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.     

Interacting partons

By analysing the asymptotic form of Feynman diagrams in quantum field theory a modified parton model is proposed, which takes into account the parton interaction leading to the breaking of the Bjorken scaling for $\text{Q}{}^2\text{? 20?30 (}\text{GeV}\text{/c)}{}^2$.     

Naive quark model and deep inelastic scattering

It is assumed that nucleon consists of three quarks with no admixture of gluons or strange quarks. Gluons as are seen in deep inelastic scattering, appear only as a result of bremsstrahlung by valence quarks. The model gives unique predictions for observable quantaties and imitates the scaling behavior at Q² ? 2 GeV² provided the coupling constant of strong interactions is relatively small at such values of $\text{Q}{}^2\text{(}\text{g}{}^2\text{(2}\text{GeV}{}^2\text{)}\text{4π ≈}\text{1}\text{4}\text{)}$. The predictions of the model agree with the data within (10 – 20) % accuracy and links consideration of deep inelastic scattering with the most naive quark model. The effect of charmed particles production is estimated within the model developed. It is shown that the standard four-quark model of weak interactions is inconsistent with observed anomalies in ν, $\text{ν}$-interactions.     

Some aspects of the quark parton model

A modified Kuti-Weisskopf model which satisfies the Feynman threshold constraints is considered further. Detailed predictions for the sum of neutrino and anti-neutrino differential cross sections on nucleon (which can be readily compared with forthcoming NAL data), the shapes of the structure functions $\text{?}{}_2{}^{\mathrm{\nu p,\nu n}}$ and the ratio $\text{?}{}_2{}^{\mathrm{\nu p}}\text{/?}{}_2{}^{\mathrm{\nu n}}$, and spin-dependence of inelastic electron-nucleon scattering versus scaling variable x are delineated. We also compare in some detail the general features of our model with the “model independent” approach of Feynman for quark parton theory.     

Nucleon charge form factors and chiral quark models

Calculations of the proton and neutron charge form factors G_E^p,n(q²) are presented, based on chiral bag as well as confining Dirac potential models with chiral pion-quark coupling. Special emphasis is placed on a detailed treatment of the charged pion cloud contribution to the nucleon current. The role of a finite extension of the pion-quark vertex in truncating the summation over intermediate quark bag states is studied. Quark core radii (including recoil corrections) are constrained by a simultaneous calculation of the nucleon axial form factor. The proton charge form factor is well reproduced for $\text{|q}{}^2\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 0.7}\text{GeV}$ with quark core rms radii between 0.5–0.6 fm. About $\text{1}\text{3}$ of the proton charge is carried by the pion cloud in this model. The neutron charge form factor is obtained with the correct sign and overall q² dependence but needs further refinements, probably at the level of the isoscalar form factor.     

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.     

Non-perturbative QCD effects at large momentum transfers

We calculate the simplest one-instanton correction to the perturbative QCD prediction for e⁺e^? annihilation to hadrons. At high centre-of-mass energies Q we find a contribution to the total cross section from a simple fermion loop of the form

$\text{δR}\text{R}\text{∝}\text{Q}{}^2\text{→∞}\text{Q}{}^{\mathrm{<mtext>?11?</mtext><mtext>Nf</mtext><mtext>3</mtext>}}\text{(1n Q}{}^2\text{)}{}^{\mathrm{<mtext>6(33?4Nf)</mtext><mtext>(33?2Nf)</mtext><mtext>or</mtext>}}\text{(1n Q}{}^2\text{)}{}^{\mathrm{<mtext>6(33?4Nf)</mtext><mtext>(33?2Nf)?1</mtext>}}$

where N_f is the number of quark flavours. The numerical value of this contribution is O(1) for Q ～ 1 to 2 GeV.     

Mesonic degrees of freedom in nuclei and retardation effects in meson-exchange currents

In the present paper we give a brief review of a consistent calculation of meson-exchange effects. For the charge density these currents are calculated up to the order of $\text{O(}\text{1}\text{M}{}^3\text{)}$ for π, ρ- and ω-exchange. The retardation currents arising from the recoil and wave function reorthonormalization currents are derived. A quantitative discussion of the retardation currents is done for the example of the deuteron form factors. As for the quadrupole form factor the retardation contribution is shown to be important. In the case of the charge form factor these effects are unimportant for our choice of deuteron wave functions.     

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.     

Decays of high spin Δ1 and N1 resonances in the quark model

Starting with a set of harmonic oscillator wavefunctions, we calculate partial decay rates of excited $\text{Δ}{}^1$ and $\text{N}{}^1$ states into a nucleon with single pion emission. Good agreement with values estimated from data is obtained for N ≤ 6, thus indicating that the simple quark model is reasonable over a much wider range than expected. The calculated decay rates of the even higher states depend more sensitively on the finer details of the nucleon wavefunction.     

On the ratio Σ0/Λ in electroproduction off protons

Recent experimental results on electroproduction off protons show that the ratio σ(ep → eK⁺Σ⁰)/σ(ep → eK⁺Λ) decreases strongly with increasing Q². A simple argument is given in the framework of the quark parton model which could provide a qualitative understanding of this fact. The decrease of the Σ⁰/Λ ratio is related to the decrease of the ratio $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}\text{/F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}$ as Q² increases, where $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}\text{and F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}$ are the usual structure functions for deep inelastic electron-nucleon scattering.     

Charge properties of the hadronic system in vp and νp interactions

Charge properties of the hadronic systems from νp and $\text{ν}\text{p}$ scattering in BEBC are studied in the framework of the quark-parto model (QPM). The average charges $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ and $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ of a quark jet and a d-qua jet, respectively, are determined according to two different methods. The difference $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{\nu }}\text{? 〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ is in agreement with e QPM value of 1. Scaling of charge and energy flow in the angular variable λ is demonstrated. The ratios $\text{ΔQ}{}^{\mathrm{<mtext>\nu </mtext>}}\text{/ΔQ}{}^{\mathrm{\nu }}$ of charge flows in νp a $\text{ν}\text{p}$ scattering are in accord with the QPM in both hemispheres.     

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 $\text{V}{}_{\mathrm{<mtext>Fe</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{≈ 1.3}$.     

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.     

Right-handed weak currents in neutrino scattering

We investigate transition strengths of right-handed weak charged currents in deep inelastic neutrino scattering, exploiting the dominance of p, n valence quarks in the nucleon. The energy dependence of σ_t and the average quantities 〈y〉 and 〈Q²〉 are shown to provide sensitive measures of new quark production thresholds and right-handed currents in $\text{ν}\text{N}$ scattering. With our analysis, the present data give an upper bound on the right to left hand structure function ratio of $\text{F}{}_{\mathrm{<mtext>R</mtext>}}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}\text{F}{}_{\mathrm{<mtext>L</mtext>}}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}\text{≈}\text{1}\text{2}$, above a threshold of W≈7.5 GeV.     

Light-cone expansions,the parton model and virtual γγ scattering

It is shown that it is sufficient to use the light-cone algebra of currents and the algebra of bilocal operators to find the asymptotic behaviour of the γγ scattering amplitude when one (or two) of the photon masses q_1,2² is large, and for an arbitrary value of the energy squared s = (q₁+q₂)². A general form of this asymptotic behaviour is obtained. The box-diagram is dominant over the wide region in $\text{s(μ}{}^2\text{« s « q}{}_1{}^2\text{q}{}_2{}^2\text{/μ}{}^2\text{,μ ～ 1}\text{GeV}\text{)}$ and so the asymptotic amplitude is known completely. It is shown that the parton model of the type of ref.[8] gives the same predictions for the asymptotic behaviour of the γγ amplitude.     

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.     

A direct method for modifying certain phase-integral approximations of arbitrary order

The approximate solution of the differential equation $\text{d}{}^2\text{ψ}\text{dz}{}^2\text{+ Q}{}^2\text{(z)ψ = 0}$ by a general modification of certain phase-integral approximations of arbitrary order is considered. A consistent modification of these higher-order phase-integral approximations is derived on the assumption that one has found a function Q_mod²(z) which makes the modified first-order approximation good at certain singular points of Q²(z), where the unmodified approximation would break down.     

On proton-deuteron backward elastic scattering at medium energies (II)

We examine rescattering corrections to the single nucleon exchange model of backward p-d elastic scattering and find them to be important at all energies. Using realistic deuteron wave functions we conclude that the rise at E_p (lab) ～ 400–600 MeV results from another mechanism, possibly the opening of the $\text{p}\text{+}\text{d}\text{→}\text{NNN}{}_{33}{}^1$ channel.