Inclusive φ-meson production in 93 and 63 GeV hadron interactions

The inclusive reactions h+p→φ+X, (h=π^±,,K^±,p^±), are studied for 0?x_F?0.3 and p⊥ ? 1 GeV at 93 and and 63 GeV incident momentum. Differential cross sections dσ/dp_⊥² anddσ/dx_F are presented and are compared with predictions of the naive parton model.     

Inclusive single-particle distributions in π±p reactions at 8 and 16 GeV/c

Invariant single-particle cross sections for pion and proton production in π^±p interactions at 8 and 16 GeV/c are presented in terms of integrated distributions as functions of x, reduced rapidity ζ and p_⊥², and also in terms of double differential cross sections E d²σ/(dx dp_⊥²) and dζ dp_⊥²). A comparison of π^± and π^? induced reactions is made and the energy dependence is discussed. It is shown that the single-particle structure function cannot be factorized in its dependece on transverse and longitudinal momentum. For the beam-unlike pion, there is an indication for factorizability in terms of rapidity and transverse momentum in a small central region.     

The energy dependence of single particle spectra in e+e− annihilation

We present explicit predictions of the statistical bootstrap model for inclusive single particle spectra in e⁺e^? annihilation. The distribution (ω/σ_tot·E) (dσ/p² dp) is found to become, for E ? 3 GeV, a function only of the secondary energy ω, independent of the incident e⁺d^? energy E.     

Simple model for spin-crisis

Starting from the additive quarkSU(6) model and taking into account the pion and kaon (η) emission during the initial stage of evolution (fromq ²～m _quark ² toq ²～1 GeV²) we convert the main fraction of the proton spin into the orbital momentum of the pseudoscalar mesons. The results are in a good agreement with the experimental data. We get ∫g ₁(x)dx=0.152 for proton and +0.007 for the Λ hyperon (i.e. the quarks carry out only about 39% of the Λ spin). In the same model we explain the violation of the Gottfried sum rule ?∫(F ₂ ^p(x)?F ₂ ⁿ(x))dx=0.23 due to the charged meson exchanges at the beginning of the evolution. The Gribov-Lipatov relation between the polarized structure functions in DIS ande ⁺ e ^?-annihilation is discussed. It gives the possibility to study the spin structure of Λ hyperon produced through the decay of the jet originated by a polarized quark ine ⁺ e ^?-annihilation or in DIS.     

New results on deep inelastic processes from generalized vector dominance

A formulation of generalized vector dominance (GVD), consistent with the parton model (PM) for deep inelastic electroproduction, is presented. The parton distributions at small x are correctly predicted in terms of the photoabsorption parameters. It is found that no charmed partons exist in the sea of the nucleon. The pomeron ??_c coupling and the ?_c ? photoproduction cross section are negligible. The ratio σ_L/σ_T for deep inelatic and diffractive electroproduction is found to be small. This is related to the prediction that the highest Regge singularity coupled to longitudinal vector mesons is a cut with intercept minus one. In the time-like region it implies that the angular distribution in e⁺e^?→ π + X is ～ (3?cos²Θ), in consistence with experiment and disagreement with PM. Finally the large value of σ(e⁺e^? → hadrons) is attributed to a series of ?_c's.     

Comparison of planar features of K−p interactions with e+e− annihilations and deep inelastic μp scattering

The planar features of hadronic final states in K^?p interactions at 4.5, 5.6 and 14.3 GeV c.m. energy are compared with data from e⁺e^? annihilation and deep inelastic μp scattering. A strong energy variation of the distributions (1/σ)dσ/dp_t², 〈p_t²〉_in and Σp²_{t in} is observed over this energy range. Striking agreement is found between the K^?p data at 14.3 c.m. energy and the leptonic data at similar hadronic c.m. energies. The behaviour of these distributions from K^?p data is not well described by the simple quark fragmentation model, but shows deviations similar to those attributed to hard gluon effects in leptonic interactions.     

Cross sections and angular distributions of three-jet final states ine + e − annihilation for heavy quarks

The cross sectionsdσ _U ,dσ _L ,dσ _T anddσ _I fore ⁺ e ^?→q \(\bar q\) g are calculated for heavy quarks, and the resultant angular distribution is discussed.     

The effect of the parton transverse motion in large-p⊥ reaction

The parton transverse motion within the incident hadrons cannot be neglected when calculating large-p_⊥ reaction cross sections in the framework of hard scattering models. We give a general discussion of this effect for a large class of models. The results depend strongly on the parametrization of the hard scattering cross section at small momentum transfer in the parton-parton center of mass. With reasonable assumptions, we find that the parton transverse motion enhances the hard scattering model predictions for Edσ/dp by a factor of two and reduces

$\text{E}\text{d}\text{N}\text{d}\text{p}\text{=}\text{∫}\text{d}\text{p′}\text{E′}\text{EE′}\text{d}{}^{\mathrm{(2)}}\text{σ}\text{d}\text{p}\text{d}\text{p′}\text{E′}\text{E′}\text{d}\text{σ}\text{d}\text{p′}$

by a comparable factor, in the range p_⊥ ? 2?3 GeV/c. We study the correlations between the large-p_⊥ trigger and the background low-p_⊥ secondaries and give an estimate of the encountered azimuthal asymmetry around the beam momentum with a simple model.     

A possibility of asymptotic freedom without non-Abelian gauge theories

We discuss solutions of the renormalization group equations for a Yukawa field theory. For an increasing effective boson mass we find that the leading terms in the vertex functions in the high-energy region are given by diagrams which contain no internal boson lines. In e⁺e^? annihilation into hadrons we get the parton model formula R(s) = Σ_iQ_i², whereas in the deep inelastic e^?p scattering the simple parton model behaviour is modified by the (in general) non-canonical dimension of the quark field.     

Inclusive ϕ meson production,the parton fusion model and strange quark structure functions

The parton fusion model is used to describe the longitudinal differential cross section (dσ/dx _F ) of hadronic ? production. Thedσ/dx _F for ? production in π^± p, \(\mathop p\limits^{( - )} p\) andK ^± p interactions is evaluated in the model by using structure functions for the constituents of the interacting particles. A comparison between the model and high statistics data in the Feynmanx range 0.0<x _F (?)<0.4 allows the determination of the strange valence quark distribution inK mesons and the strange sea quark distribution in π mesons, which appears to be harder than the light sea quark distribution. The comparison also shows that a significant part of inclusive ? production is due to the OZI allowed fusion of strange quarks, while the OZI inhibited fusion diagrams are strongly suppressed.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.     

Quark and gluon jets in the breit frame of lepton-nucleon scattering

Gluon bremsstrahlung,q→Gq, and quark pair production from gluons,laggy, in deep inelastic reactions is investigated in the Breit frame (moving alongQ in the laboratory). These QCD effects diminish the overall forward momentum. There are also events with asingle largep _⊥ forward jet. One spectacular class of events is predicted in which no forward going hadrons emerge, in the Breit frame. These effects are not mimicked by nonperturbative (limitedp _⊥) parton jets at large but attainableQ ².     

Gleichzeitige Messung von Hyperfeinstruktur,Starkeffekt und Zeemaneffekt des85Rb19F mit einer Molekülstrahl-Resonanzapparatur

A molecular beam resonance apparatus with electric quadrupole lenses asA- andB-fields and with superimposed parallel electric and magnetic transition-fields was used. Molecules in different rotational statesJ, m _J are separated by theA-field. Spectra of molecules in different vibrational states are resolved by their different Starkeffect energies. By this means the following electric and magnetic properties of the molecule could be measured in the rotational stateJ=1 and vibrational statesv=0 and 1: The magnetic and electric dipole moment of the molecule, the scalar and the tensor nuclear dipole — dipole interactiond _s andd _T, the nuclear spinrotational interactionc _F andc _Rb, the nuclear quadrupole interactioneqQ, the nuclear magnetic moment μ_Rb, the anisotropy of the diamagnetic susceptibility ξ_⊥?ξ_∥, the anisotropy of the diamagnetic shielding of the external field by the electrons at the position of the nuclei σ_⊥?σ_∥. Using these quantities it was possible to calculate the quadrupole moment and a weighted quadrupole moment of the electronic charge distribution. The results are: (J=1,v=0) μ_el=8,5464 (17) debμ _J/J=?29,79(2)x10^?6 μ _B d _s/h=0,36(23) kHzd _T/h=0,69(22)kHzc _F/h=10,42(70) kHzc _Rb/h=0,479 (48) kHz.eqQ _Rb/h=?70,3410(26) MHzμ(1?σ_S)Rb=1,3474(5) μ_k (ξ⊥-ξ _∥)=12(6)×10^?30 erg/Gauß² (σ_⊥-σ∥)_Rb=?3,8(2,1)×10^?4 (σ⊥-σ _∥)_F=?2,6(3)×10^?4     

Approach to scaling in deep inelastic scattering and lepton pair production

The covariant parton model is used to investigate the approach to scalling in deep inelastic lepton scattering and in lepton pair production by hadron beams. The subasymptotic effects in these two reactions are controlled by rather different features. Of particular importance for lepton pair production is how far the partons are off shell before they annihilate, while for deep inelastic scattering what matters is rather the mass of the parton after it has absorbed the virtual photon. There are uncertainties because of problems with gauge invariance, but it seems that subasymptotic effects in lepton pair production may be large even at SPS/Fermilab energies.Transverse momentum and x distributions of partons in hadrons are discussed in a very simple model. In particular it is found that, while the model is constructed such that F₂(x) ～ (1 ? x)³ as x → 1, for values of x up to 0.85 F₂(x) is better approximated by (1 ? x)⁴.     

Line shape and excitation strength of the first excited state in9Be

The line shape and the excitation strength of the very weak first excited J ^π =1/2⁺ state at E_x=1.684 MeV in Zeitschrift für Physik Zeitschrift für Physik⁹Be has been investigated with high-resolution inelastic electron scattering at E₀=45 and 49 MeV and scattering angles θ=105°, 117°, 129° and 165°, and with high-resolution inelastic proton scattering at E₀=13MeV and θ=15° and 18°. Due to lying just above the neutron threshold the level has a strongly asymmetric line shape which in both experiments can be described consistently with a Breit-Wigner expression modified on the low energy side by the threshold behaviour of the cross section. The resonance energy is E_R=1.684 ± 0.007 MeV and the width T=217± 10 keV in thec.m. system. A single particle potential model calculation reproduces the line shape and the resonance parameters fairly well. In addition, the inelastic electron scattering form factor has been measured. In the range of momentum transfersq =0.24-0.46 fm^?1 it is dominated by a 0p_3/2→ 1s_1/2 particle-hole transition. The transition is mainly longitudinal and of isoscalar nature with a strength of B (E1)↑ =0.027 + 0.002 e² fm², but a small M2 contribution ofB(M2)↑=8.8 ±1.5 μ _N ² fm² has also been detected.     

Preliminary results on SKAT neutrino experiment at 2–30 GeV

The data on inclusive deep inelastic neutrino scattering at 2–30 GeV were obtained with the bubble chamber SKAT. Distributions in q², x, y and mean q² dependence on neutrino energy are in agreement with quark parton model.     

Parton densities beyond perturbation theory

I compute non-perturbative corrections to the kernel governing the evolution of non-singlet parton densities. The model used is QED in the limit of many charged particles. I find an infrared renormalon at b₀t = −1, where t is the Borel variable and b₀ is the first coefficient of the β-function. This term has a non-trivial dependence on the variable x = -q²/(2p · q) and its coefficient scales as x³/(1 − x)² (p is the momentum of the hadron and q is the momentum transfer). An extrapolation of my results to QCD implies a breakdown of the parton model near the elastic region.     

Perturbative quantum chromodynamics

A large variety of modern perturbative aspects of QCD is critically reviewed from a theoretical as well as phenomenological point of view. The first part of this review is devoted to the classical more formal approach of summing leading logs: After a brief discussion of the basic concepts of renormalization theory, we review the renormalization group and its predictions for the effective (running) coupling constant in any field theory (asymptotic freedom as well as ‘fixed point’ theories). Using, in addition, the operator product expansion for deep inelastic scattering we calculate scaling violations of structure functions and show how to compare these results with experiment. Furthermore, dynamical calculations of parton distributions are discussed, as well as σ_L/σ_T, jets in leptoproduction and subleading corrections. We then proceed to show how these renormalization group improved results can be also derived using a simple perturbative language (Kogut-Susskind; Altarelli-Parisi) or by summing parton (Bethe-Salpeter) ladders. The universal validity (process independence) of the resulting Q² dependencies of parton distributions is emphasized and their factorization from the uncalculable non-perturbative piece (infrared divergences) is discussed. These latter results enable us to make rather unambiguous predictions for processes other than deep inelastic scattering, to which the remainder of this review is devoted. The hard scattering processes discussed indetail include hadronic (Drell-Yan) production of lepton pairs as well as their transverse momenta, the hadronic production of heavy quark flavors, semi-inclusive processes and fragmentation functions, high-p_T reactions and some recent topics and problems of jet production in e⁺e^? annihilation.     

Model for nucleon valence structure functions at allx,allp ⊥ and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon valence structure functions at allx, allp _⊥ and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =3 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ². Excellent agreement is obtained with existing data.