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.     

Non-perturbative effects and infrared renormalons within the 1/N expansion of the O(N) non-linear sigma model

We analyze the structure of the Borel transform of the two-dimensional O(N) non-linear σ model within its $\text{1}\text{N}$ expansion. We check the existence of IR singularities (IR renormalons) and the presence of non-perturbative terms which organize themselves in an operator expansion à la Shifman-Vainshtein-Zakharov. We prove that renormalons cancel between the different terms of the operator expansion, so that there is a well-defined resummation procedure of the perturbative series. We suggest that this mechanism provides a general solution of the IR renormalons problem for massless UV free field theories.     

Proton-neutron correlations in nuclei with N = 30

Structure of the nuclei with N = 30 and Z = 20–28 is investigated by the nuclear shell model within the proton-neutron configurations (1f_{$\text{7}\text{2}$})^z?20_p × (2p_{$\text{3}\text{2}$}, 2p_{$\text{case1}\text{2}$}, 1f_{$\text{case5}\text{2}$})²_n. Effective proton-neutron interactions determined by a least-squares fit to the observed spectra of N = 29 nuclei are adopted. Agreement of the calculated spectra with experimental spectra is satisfactory. Strong correlations between protons and neutrons break down the pairing scheme and lower the first J = 2 levels in doubly even nuclei, which is shown from the resultant wave functions. A relation between the shell model and collective rotational model is discussed concerning the calculated rotation-like spectrum of ⁵⁶Fe. Electromagnetic properties and spectroscopic factors of single-nucleon transfer reactions are calculated. They are in good agreement with experiments.     

More about the S-matrix of the chiral SU(N) Thirring model

We fix the bound state poles of the S-matrix of the chiral SU(N) Thirring model by general arguments. Avoiding an infrared problem by using a modified $\text{1}\text{N}$ expansion, the result is confirmed in leading order.     

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.     

Some properties of the (ψψ)2 model in two dimensions

We show that the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model is, for N = 3, equivalent to the supersymmetric sine-Gordon equation, and for N = 4, equivalent to two decoupled sine-Gordon systems. In addition, we argue that the kinks of this model are isospinors, and we construct some of the higher conservation laws that are responsible for the exact solubility of this system.     

The S-matrix of the kinks of the (gyψ)2 model

We consider the particle-kink and kink-kink S-matrix elements of the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model, where the Majorana spinor ψ is an O(N) isovector. Our results confirm many qualitative ideas about the model, including the mass spectrum, the decoupling at N = 4, and the isospinor nature of the kinks.     

Dynamical calculation of the decay ψ′ → ψ + 2π

We calculate the ψ′ → ψ + 2π decay width on the basis of partial wave dispersion relations in the ππ channel. This is basically a coupled channel problem involving ππ, D$\text{D}$, etc. intermediate states. The calculation acquires anomalous thresholds due to the fact that the vertex ψ′ ψ (2π) is internally unstable. It is found that anomalous singularity contributions provide by far the most dominant contribution, which explains the rather large ψ′ → ψ + 2π decay mode. Very good agreement with the experimental width and mass distribution is achieved.     

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.     

Spontaneous chiral symmetry breaking for a U(N) gauge theory on a lattice

We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.     

Migdal approximation and 1/N expansion in QCD

We show that the Migdal approximation for the renormalization group in gauge theories in exact in the leading order in $\text{1}\text{N}$, above a critical value of the coupling constant. A systematic expansion in $\text{1}\text{N}$ is proposed. The string tension is calculated in the leading order in $\text{1}\text{N}$ in a theory without fermions.     

Isomers in the N = 83 nucleus 149Dy

Energy levels in the N = 83 nucleus ¹⁴⁹Dy were studied by the reaction ¹⁵²Gd(α, 7n) at 106 MeV bombarding energy using in-beam γ-ray spectroscopy methods. The measurements identified three isomers in this nucleus, at 1073 keV (13 ± 3 ns), at 2700±150keV (5 μs < T_{$\text{1}\text{2}$} < 0.5 s), and above 3.5 MeV (50 ± 15 ns). The low-lying isomer is interpreted as i_{$\text{13}\text{2}$}. The configuration $\text{27}\text{2}$^?(πh_{$\text{11}\text{2}$}²)₁₀₊ ×vf_{$\text{7}\text{2}$} is suggested for the state at 2.7 MeV.     

Experimental comparison of Jψ production by π±, K±, p and p̄ beams at 39.5 GeV/c

Measurements have been made of relative production cross sections of the $\text{J}\text{ψ}$ by π^±, K^±, p and p? at 39.5 GeV/c incident on copper. $\text{J}\text{ψ}$ production rates from π^?, K^? and p? are similar. The $\text{J}\text{ψ}$ relative particle/anti-particle production cross sections for x>0 are $\text{σ(π}{}^{\mathrm{+}}\text{)}\text{σ(π}{}^{\mathrm{?}}\text{)=(0.87±0.14)}$, σ(K⁺)/σ(K^?)=(0.85±0.5) and $\text{σ(}\text{p}\text{)}\text{σ(}\text{p}\text{?}\text{)=(0.15 ±0.08)}$. The small p/p? cross section ratio disagrees with models of J/ψ production by gluon amalgamation.     

Experimental results on J/ψ production by π±, K±, p and p incident on hydrogen at 39.5 GeV/c

J/ψ production at 40 GeV/c by π^±, K^±, p and $\text{p}$ incident on hydrogen has been studied and results compared with those obtained on tungsten in the same experiment. On hydrogen, J/ψ cross-section ratios relative to π^? have been measured to be (for $\text{x}{}_{\mathrm{<mtext>F</mtext>}}\text{> 0) σ(π}{}^{\mathrm{?}}\text{) : σ(π}{}^{\mathrm{+}}\text{) : σ(}\text{p}\text{) : σ(}\text{p}\text{) = 1 : (0.78 ± 0.09) : (0.83 ± 0.35) : (0.07 ± 0.04)}$. The suppression of the proton induced cross sections shows the importance of calence quark-antiquark fusiin J/ψ production at this energy (i.e. M_J²/_ψ/s=0.13).     

Quantum fluctuations in the one-instanton sector of the CPn−1 model

Within the two-dimensional CP^n?1 model we calculate the instanton density function in the dilute-gas limit by studying the quantum fluctuations in the one-instanton sector in the one-loop approximation. The result disagrees with the $\text{1}\text{n}$ expansion. Green functions in the one-instanton background are displayed.     

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.     

Single-particle approximation to the canonical density operator of a system of N interacting fermions

A necessary condition for the minimum of free energy Tr(ρH^N) + β^-1 Tr(ρlnρ) is investigated for a system of N interacting fermions on the set of all density matrices of the form ρ=Z^-1 exp(-βNΓ^N₁h¹), where Γ^N₁ is Kummer's (1,N)-expansion map, and h¹ is a finite- dimensional one-particle operator. It is shown that for values of β in an open circle $\text{C}\text{(0,β}{}_0\text{)}$ in the complex plane there exists a unique bounded analytic in β one-particle operator X¹(β) such that Z^-1exp(-βNΓ^N₁X¹(β)) satisfies this condition.     

Shell-model study on magnetic dipole excitation of N = 28 isotones

Magnetic dipole excitation of N = 28 isotones — ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr, ⁵⁴Fe and ⁵¹V — is studied in terms of the shell model by assuming $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{n?m}}\text{(}\text{p}\text{3}\text{2}\text{p}\text{1}\text{2}\text{f}\text{5}\text{2}\text{)}{}^{\mathrm{m}}$ configurations with m = 0, 1 and 2 on an inert ⁴⁰Ca core. Strength distributions observed in (e,e′) and (p,p′) experiments are fairly well reproduced. Interference of proton and neutron excitations enhances B(M1) values around E_x = 10 MeV and reduces those of low-lying states. The strength for T = T₀ + 1 states substantially increases when orbital magnetization is not taken into account, whereas no appreciable consequences can be seen for T = T₀ states. In comparison with single-particle model predictions with m = 0, about 20–30% reduction of the total strength is obtained due to ground-state configuration mixing. It is shown that the isoscalar spin component is reduced as well as the isovector one. However, the theoretical total strength is still much larger than experimental values, and coupling with high-lying configurations and possible delta-hole excitation might be required in order to account for the discrepancy. In an odd-mass nucleus ⁵¹V, the ground-state transition strength is distributed continuously over a wide energy range, being very strongly fragmented.