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.     

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.     

Measurement of elastic scattering in antiproton-proton collisions at 52.8 GeV centre-of-mass energy

We measured the differential cross section for p?p and pp elastic scattering in the momentum-transfer range 0.01 <|t| < 1.0 GeV² at the CERN Intersecting Storage Rings with center-of-mass energy $\text{s}\text{= 52.8}\text{GeV}$. Fitting the differential cross section with an exponential [Aexp (bt)], we found $\text{b}\text{p}\text{p = 13.92 ± 0.59}\text{GeV}{}^{\mathrm{?2}}$ for |t| < 0.05 GeV², whilst for |t| > 0.09 GeV², $\text{b}\text{p}\text{p = 10.68 ± 0.26}\text{GeV}{}^{\mathrm{?2}}$. Using the optical theorem, we obtained for the total cross section $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{p}\text{p)= 44.86 ± 0.78}\text{mb}$ and, by integrating the differential cross section, we obtained for the total elastic cross section $\text{σ}{}_{\mathrm{<mtext>el</mtext>}}\text{(}\text{p}\text{p) = 7.89 ± 0.28}\text{mb}$. Calculations of σ_tot combining elastic-rate and total-rate measurements are also given. All of these measurements were also performed for pp scattering at the same energy, and the results for both reactions are compared.     

Observation of a direct low-mass e+e− continuum in π-p interactions at 16 GeV/c

The production of prompt electron-positron pairs in 16 GeV/c π^-p collisions has been measured using the LASS spectrometer at SLAC. An excess of events is observed above the estimated contribution of direct and Dalitz decays of known resonances in the kinematic range defined by $\text{0.1?χ?0.45, 0?p}{}_{\mathrm{T}}\text{?0.8}\text{GeV}\text{c}$ and $\text{0.2?M(e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)?0.7}\text{GeV}\text{c}{}^2$. The excess signal decreases slowly with increasing M, but exhibits very steep χ and p_T² dependence.     

Peripheral pn production and decay angular distributions in the reaction π−p → (pn)p at 12 GeV/c incident momentum

The reaction $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}$, where p_s is a slow proton, was measured at 12 GeV/c incident momentum with the CERN-OMEGA spectrometer. Both antiproton and proton were identified uniquely by electronics information. We obtained 1844 events with four-momentum Transfer squared in the range 0.13 ? |t| ? 0.33 GeV² and with invariant masses $\text{M(}\text{p}\text{n}\text{)}$ up to 2.5 GeV. The corresponding cross section in this t range is determined to be σ = 4 ± 0.4 μb. Extrapolating the differential cross section over the whole t range assuming dσ/dt ≈ exp(5.3t) we estimate a cross section of σ = 9.3 ± 2.0 μb. Comparison with data on $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ (where n_s is a slow neutron) in the same t range shows that the $\text{(}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}\text{and}\text{(}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ cross sections have approximately the same magnitude.     

The reactions K−p → K1− + nucleon at 3.13 and 3.3 GeV/c

Results are presented of a 12 event/μb bubble-chamber experiment; the reactions discussed in detail are $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^1\text{(890)}{}^{\mathrm{?}}\text{p, K}{}^1\text{(1420)}{}^{\mathrm{?}}\text{p and K}{}^1\text{(890)}{}^{\mathrm{?}}\text{Δ}{}^{\mathrm{+}}$.The K¹ (890)^?p channel is dominated by the forward peak. The suggestion of flattering at cos θ = 1 is more pronounced in $\text{(?}{}_{11}\text{+ ?}{}_{\mathrm{1?1}}\text{)}\text{d}\text{σ}\text{d}\text{t}$; which is mainly natural-parity exchange. Pseudoscalar exchange contributes to $\text{?}{}_{00}{}^{\mathrm{J}}\text{d}\text{σ}\text{d}\text{t}$; this is more sharply peaked in t. The value of $\text{(?}{}_{11}\text{? ?}{}_{\mathrm{1?1}}\text{)}\text{d}\text{σ}\text{d}\text{t}$ is somewhat larger than the upper limit from the dominant natural-parity exchange. There is significant structure in $\text{?}{}_{00}{}^{\mathrm{H}}\text{d}\text{σ}\text{d}\text{t}\text{at}\text{t ≈ ?0.6 (}\text{GeV}\text{/c)}{}^2$.The K¹ (1420)^?p channel is much more pronounced at 3.3 GeV/c than at 3.13 GeV/c, but is not markedly peripheral. The width of the K¹ (1420) in the 3.3 GeV/c data is 42 ± 12 MeV/c².The cross section for $\text{K}{}^{\mathrm{1?}}\text{Δ}{}^{\mathrm{+}}$ agrees with that expected from $\text{K}{}^{\mathrm{+}}\text{p}\text{→}\text{K}{}^1\text{Δ}$, assuming a single t-channel exchange. Our measured density matrix elements are consistent with a strong pseudoscalar exchange.     

Determination of the spectroscopic quadrupole moments of 131Cs, 132Cs and 136Cs

Nuclear spectroscopic quadrupole moments of the radioactive isotopes ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs have been determined from the hyperfine structure of the $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state by the level crossing method. The results including a Sternheimer correction are: $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{131}\text{Cs}\text{) = ?0.625(6)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = +0.508(7)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = +0.225(10)}\text{b}$. The quadrupole moments of all the Cs isotopes from A = 131 to A = 137 are recalculated. It is shown, that nuclear quadrupole moments of a specific isotope obtained from different atomic P-states only agree within the limits of error after application of the Sternheimer correction. The increase of Q_s with decreasing neutron number conforms with other observations and theoretical calculations stating that for elements around Z = 55 nuclear deformation develops below N = 82. The staggering of the sign of Q_s may be interpreted as consequence of an oblate-prolate degeneracy of the nuclear energy surface. Some magnetic moments have been slightly improved: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = 2.219(7) μ}{}_{\mathrm{<mtext>N</mtext>}}$, $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = 3.705(15)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetism).     

Centrifugal distortion effects in the hyperfine spectrum of KCl

The hyperfine spectrum of KCl has been examined at near-zero electric field and zero magnetic field using a molecular beam electric resonance spectrometer. Rotational as well as vibrational shifts have been observed in both nuclear quadrupole interactions. With $\text{eqQ = Q}{}_{00}\text{+ Q}{}_{10}\text{(v +}\text{1}\text{2}\text{) + Q}{}_{20}\text{(v +}\text{1}\text{2}\text{)}{}^2\text{+ Q}{}_{01}\text{J(J + 1)}$, we find (all in units of kHz) for K in ³⁹K³⁵Cl: Q₀₀ = ?5691.47 ± 0.04, Q₁₀ = 51.32 ± 0.06, Q₂₀ = ?0.205 ± 0.020, Q₀₁ = 0.014 ± 0.007, Q₀₀(K³⁷Cl) ? Q₀₀(K³⁵Cl) = ?0.03 ± 0.07; for Cl in ³⁹K³⁵Cl: Q₀₀ = 137.0 ± 0.3, Q₁₀ = ?163.2 ± 0.5, Q₂₀ = 1.57 ± 0.15, Q₀₁ = 0.07 ± 0.03, $\text{[}\text{Q(}{}^{35}\text{Cl}\text{)}\text{Q(}{}^{37}\text{Cl}\text{)}\text{]Q}{}_{00}\text{(}\text{K}{}^{37}\text{Cl}\text{) ? Q}{}_{00}\text{(}\text{K}{}^{35}\text{Cl}\text{) = ?0.5 ± 0.6}$; and magnetic constants c_K = 0.154 ± 0.007, c_Cl = 0.435 ± 0.010, c₃ = 0.035 ± 0.012, and c₄ = 0.009 ± 0.006. These have been used to provide a mapping of the field gradients at both nuclear sites to fourth order in $\text{ξ =}\text{(r ? r}{}_{\mathrm{e}}\text{)}\text{r}{}_{\mathrm{e}}$. We find eQq_K(ξ) = (?5692.5 ± 2.5) + (1.7 ± 0.8) × 10⁴ξ + (?2. ± 4.) × 10⁴ξ² + (?8. ± 18.) × 10⁵ξ³ + (8. ± 15.) × 10⁶ξ⁴ and eQq_Cl(ξ) = (120. ± 22.) + (8. ± 4.) × 10⁴ξ + (?5.8 ± 2.0) × 10⁵ξ² + (?1.1 ± 1.6) × 10⁷ξ³ + (1.1 ± 1.3) × 10⁸ξ⁴.     

The QCD effective coupling constant in e+e− annihilation

The QCD effective coupling constant α_s(Q²) is determined by comparing the O(α_s)² jet-distributions with the high-energy e⁺e^? data from PETRA. We get α_s(Q² = 1225 GeV²) = 0.125 ± 0.01, which corresponds to $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}\text{= 110}{}^{\mathrm{+70}}{}_{\mathrm{?50}}\text{MeV}$ with five flavours.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Simultaneous measurement of 2 and 3 spins in proton proton elastic scattering at 6 GeVc

The elastic cross section for proton proton scattering at 6 $\text{GeV}\text{c}$ was measured using a 70% polarized beam and a 75% polarized target at the Argonne ZGS. In the range $\text{P}{}_{\mathrm{\perp }}{}^2\text{= 0.5 → 2.0(}\text{GeV}\text{c}\text{)}{}^2$ we obtained small error measurements for the ↑↑, ↓↓ and ↑↓ initial spin states perpendicular to the scattering plane. At P_⊥² = 0.5 we also measured the recoil spin and found that the 5 different cross sections were very unequal.     

Measurement of the polarization parameter in π−p elastic scattering at 40 GeV/c

We report our first measurements of the polarization in the elastic scattering of negative pions from polarized protons at an incident pion momentum of 40 GeV/c. The momentum-transfer region covered was 0.08 < |t| < 1.3 (GeV/c)². The angular distribution of the polarization exhibits a first minimum of ～ ? 5% and the well-known zero around t ≈ ? 0.6 (GeV/c)². The energy variation of the first minimum (at around t = ? 0.2) may be expressed in a simple form, $\text{P}{}_{\mathrm{<mtext>avr</mtext>}}\text{= ?(0.48±0.06) s}{}^{\mathrm{?0.52\pm 0.05}}$.     

Nonrelativistic distorted wave born approximation predictions for 500 MeV (p, p') spin-rotation observables

We discuss couplings of scalar gluonium σ on the basis of the low energy theorems of broken chiral symmetry and the anomalous trace of the energy—momentum tensor, implemented using a phenomenological lagrangian. Taking the ITEP value of the gluon consensate as input, we find $\text{Γ(σ → ππ) ? 0.6}\text{GeV}\text{× (}\text{m}{}_{\mathrm{\sigma }}\text{1}\text{GeV}\text{)}{}^5$ and $\text{Γ(σ → γγ) ? 90}\text{eV}\text{× (}\text{m}{}_{\mathrm{\sigma }}\text{1}\text{GeV}\text{)}{}^5$, while m_σ is undetermined. These results suggest that if the scalar gluonium mass is above 1 GeV, it is probably unobservably wide, while production in γγ collisions is probably too small to be detectable if m_σ < 1.5 GeV. We comment on the observability of J/ψ → σ + γ and on the relevance of our results to other gluonia.     

Momentum transfer distributions of some diffractive enhancements in K−p interactions at 14.3 GeV/c

We discuss the structure of the momentum transfer distributions for the diffractive dissociation processes p → nπ⁺, p → Δ⁺⁺π^? and $\text{K}{}^{\mathrm{?}}\text{→}\text{K}{}_{890}{}^{10}\text{π}{}^{\mathrm{?}}$. In the near-threshold mass region a clear break of slope is found around t′KK ～ 0.25 GeV² for the two baryonic channels, whereas no comparable structure is seen for the mesonic system. The $\text{K}\text{→}\text{K}{}^1\text{π}$ differential cross section exhibits a nearly exponential behaviour up to t′_pp ～ 0.6 GeV², falling over three orders of magnitude. The slope variations and breaks are strongly correlated both to the mass region considered and to the decay angle of the fragmentation system.     

A study of the reactions d + p → τ + π0 and d + p → τ + η0

The reactions d + p → τ + π⁰ and d + p → τ + η⁰ were studied using the missing-mass method for incident deuteron momenta between 2.8 and $\text{3.8}\text{GeV}\text{c}$. The angular distributions show a peak in the forward direction ($\text{θ}{}_{\mathrm{\tau }}{}^1\text{= 0°}$) and are flat in the backward direction. The differential cross sections at $\text{θ}{}_{\mathrm{\tau }}{}^1\text{= 180°}$ for both reactions show a maximum for total center-of-mass energies near 3.46 GeV.     

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.     

Asymptotic planarity: An S-matrix basis for the Okubo-Zweig-Iizuka rule

A mechanism is exhibited that monotonically depresses the cylinder component of the topological expansion with increasing t, and it is conjectured that all non-planar S-matrix components diminish as t increases, exchange degeneracy and the Okubo-Zweig-Iizuka rule becoming more accurately satisfied. Such asymptotic planarity is compared to the field-theoretical concept of asymptotic freedom. The characteristics low-t cylinder “quenching interval” is found to be the inverse of the mean value over a two-reggeon loop, of $\text{1}\text{2}\text{π}{}^2\text{(α′)}{}^2\text{(t}{}_1\text{? t}{}_2\text{)}{}^2\text{/(?t),}\text{where}\text{t}{}_1\text{and}\text{t}{}_2$ are the squared masses of the loop reggeons and α′ is the trajectory slope. For leading trajectories the low-t cylinder quenching interval is predicted by this formula to be roughly 0.5 GeV²-consistent with the observed pomeron intercept and slope, with the p-ω and f-A₂ mass differences and with the (φ,ω) deviation from ideal mixing. As t grows negatively over a corresponding interval, it is predicted that the pomeron will become nearly a pure SU(3) singlet. If the pion mass helps to set the scale for reggeon loops coupled to unnatural-parity trajectories, the cylinder quenching interval will be larger, explaining the large (η, η′) deviation from ideal mixing as well as the large π-η mass difference. Even when the small-t cylinder quenching is rapid (“precocious planarity”) the large-t approach to the planar limit turns out to be gentle. A by-product of this study is an explanation of the approximate reality and linearity of trajectories at large t.     

Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.