Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

Production and decay of quark-gluon strings: inclusive distributions of hadrons in p⊥ and x

The dependence of inclusive cross sections of the production of hadrons $\text{p}\text{p}\text{→ hX}$ on p_⊥ (and also on x and √s) is calculated at high energy in the region of small p_⊥ ? 1–2 GeV. The model of production and decay of quark-gluon strings is used under the simplest assumptions about the k_⊥ dependence of the quark distributions in nucleons ～ exp(?γ₁k²_⊥) and about the form of the string fragmentation function $\text{G}\text{?}{}^{\mathrm{<mtext>h</mtext>}}\text{～}\text{exp}\text{[?γ}{}^{\mathrm{<mtext>h</mtext>}}\text{(}\text{p}{}_{\mathrm{\perp }}\text{? z}\text{k}{}_{\mathrm{\perp }}\text{)}{}^2\text{]}$ where γ₁ and γ^h are some constants. The theory reproduces all existing experimental data and yields the “seagull effect” for the dependence of 〈p_⊥〉 on x. Predictions are given for the p_⊥ dependence of the spectra of π^± mesons produced at high energies at SPS and other future colliders.     

Inclusive K1±(892) production in pp and π+p interactions

A study is presented of the inclusive production cross sections of K^1±(892) vector mesons in pp interactions at 12 and 24 GeV/c and in π⁺p interactions at 16 GeV/c. The K^1± inclusive cross section is ～0.9 mb for both pp at 24 GeV/c and π⁺p interactions at 16 GeV/c. For pp interactions, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{)}$ and $\text{σ(}\text{K}{}^{\mathrm{1?}}\text{)}$ are seen to rise with energy, showing a threshold behaviour. In both pp and π⁺p interactions, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{)}$ largely exceeds $\text{σ(}\text{K}{}^{\mathrm{1?}}\text{)}$ at these energies and this excess is interpreted as K¹⁺ production by beam and target fragmentations. The decays of K^1±0 yield ～30% of the K⁰ observed in the final states. The p_T² dependence of both K¹⁺ and K^1? cross sections is described by an exponential with slope of ～3.3 (GeV/c)^?2. The longitudinal momentum spectra for K¹⁺ in 16 GeV/cπ⁺p and 24 GeV/c pp interactions are similar in shape in the target hemisphere. The K^1? spectra are similar over the whole kinematic region when viewed in the quark c.m.s. and point to a central production mechanism. Comparing K¹⁺ and ρ⁰ production, striking similarities are found.     

Lorentz contracted geometrical model

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities (β_i and β_j) and the sizes (A_i and A_j) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ_tot ∝ πA² for each reaction. The combined s-dependence of the σ_tot's and the β's gives the s-dependence of the elastic slope $\text{b}{}_{\mathrm{ij}}\text{(s) =}\text{1}\text{2}\text{(A}{}_{\mathrm{i}}{}^2\text{β}{}_{\mathrm{i}}{}^2\text{+ A}{}_{\mathrm{j}}{}^2\text{β}{}_{\mathrm{j}}{}^2\text{)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(s)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(∞)}$. This formula agrees with the experimental slope for p-p, $\text{p}$-p, K⁺-p, K^?-p and π^±-p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A_π² = 6.1, A_K² = 3.3 and A_p² = 10.5 (GeV/c)^?2.     

Deep inelastic structure functions of the photon

Three independent structure functions of a real photon can be measured in photon-photon collisions in e^±e^? storage rings. These are M₁ and M_L (related to the usual structure functions W₁andνW₂, as defined for any target) and a third function M₃, which arises from the strong plane polarisation of the colliding photons. We show, using a dispersion relation in the photon mass, that M₃ and the longitudinal structure function M_L both scale and are independent of the vector-dominant hadronic structure of the real photon. Therefore in a parton model, or in the quark light-cone algebra, they are given by the bare quark box diagrams which also dominate when both photons have large q²; this uniquely predicts the behaviour , $\text{M}{}_3\text{= [(}\text{1}\text{2}\text{π)Σ e}{}_{\mathrm{i}}{}^4\text{](?x}{}^2\text{)}$ for the real photon structure functions in the Bjorken limit (q₂² → ?∞, q₁²=0, x=?q₂²/2q₁·q₂=constant).     

On the transverse spread of QCD jets

Recent QCD results on two-particle longitudinal spectra inside quark and gluon jets are extended to the case of a fixed relative transverse momentum q_T with Λ ≈ 0.5 GeV ? 2|q_T| ? √Q². Broad q_T distributions, especially for gluon jets, are obtained which smooth out automatically the perturbative result and whose integrated versions scale in η_Max ≡ $\text{log}\text{(}\text{2q}{}_{\mathrm{<mtext>T</mtext>}}{}^{\mathrm{<mtext>Max</mtext>}}\text{Λ}\text{)/}\text{log}\text{(}\text{Q}\text{Λ}\text{)}$.     

An isospin analysis of the reaction pN→NNπ from threshold to 2.90 GeV/c

We have performed an isospin analysis of single-pion production processes in antiproton-nucleon scattering from threshold to 2.90 GeV/c. Reactions used are $\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^0\text{,}\text{n}\text{p}\text{π}{}^{\mathrm{?}}\text{and}\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{?}}$. Results show that σ₁, the total I=1 cross section, rises rapidly from threshold to reach a broad maximum around 2.5 GeV/c and σ₀, the I=0 cross section, rises from threshold and continues on a linearly rising trend at least up to 2.90 GeV/c. In the region of 2.9 GeV/c, σ₁ and σ₀ have comparable values, thus suggesting that considerable amount of $\text{I=}\text{1}\text{2}\text{N}\text{π}$ and $\text{N}\text{π}$ states is produced even in this low momentum region. We further determine that single pion production processes are not the source of the π₀ (2375,190) enhancement observed in the $\text{p}\text{p}$ and $\text{p}\text{d}$ total cross sections and may account for as much as 25±8% of the π₁ (2350,140) enhancement.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

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.     

A study of the reactions π+p→ K+∑+ and K−p→π−∑+ at 10 GeV/c

For the first time, the reactions π⁺p→K⁺∑⁺ and K^?p→π^?∑⁺ have been studied in the same apparatus. This has been done at an adequately high momentum (10.1 GeV/c) to allow a check of the prediction of exchange degeneracy, that the differential cross sections should be converging at high energy. We have measured the cross section for momentum transfers t between t_min and t = ?0.3 (GeV/c)². We find that for both reactions the differential cross section shows an exponential fall, with no deviations right in to t =t_min (where some other experiments have shown a dip in the cross section). Furthermore, we find the magnitude of the differential cross sections to be closely similar at t = 0, with a ratio

$\text{R=}\text{(}\text{d}\text{σ}\text{d}\text{t)}{}_{\mathrm{t=0}}\text{(}\text{K}{}^{\mathrm{?}}\text{p}\text{→π}{}^{\mathrm{?}}\text{∑}{}^{\mathrm{+}}\text{)}\text{(}\text{d}\text{σ}\text{d}\text{t)}{}_{\mathrm{t=0}}\text{(π}{}^{\mathrm{+}}\text{p}\text{→}\text{K}{}^{\mathrm{+}}\text{∑}{}^{\mathrm{+}}$

However, the slope for the positive reaction is about 19% steeper than that for the negative reaction.     

Reflection of long waves by interfaces

We derive comparison identities for waves satisfying the equation d²Ψ/dz²+q²(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by $\text{r=(1?2q}{}_1\text{q}{}_2\text{l}{}^2\text{)}\text{(q}{}_1\text{?q}{}_2\text{)}\text{(q}{}_1\text{+q}{}_2\text{)}$, where l is a legnth determined by the deviation of the interface profile from a step, and q₁, q₂ are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is $\text{t=(1+}\text{1}\text{2}\text{(q}{}_1\text{?q}{}_2\text{)}{}^2\text{l}{}^2\text{)}\text{2q}{}_1\text{(q}{}_1\text{+q}{}_2\text{)}$.     

The A-dependence of J/ψ-particle inclusive distributions

The differential cross sections $\text{d}\text{σ}\text{d}\text{x}$ and $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2$ of inclusive J/ψ production by 43 GeV/c π^? off Be, Cu and W nuclei have been measured. Fitting $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2\text{～ A}{}^{\mathrm{\alpha }}\text{(p}{}_{\mathrm{t}}{}^2\text{)}$ we observed the increase of α with p_t².     

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).     

The measurement of the rotational relaxation times of OCS from the nutation signals

The time dependence of microwave absorption was measured for the J = 2-1 and J = 3-2 transitions of OCS under on- and off-resonant conditions utilizing Stark and source modulation, respectively. The two effective pressure parameters obtained under the two conditions, which correspond to $\text{(T}{}_2{}^{\mathrm{?1}}\text{+ T}{}_1{}^{\mathrm{?1}}\text{)}\text{4πP}$ and $\text{(2πT}{}_2\text{P)}{}^{\mathrm{?1}}$, respectively, according to the Bloch equation, are different beyond experimental error; the difference $\text{(T}{}_2{}^{\mathrm{?1}}\text{? T}{}_1{}^{\mathrm{?1}}\text{)}\text{2πP}$ is 0.94 ± 0.38 (2.5σ) MHz/Torr for J = 2?1. This difference was also determined to be 1.19 ± 0.30 MHz/Torr from the dependence of the nutation frequency on the microwave power.     

Neutron-proton radius differences and isovector deformations from π+ and π− inelastic scattering from 18O

π⁺ and π^? elastic and inelastic scattering from ¹⁸O have been measured at T(π)=164 MeV. Consistent with the results at 230 MeV, it is found that the ratio $\text{σ(π}{}^{\mathrm{?}}\text{)}\text{σ(π}{}^{\mathrm{+}}\text{)}$ for the 2₁⁺ state is 1.86(16), while for the 3₁^? state it is 0.89(6). These results are interpreted as indicating differences in neutron and proton deformations characterizing the 2₁⁺ transition and partial neutron blocking for the 3₁^? transition. Optical model analysis of elastic scattering leads to the conclusion that $\text{〈r}{}_{\mathrm{<mtext>n</mtext>}}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?〈r}{}_{\mathrm{<mtext>p</mtext>}}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{=0.03(3)}\text{fm}$.     

A test of factorisation predictions for the fragmentation processes pp→π± at p momenta of 9.1 and 4.6 GeV/c

Relations have been derived between the invariant cross sections for various inclusive processes by assuming factorisation of the leading (pomeron) and non-leading (meson) trajectories. In this paper predictions for the invariant cross sections $\text{f(}\text{p}\text{p}\text{→π}{}^{\mathrm{\pm }}\text{)(2E}{}^1\text{/π√s)}\text{d}{}^2\text{σ/}\text{d}\text{x}\text{d}\text{p}{}^2{}_{\mathrm{\perp }}{}^2$ have been tested using data from $\text{p}\text{p}$interactions at 4.6 and 9.1 GeV/c.A large discrepancy between experiment and theory is apparent for the π^? data: in the π⁺ case the discrepancy is less marked but still present.     

Diffraction dissociation of neutrons into (pπ−) on protons in the momentum range 35 to 65 GeV/c

The diffraction dissociation reaction n + p → (pπ^?) + p was studied at the Serpukhov accelerator neutron beam in the momentum range 35–65 GeV/c in an electronics experiment. The differential cross sections of the reaction are analysed and presented in the five-dimensional phase space $\text{(p}{}_{\mathrm{<mtext>n</mtext>}}\text{, m}{}^1\text{, t,}\text{cos}\text{θ}{}^1\text{, φ}{}^1\text{)}$. The backward peak observed in the distribution over if cosθin GJ ¹ in the Gottfried-Jackson frame of if(pπ) is interpreted as a baryon-exchange effect. The angular distribution of the (pπ^?) system is compared with Deck-type models.     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.