Inclusive production of vector and tensor mesons in antiproton-proton annihilation and non-annihilation interactions at 9.1 GeV/c

Cross sections have been determined for the inclusive production of vector $\text{(?}{}^0\text{, ω,}\text{K}{}^1\text{)}$ and tensor (f, A₂^±) mesons in $\text{p}\text{p}$ reactions at 9.1 GeV/c for both annihilation and non-annihilation processes. Distributions in the Feynman variable x and transverse momentum squared, p_T², have been examined for the ?⁰, ω and f mesons. The slopes for p_T² appear to be exponential and decrease with increasing particle mass for both annihilation and non-annihilation reactions, furthermore the slopes have consistently higher values for non-annihilation reactions. Comparisons with other data indicate that the ratio ?⁰/π^? is independent of antiproton momentum in annihilation processes.     

Determination of parton sea from μ pair production data

We describe a determination of the parton sea from pN → μ⁺μ^?X via the Drell-Yan formula, making a minimum of theoretical assumptions. The method requires deep inelastic eN, μN structure functions to be extrapolated to suitable values of x, Q². We determine the non-strange sea component $\text{u}\text{(x, Q}{}^2\text{) +}\text{d}\text{(x, Q}{}^2\text{)}$ between x = 0.2 and 0.5 with Q² = x²s, and s = 750 GeV².     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

A study of high transverse momentum π0's at ISR energies

We present a study of the transverse momentum spectrum of π⁰'s produced at c.m. angles θ = 90° and 53° in pp collisions at √s = 23.6, 30.8, 45.1, 53.2, and 62.9 GeV. The experiment was performed with a lead-glass detector. The data can be described with the usual parametrization $\text{p}{}_{\mathrm{<mtext>T</mtext>}}{}^{\mathrm{?n}}\text{?;(x}{}_{\mathrm{<mtext>T</mtext>}}\text{, θ)}$, with n = 7.2 ± 0.2. Comparison between the 90° and 53° data further indicates no appreciable dependence on θ, at least for x_T < 0.3. Two-particle inclusive cross sections for π⁰'s produced alongside are also presented. They are observed to have a dependence upon the transverse momentum of the dipion similar to that of single-particle cross sections and with the same value of n. Two-photon decays of η mesons are observed between 3 and 4 GeV/c transverse momentum with a production cross section half of that of π⁰.     

Inclusive V0 production in pp interactions at 12 GeV/c

Results are presented on the inclusive reactions $\text{p}\text{p}\text{→}\text{K}{}^0\text{X}\text{,}\text{p}\text{p}\text{→ Λ}\text{X and}\text{p}\text{p}\text{→}\text{Λ}\text{X}$ at an incident antiproton momentum of 12 GeV/c in BEBC. The cross sections are studied as functions of the Feynman scaling variable x, the rapidity, the transverse momentum of the V⁰ and the missing mass squared. The dependence of the Λ and $\text{Λ}$ polarization on x are also studied. Comparisons with proton-proton data at 12 GeV/c are also made. Finally, events with two detected V⁰ are analyzed in order to study correlations arising from the production of two strange neutral particles.     

Elastic scattering of π±p, K±p,pp ANDprmpp AT 39 AND 44.5 GeV/c

The differential cross sections for elastic $\text{π}{}^{\mathrm{?}}\text{p, K}{}^{\mathrm{?}}\text{p}\text{,}\text{p}\text{p and}\text{π}{}^{\mathrm{+}}\text{p, pp}$ scattering at 39 and 44.5 GeV/c, respectively, have been measured in the interval of momentum transfer squared 0.15 ≤ ovbt| ≤ 2 (GeV/c)².     

Ko and λ production at the CERN ISR

Transverse momentum distributions of $\text{λ}{}^{\mathrm{o}}\text{,}\text{λ}{}^{\mathrm{o}}$, and K^o, produced in pp collisions at x = 0, have obtained at the CERN ISR. The K^o yield is in agreement with published K⁺, K^? results, obtained at this centre-of-mass energy (√s≈44 GeV). The results on $\text{λ}{}^{\mathrm{o}}\text{and}\text{λ}{}^{\mathrm{o}}$ production obtained in this experiment are compared with results obtained at lower centre-of-mass energies.     

The average transverse distance between partons as measured by nucleon form factors

The values of $\text{d}\text{F}{}_1\text{(q}{}^2\text{)}\text{d}\text{q}{}^2$ at q²=0 for the neutron and the proton provide a measure of the average transverse separations squared, 〈$\text{y}{}^2$〉, between a u or d quark and the rest of the partons in a nucleon. Using the measured values of the form factors (together with parton x-distributions), we find that 〈$\text{y}{}^2\text{= 17.4}\text{GeV}{}^{\mathrm{?2}}$ for u quarks and 16.4 GeV^?2 for d quarks in a proton. We speculate that the small difference between u and d quarks is caused by “quark pairing” and discuss other possible experimental signatures of quark pairing.     

Thermodynamical analysis of the EMC effect

Assuming that the sea quark distribution vanishes for x > 0.3, we analyse the F₂^Fe(x, Q²) and F₂^D(x, Q²) structure functions measured by the European Muon Collaboration in the framework of a thermodynamical model of the valence quarks. The experimental ratio $\text{F}{}_2{}^{\mathrm{<mtext>Fe</mtext>}}\text{(x)}\text{F}{}_2{}^{\mathrm{<mtext>D</mtext>}}\text{(x)}$ is well reproduced over the whole x range by the ratio of two valence quark distributions at different temperatures T and confinement volumes V. We obtain T_D?T_Fe≈3 MeV and $\text{V}{}_{\mathrm{<mtext>Fe</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{≈ 1.3}$.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

Cluster models,local compensation of transverse momenta and transverse data

We analyse various data available on transverse momentum properties of high-energy collisions, within the framework of cluster models. The mean transverse momentum square of clusters is estimated to be of the order of 0.3 (GeV/c)². The transverse data at FNAL are found to be unable to discriminate between various production amplitudes. We give predictions at ISR on the transverse momentum transfer fluctuation $\text{D}{}_{\mathrm{?}}{}^2\text{(Δy)}$, which would permit this discrimination.     

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ? Q² ? 16 GeV². Excellent agreement is obtained using $\text{g}{}^2\text{(2}\text{GeV}\text{)}\text{4π}{}^2\text{= 0.17}$ for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of $\text{M}{}_0{}^2\text{Q}{}^2$. We use data from the resonance region to show $\text{M}{}_0\text{? 400}\text{MeV}$, in agreement with theoretical expectations. Our fit to νW₂ in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of $\text{R =}\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ at large x and Q² are systematically higher than our predictions.     

Dynamical rescaling and universality of hadron structure functions

We argue that pion and nucleon structure functions differ principally due to their different numbers of quarks and different scales of confinement. The former generates an x rescaling while the latter, in QCD, gives rise to a Q² rescaling. Together these lead to the relation

with $\text{ξ}{}_{\mathrm{<mtext>N</mtext><mtext>\pi </mtext>}}\text{? 0.16}$, for x values away from the end points. This relation is in good agreement with data.     

Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.     

New form of dynamics and current algebra

We study a new form of dynamical system, in which the commutation relations for the dynamical variables of a quantized field are defined on a “lightlike surface $\text{τ≡}\text{(t+z)}\text{2}\text{=0}$ rather than at one instant of time t = 0. We clarify the physical implications of the use of the new variables x¹ = x, x² = y, $\text{x}{}^{\mathrm{+}}\text{=}\text{(t+z)}\text{2}\text{, x}{}^{\mathrm{?}}\text{=}\text{(t?z)}\text{2}$ and explore its significance as a new form of relativistic dynamics, which holds in any Lorentz frame but not in the so-called “infinite momentum frame.” Using the quark model, we build up a new algebra of currents, in which the current commutators are defined at equal τ. The sum rules and other results of the usual current algebra can be obtained without taking the unjustifiable limit of infinite momentum. In particular, we obtain the Gell-Mann-Okubo mass formulas in quadratic form for both mesons and baryons without the trouble due to momentum dependence. We derive the reduction formula and find the physical high energy limit (not the Bjorken limit) of an amplitude is determined by the equal τ commutator.     

Author index

High-spin states in ^167,168Hf and ^{170, 171}W have been excited by the reactions ${}^{159}\text{Tb}\text{(}{}^{14}\text{N}\text{, x}\text{n}\text{)}{}^{\mathrm{173\; ?\; x}}\text{Hf and}{}^{155}\text{Gd}\text{(}{}^{20}\text{Ne}\text{, x}\text{n}\text{)}{}^{\mathrm{175\; ?\; x}}\text{W}$. The yrast bands have been observed up to $\text{J}{}^{\mathrm{\pi }}\text{=}\text{49}\text{2}{}^{\mathrm{+}}$ in ¹⁶⁷Hf, J^π = 28⁺ in ¹⁶⁸Hf, $\text{J}{}^{\mathrm{\pi }}\text{=}\text{45}\text{2}{}^{\mathrm{+}}$ in ¹⁷¹W and J^π = 22⁺ in ¹⁷⁰W. Both even-even nuclei display a strong backbend around J^π = 14⁺, whereas ¹⁶⁷Hf shows an upbend at ω ～- 0.33 MeV and ¹⁷¹W exhibits a progressive gain in aligned angular momentum above ω ～- 0.26 MeV. At even higher rotational frequencies, bridges have been found in the central valleys of the γ-γ correlation matrices at ω ～- 0.42 and 0.52 MeV for the Hf isotopes and ω ～- 0.45 and 0.47 MeV for the W isotopes. Deduced moments of inertia for the Hf isotopes using the correlation data show a smooth increase up to about the rigid-sphere value at ω ～- 0.5 MeV. The data are satisfactorily accounted for by cranked shell-model calculations. In particular, a qualitative interpretation is given for the experimentally observed systematic difference in the strength of the interaction potential for the N = 95 and N = 97 isotopes of Hf and W.