering

We discuss the decay of false vacua which originate from quantum mechanical effects. In particular we examine the $\text{1}\text{N}$ expansion of the O(N) λφ⁴ model. This model has an effective potential which is complex for large values of the field. In a previous paper we showed that this effective potential could not be used to calculate the decay rate directly. In the present work we show that the vacuum can decay via poles in the effective action which are evident when it is written in terms of scattering variables.     

The YN interactions and K− reactions on deuterium at low energies

The K^?d → π^?Λp reaction, as well as the other three-body K^? reactions on deuterium, are considered for s-wave kaons in the Faddeev formalism for charge-independent separable two-body coupled-channel interactions fitted to the available low-energy data. In particular we study the effect of a hypothetical $\text{I =}\text{1}\text{2}\text{, S = 1, Σ}\text{N}$ unstable bound state near the πΣN threshold on the shape of the calculated Λp invariant mass distribution near the ΣN threshold. This calculated distribution always exhibits a cusp behavior at the ΣN threshold, but considerable structure and broadening may be reached by varying the parameters of the YN interaction. Multiple scatterings in the initial K?NN and intermediate πΣN channels play a dominant role at low energy. The calculation compares favorably with the measurements at rest and at low energies. This comparison suggests that a ΣN bound state does not exist near the ΣN threshold.     

On chiral realizations of confining theories

It is argued that chirality is not necessarily broken in SU(N) colour theories with a chiral flavour symmetry. In this case, massless fermion bound states contributr to anomaly equations, and loop expansions in a 1/N approach are invalid. As a hint to understanding which option is realized by the theory, we investigate it in two dimensions for very small quark masses. The light spectrum shows a rich structure not obtained in a $\text{1}\text{N}$ expansion. Light flavoured baryons and mesons indicate a partial realization of the chiral symmetry.     

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.     

Effective lagrangian of mesons and baryons in the strong-coupling expansion of lattice QCD

U(N) and SU(N) lattice QCD are considered. By using a method of the strong-coupling expansion, the effective lagrangian of hadrons is calculated up to the first order in 1/(g²N). For the Susskind lattice fermions, it is shown that chiral symmetry is spontaneously broken and as a result there appears the Nambu-Goldstone boson (pion). The fermion condensation 〈$\text{ψ}\text{ψ}$t>, the masses of hadrons and the pion decay constant are calculated and compared with the results of Monte Carlo (MC) simulations. In the strong-coupling region, our result of the order parameter 〈$\text{ψ}\text{ψ}$〉 coincides very well with that calculated by MC simulations.     

Shell model study of N = 50 nuclei

Measured E2 and M4 transitions and energy levels in the N = 50 isotones with Z > 38 are satisfactorily reproduced by a shell model with proton configurations $\text{(2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, 1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{n}}$. Four sets of two-body matrix elements are found by least-squares fitting to energy levels and transition rates in the N = 50 isotones. These interactions include one that exactly conserves seniority and another that fits the strongly inhibited 8⁺→ 6⁺ transition in ⁹⁴Ru. Slight seniority nonconservation is required to predict inhibited N = 50 transition rates. The sign of the off-diagonal matrix element is determined by comparison with experimental M4 rates. The seniority conserving interaction is found to be equivalent to the best seniority nonconserving interaction for prediction of energy levels.     

Higher orders in N−1 in the Gross-Neveu model

We study higher-order terms in the N expansion of the two-dimensional model field theory of Gross and Neveu. The quantity $\text{M}{}_{\mathrm{\sigma }}\text{2M}{}_{\mathrm{<mtext>F</mtext><mtext>?1</mtext>}}$ (M_F is the fermion mass, M_σ is the scalar bound-state mass), is conjectured to deviate from zero in O(N^?4). Order N^?1 corrections are found to leave unchanged both the symmetry-breaking, and the absence of zeros of the Callan-Symanzik function β for real non-zero coupling constant. Behavior of β for complex coupling constant is altered considerably by the corrections; consequences are discussed.We obtain the following additional results: proof that the model is renormalizable without the necessity of additional interactions; construction of a perturbation theory in the asymmetric vacuum; proof of a lemma on fermion-antifermion thresholds in two-dimensional space-time; derivation of closed formulae for arbitrary one-loop integrals in two-dimensional space-time.     

Current algebra theorems for the U(1) “Goldstone boson”

The U(1) problem is reconsidered from the point of view of the $\text{1}\text{N}$ expansion. It is argued that various heuristic ideas about the η′ are valid from this point of view. Current algebra theorems, similar to soft π theorems, are derived for the η′. They are valid to lowest order in $\text{1}\text{N}$.     

Magnets with random anisotropies: The random cubic model and other models with p-fold spin interactions

In this paper we investigate in detail models with random anisotropies and p-fold spin interactions. We construct the random cubic model (p = 4) and show that when N > 2 (N being the number of spin components) its properties are similar to the random uniaxial anisotropy model, since quartic interactions, characteristic of the random uniaxial model, are generated through renormalization even if they vanish to start with. Similar conclusions apply to a random p-fold interaction model of the form $\text{?D∑}{}_{\mathrm{i}}\text{(}\text{n}\text{?}\text{,}{}_{\mathrm{i}}\text{·}\text{S}{}_{\mathrm{i}}\text{)}{}^{\mathrm{p}}$, when p is even. In the case of odd p, a random field interaction is generated. Other models are also discussed.     

Evidence for a narrow width boson of mass 2.95 GeV

In a search for resonances coupled to the $\text{p}$pπ^? system, we have studied π^?p interactions at 16 GeV/c giving a forward antiproton, using the Omega spectrometer at CERN. In the final states involving a $\text{p}$, p and π^? we observe a 5.6 (6.3) standard deviation enhancement in the $\text{p}$pπ^? mass spectrum at (2.95 ± 0.01) GeV with a width consistent with the resolution (σ = 15 MeV). The production cross section × branching ratio is estimated to be of the order 1 μb. The data are consistent with a resonance decaying partly via intermediate $\text{p}$p final states.     

CPN−1 model: A toy model for QCD?

We examine the CP^N?1₂ models and discuss their relevance as toy models for QCD₄. Specifically, we study the role of instantons, θ vacua, and confinement in the $\text{1}\text{N}$ expansion. Our results, and comparisons with other two-dimensional models, suggest that most of the interesting features of these models are peculiarities of two-dimensional space-time and cannot be expected to reappear in QCD₄.     

The K-Mesic atom

Assuming that the Y¹_o(1405) resonance dominates the $\text{K}\text{N}$ system at threshold, we show in a three-body K^?d model that to get the correct sign of the real part of the kaon-nucleus optical potential, we must use an off shell $\text{K}\text{N}$ amplitude and that higher $\text{K}\text{N}$ multiple scattering including intermediate nuclear excitations are important.