Infra-red asymptotic behaviour of the one-fermion green's function in a scalar model with isospin

In a theory where massive fermions interact with a massless scalar field of isospin 1, the behaviour of the one-fermion Green's function is found to differ from the free Green's function by a factor $\text{(1 ? (2g}{}^2\text{/π}{}^2\text{)1}\text{n}\text{m|x ? y|)}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>8</mtext>}}$, in the limit of large separation |x ? y|.     

What is the relativistic generalization of a linearly rising potential?

Recent progress in summing graphs of non-Abelian gauge theories focuses attention on certain manifestly Lorentz-invariant classical action-at-a-distance theories, whose solution allows for the construction of field-theoretic Green functions in the WKB approximation. The sum of graphs is of QED type, except that the gluon propagator is modified to incorporate the renormalization-group-invariant charge $\text{g}\text{(k)}$. The purely phenomenological choice $\text{g}{}^2\text{～ k}{}^{\mathrm{?2}}$ is equivalent non-relativistically to a linearly rising potential and yields a fully relativistic classical action-at-a-distance theory with exactly soluble circular orbits, whose Bohr quantization yields an asymptotic approximation to the poles of the Green function. One finds asymptotically linear Regge trajectories, but other phenomenological aspects are not as promising when only a linearly rising potential is used (in common with other phenomenological studies). As a redeeming feature, there do not appear to be any obvious pathologies of the sort familiar from string theories and ad hoc generalizations of linearly rising potentials.     

Energies and orbital sizes for some Rydberg and valence states of the nitrogen molecule

Accurate SCF computations are reported on the Rydberg states of N₂ of electron configurations $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$, $\text{---1π}{}_{\mathrm{u}}{}^3\text{3σ}{}_{\mathrm{u}}$, and ---3σ_g2π_g, also on the valence states of the configuration $\text{---1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$. The Rydberg state calculations supplement those of Lefebvre-Brion and Moser. A comparison is made between the $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ states and the parallel set of states of the $\text{1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$ configuration. This comparison shows a sharp difference in the ¹Σ⁺ states of the two configurations, the ¹Σ⁺ state being very high in the latter but relatively low in the former configuration. Recknagel coefficients are given for the several states of the two configurations; as expected, these are much smaller for the $\text{1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ configuration. Also, the ¹Δ state is relatively lower for the latter configuration.     

Laser excitation spectra of He2

Metastable $\text{a(2sσ)}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ He₂ molecules are produced by a dc discharge in a flowing He stream. Laser excitation downstream of the discharge produces excitation spectra for a number of He₂ states. LIF spectra are observed for the $\text{(npπ)}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ series for n = 4–9, excepting 5 and the $\text{(npπ)}{}^3\text{Π}{}_{\mathrm{g}}$ series for n = 5–15.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

On the challenge of measuring the colour charge of gluons

We propose two ways of measuring “directly” the chromodynamic gluon self-couplings. We argue that the measurements would serve to establish (or disprove) the gauge and non-Abelian nature of the candidate strong-interaction theory: QCD. Both experiments concern the production in e⁺e^? annihilation of a heavy vector meson resonance, followed by its hadronic decay into three “gluon jets”. The asymmetry of the decay plane relative to the electron axis is a measure of $\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{=}\text{g}{}^2\text{4π}$, with g the coupling for gluon self-interactions. If QCD is right, this value of g should coincide with the measured coupling of quarks to gluons. The two proposed experiments are difficult: they both demand very large statistics, one requires longitudinally polarized beams, the other the detection of weak-electromagnetic interferences. But the stakes are high.     

Lifetime and g-factor results for the 132− 1985 keV level in 91Nb and the 152− 2288 keV level in 91Zr

Lifetime and g-factor measurements have been made with pulsed beam-γ time-differential techniques using the ⁸⁹Y(α, 2n)⁹¹Nb and ⁸⁸Sr(α, n)⁹¹Zr reactions. A mean lifetime τ = 14.4 ± 0.5 nsec and a g-factor of 1.26 ± 0.04 were obtained for the $\text{13}\text{2}{}^{\mathrm{?}}$ 1985 keV level in ⁹¹Nb and τ = 41.9 ± 1.2 nsec and g = 0.70 ± 0.01 were obtained for the $\text{15}\text{2}{}^{\mathrm{?}}$ 2288 keV level in ⁹¹Zr. These results are compared to theoretical calculations for $\text{(π}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^2\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ and $\text{(π}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)(π}\text{p}\text{1}\text{2}\text{)(v}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ configurations in ⁹¹Nb and ⁹¹Zr, respectively.     

A mechanism for quark confinement

Euclidean field configurations carrying half integral topological charge, merons, can, unlike ordinary instantons, confine quarks at moderate coupling g. Logarithmic interactions between merons prevent isolated ones from existing for small g. However, in four dimensional QCD a crude calculation indicates a phase transition to a quark confining plasma at an effective coupling $\text{g}{}^2\text{4π}{}^2\text{≈}\text{1}\text{4}$.     

Dual parton model and the photoproduction of pseudoscalar and vector mesons in the high energy region

On the basis of the dynamical dual model of strong interactions followed from the parton model of hadrons as discussed in an earlier paper, we study here the photo-production of pseudoscalar and vector mesons in the high energy region. To incorporate the concept of duality, it is taken that any two spin $\text{1}\text{2}$ pointlike constituents (partons) can form a π-meson cluster in the structure of a nucleon and the basic interaction involved in MB scattering is the interaction of the incident meson with the π meson in the structure of the nucleon. In this scheme, the amplitudes for the photoproduction of mesons such as γN → Nπ, γN → N?, and γN → Nω in the high energy region can be related with the amplitudes for the process γπ → ππ, γπ → π?, and γπ → πω, respectively. To calculate the amplitudes for the relevant process we also consider a factor corresponding to the structural rearrangement of partons involved in duality diagrams. To obtain the cross sections, we take into account the photon-vector meson analogy, though the naive form of the vector dominance model (VDM) has not been considered here. From a knowledge of the coupling constants $\text{γ?}{}^2\text{4π}$, $\text{γω}{}^2\text{?π}$, , and we obtain the differential cross sections which are in excellent agreement with experimental results. Also we obtain a good fit for the scattering process γN → Nπ at backward angles. For the vector meson production processes, we have contributions from the diffraction mechanism also apart from the amplitudes considered here. In the region where the contribution from the diffraction part is negligible, we obtain the relation

which is in nice agreement with experiments. Finally, it is shown that, though the vector meson dominance is not considered here, the universality of the vector meson coupling with hadrons follows directly from the present model.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

Diffraction and resonance production in exclusive pp interactions at 100 GeV/c

We have investigated the reactions $\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{a}\text{?}\text{and}\text{p}\text{p}\text{a}\text{?}\text{p}\text{p}\text{2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}\text{at}\text{100}\text{GeV}\text{/c}$. The $\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ final state is dominated by diffractive production of a $\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{(}\text{or}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ system which shows a strong tendency to form $\text{Δ}{}^{\mathrm{++}}\text{π}{}^{\mathrm{?}}\text{(}\text{or}\text{Δ}{}^{\mathrm{++}}\text{π}{}^{\mathrm{+}}\text{)}$. The process $\text{p}\text{p}\text{a}\text{?}\text{Δ}{}^{\mathrm{++}}\text{Δ}{}^{\mathrm{++}}$ is also observed in this reaction, indicating an energy dependence of s^?1.5±0.1. The $\text{p}\text{p}\text{2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}$ channel shows less single diffraction, and has a doubly diffractive component consistent with pomeron factorization. Strong Δ⁺⁺(Δ⁺⁺) production is agoain seen, but in contrast to the $\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ channel we also observe considerable ?⁰ production.     

Asymptotic behavior of the pion electromagnetic form factors in Bethe-Salpeter model

Asymptotic behavior of the pion form factors has been discussed treating pion as a bound state of the elementary nucleon and antinucleon system. The matrix-element of the electromagnetic current is written in terms of the Bethe-Salpeter amplitude for the nucleon-antinucleon bound system. Using suitable approximations the Bethe-Salpeter equation for nucleon-antinucleon bound state with nucleons as Dirac spinors has been solved and the corresponding off-shell pion form factors are determined. The form factors are strongly interaction dependent. For coupling $\text{g}{}^2\text{16π}{}^2\text{=}\text{15}\text{4}$ the form factors vanish asymptotically like t^?1 and for $\text{14}\text{4}\text{<}\text{g}{}^2\text{16π}{}^2\text{<}\text{15}\text{4}$ the form factors still vanish but less rapidly than t^?1.     

Photoproduction of charged π mesons from protons and neutrons in the energy range between 250 and 790 MeV

The differential cross sections for γp→π⁺n from hydrogen and the $\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ ratios from deuterium were measured at nine c.m. angles between 30° and 150° for laboratory photon energies between 260 and 800 MeV. A magnetic spectrometer with three layers of scintillation hodoscope was used to detect charged π mesons. The cross section for γn→π^?p was obtained as a product of $\text{d}\text{σ}\text{d}\text{Ω}\text{(γ}\text{p}\text{→π}{}^{\mathrm{+}}\text{n}\text{)}$ and the $\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ ratio. The overall features in the cross sections of the two reactions, γp→π⁺n and γn→π^?p, and in the ratios, $\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$, agree with predictions by Moorhouse, Oberlack and Rosenfeld, and Metcalf and Walker. An investigation of the possible existence of an isotensor current was made and a negative result was found. In detailed balance comparison with the new results on the inverse reaction π^?p→γn, no apparent violation of time-reversal invariance was observed.     

The magnetic moment of the 22 μs isometric state in 38K

The g-factor of the $\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{=22 μ}\text{s}\text{, J}{}^{\mathrm{\pi }}\text{=(7}{}^{\mathrm{+}}\text{), T=0}$ isomeric state at 3.46 MeV in ³⁸K has been measured by the differential spin precession method with the ${}^{35}\text{Cl}\text{(α,}\text{n}\text{)}{}^{38}\text{K}$ reaction. The result of g=+0.548 (μ=+3.836± 0.014 n.m.) is consistent with a pure configuration.     

Study of the Kππ system produced in K−p → KππN reactions at 14.3 GeV/c

We have studied the $\text{K}\text{ππ}$ system in the 14.3 GeV/c reactions K^?p → K^?π⁺π^?p, $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^0\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{and}\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^0\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{n}$. The data have been obtained from a 500 000 picture exposure of the CERN 2m HBC. The first two final states are dominated by Q-production in the Kππ system; there is also an L-signal at M (Kππ) ～ 1.75 GeV. The reaction cross sections are compared to K^?p data at other energies. We discuss the Kππ mass dependence of the diffractive production slope. Evidence is presented for a Q^?p versus Q⁺p differential cross section cross-over around |t| = 0.17 GeV². A t-channel isospin analysis for the $\text{KN}\text{→}\text{K}\text{1(890)π}\text{N}$ channels in the Q-region shows that the I = 1 exchange amplitude is $\text{? 10\%}$ of the dominant I = 0 exchange amplitude. The Kππ decay distributions indicate a predominant J^P = 1⁺ state in the Q-region, and an important J^P = 2^? contribution in the L-region. We find neither s-channel nor t-channel helicity conservation at the meson vertex in the Q- or L-regions. The Kπ angular correlation moments within the Kππ diffractive system are characteristic of Kπ elastic scattering, suggesting a π-exchange Deck-type production mechanism. There is evidence for a Kf⁰ and κπ contribution (where κ is the J^P(Kπ) = 0⁺ state) to the diffractive Kππ system. A fit to the $\text{K}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{and}\text{K}{}^0\text{π}{}^{\mathrm{?}}\text{π}{}^0$ Dalitz-plot distributions for the Q-re gion indicates that the ratio of $\text{K}\text{?}\text{to K}{}^1\text{π}$ decay amplitudes decreases with increasing Kππ mass.     

Masterfields and the phases of quantum chromodynamics in two dimensions with fermions

The phase structure of two-dimensional quantum chromodynamics is analyzed in the large-N limit. Using a variational approximation, we show that a first-order phase transition occurs as the quark bare mass squared m₀² is made less than $\text{g}{}^2\text{N}\text{π}$. This novel phase structure goes beyond summing the perturbative large-N planar graphs.     

Partial-wave analysis of the low-mass (π+π−p) system produced in K−p interactions at 4.2 GeV/c

A partial-wave analysis of the low-mass (π⁺π^?p) system produced in the reaction K^?p → K^?(π⁺π^?p) at 4.2 GeV/c incident momentum is performed in order to study the two (π⁺π^?p) enhancements around 1500 and 1700 MeV. It is found that the low-mass (π⁺π^?p) system can be described using the spin-parity states $\text{J}{}^{\mathrm{P}}\text{=}\text{1}\text{2}{}^{\mathrm{+}}\text{,}\text{3}\text{2}{}^{\mathrm{?}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ only. In the 1500 MeV region contributions are observed from the $\text{1}\text{2}{}^{\mathrm{+}}$ wave decaying into p? and the $\text{3}\text{2}{}^{\mathrm{?}}$ wave decaying into Δ⁺⁺π^?; in the 1700 MeV region contributions are found from the $\text{1}\text{2}{}^{\mathrm{+}}$ wave decaying into Δ⁺⁺π^?, the $\text{3}\text{2}{}^{\mathrm{?}}$ wave decaying into p?, and the $\text{5}\text{2}{}^{\mathrm{+}}$ wave decaying into p?.     

Nuclear magnetic moment of the 9.7 h 12− isomer 196mAu

The magnetic hyperfine splitting v_M=|gμ_NB_HF/h| of ^196mAu (j^π=12^?; configuration ¦(π$\text{11}\text{2}$($\text{v}\text{13}\text{2}{}^{\mathrm{+}}\text{)〉}{}_{12}{}^{\mathrm{?}}$; $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 9.7}\text{h}\text{)}$ as dilute impurity in Ni has been determined with nuclear magnetic resonance on oriented nuclei as 96.0(2) MHz. With the known hyperfine field B_HF = ?264.4(3.9) kG corrected for hyperfine anomalies the g-factor and magnetic moment of ^196mAu are deduced to be |g| = 0.476(7) and |μ| = 5.72(8) μ_N. Taking into account the known magnetic properties of $\text{π}\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{v}\text{13}\text{2}{}^{\mathrm{+}}$ isomeric states in the neighbouring odd Pt, Au and Hg nuclei the structure of the 12^? state is discussed.     

Evidence for double dissociation in K-p interactions at 14.3 GeV/c

We have studied the reaction K^-p → K^-π⁺π^-π⁺π^-p at 14.3 GeV/c to search for evidence of the double dissociation process $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{QN}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$. In the channel $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{K}{}^{10}\text{(890)}$π₁^-π₂^-Δ⁺⁺ (1236) there is evidence for simultaneous production of low-mass enhancements in the $\text{K}{}^{10}\text{π}{}_1{}^{\mathrm{-}}$ and Δ⁺⁺(1236)π₂^- subsystems which correspond to the $\text{Q}\text{→}\text{K}{}^1\text{(890)π}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1\text{→ Δπ}$ decay modes. In this particular final state the double fragmentation system is produced with a cross section of the order of a few microbarns. Our data are consistent with the factorizable pomeron exchange model of double diffractive dissociation.