Chou-Yang Model Research Articles

Charge, magnetization and hadronic-matter densities inside the proton

We present a scheme by means of which one can infer the charge and magnetization structures of any quantum system from its electromagnetic form factors. For spin-1/2 and spin-0 particles the new results here obtained lead us to a correct nonrelativistic limit as well as to a consistent description of the mean charge radii. Our analysis of the existing data on elastic electron-proton scattering suggests that the charge density should be more concentrated than the magnetization density within the proton. The hadronic-matter density of the proton is obtained from the experimental data on pp elastic collisions at high energy, by assuming the Chou-Yang model. It is found that, as the energy increases, the hadronic-matter distribution becomes more similar to the magnetization than to the charge density inside the proton. The same seems to be true for the neutron.

Gluon Distribution inside Proton and Deuteron

The neutral matter distribution inside proton and deuteron is deduced from the ela,;tic pp and dd differential cross sections at v s =53 GeV. A model is proposed, which predicts correctly the elastic pd differential cross section quantitatively for the diffraction peak and qualitatively in the large t region. A new criterion is given to distinguish models \\·hich contain a distribution function. Our model leads to the result that the space integral of the deuteron matter distribution function is twice that of proton, as is expected from their masses. It is pointed out that the original Chou-Yang model does not have this feature. Recently very precise measurements have been performedn for the differential cross sections in the elastic pp, pd and dd scatterings at CERN-ISR energies in the large t region. In this paper we deduce a neutral matter distribution of proton from the pp scattering data and that of deuteron from the dd scattering data. On the basis of the distribution functions of the proton and deuteron lYe predict the differential cross section of the elastic pd scattering and compare it with the experimental data. We get quantitatively a very good prediction for the diffraction peak in pd scattering and see qualitatively a good feature in the large t region. There have been many studies to deduce the internal structure of the nucleon. First the electron scattering from the proton gives the charge Se­ condly the large Pr phenomena of the inelastic scatterings give the information for the internal structure of hadron. 3J Thirdly the deep inelastic scatterings supply several results 1> for the quark-parton distribution in the limited momentum space. On the other hand, the pp elastic scattering has been analyzed by the Chou-Yang model6J and so on. By means of one variation of the Chou-Yang model it is suggested 7J that the number of quarks is three inside the proton. But as far as the author knows, it seems that there are few works 8J for the deduction of the matter distribution inside the proton from the viewpoint of the elastic hadron-hadron differential cross section. Since the equality Utot (PP) =Gtot (np) is experimentally confirmed 9J for ys>5 Ge V, we interpret that the obtained matter distribution is not charged but neutral, which is called a gl uon distribution. Since the Chou-Yang model 6> is constructed based on the matter distribution function, this model can give us the matter distribution of proton from PP scatter­ ing data. In the Appendix the explicit method is given to deduce the distribution.

Chou-Yang model and s-channel helicity conservation

The Lorentz and SU(3) structure of the “matter” form factor in the Chou-Yang model is examined. It is argued that the time component of an SU(3) singlet current J μ , evaluated in the infinite-momentum frame, should be used. The s-channel helicity flip amplitude in NN → NN is shown to be suppressed if the quark model result on the additivity of magnetic moments is generalized to the singlet current.

Is the Energy Dependence inp−pScattering Due to Spin?

A spin-dependent eikonal amplitude for the scattering of two fermions by vector-meson exchanges is extended to include spin dependence due to pseudoscalar exchanges as well. The result is applied to elastic p-p scattering by using a primitive, energy-dependent Chou-Yang model augmented by pion exchange. The spin dependence introduced dramatic energy dependence resembling that observed.

Implication of the Chou-Yang model inπpelastic scattering

With some knowledge of the pion form factor, we study $\ensuremath{\pi}p$ elastic scattering within the Chou-Yang model. We find it agrees very well with recent Fermilab measurements and we predict the existence of a dip at $\ensuremath{-}t=4\ensuremath{-}5$ ${\mathrm{GeV}}^{2}$. The sensitivity of the dip structure due to the variation of the shape of the pion form factor is studied.

High-energy collisions of intrinsically deformed particles

The Chou-Yang model of the elastic profile function for high-energy collisions is modified to take into account the possibility that the projectile, the target, or both, are deformed from sphericity. Simple expressions for the elastic amplitudes and total cross sections are derived under the assumption that the collision times are much shorter than the rotation periods of the projectile and target (adiabatic approximation). A simplified, purely geometric interpretation of the results on total cross sections is given and justified in terms of the quantum-mechanical treatment.

The Chou-Yang Model and High Energy p-p Elastic Scattering

The Chou-Yang Model and High Energy p-p Elastic Scattering

The Chou-Yang model and the form factors of elementary particles

The form factors of the proton, pi - and K-mesons are extracted from high-energy pp, pi +or-p and K+or-p elastic scattering data on the basis of the Chou-Yang model. Within the meaningful error bars generated by our 'density-model-independent analysis' the meson form factors are in reasonable accord with available direct measurements and the predictions of simple vector dominance. Minor discrepancies between the results for particles and antiparticles are evidence for secondary effects at low energies. In the case of the proton the identification with the measured GE or GM gets better as the energy increases.

Hadron scattering in an additive eikonal quark model

Total and differential cross sections for p̄p, pp, π ±p, K +-p and Ψp at high energies are analysed in an additive eikonal quark model. It is shown that the exceptionally small Ψp slope contradicts the Chou-Yang model at present energies but can be accounted for by a quark-quark potential with different ranges for different pairs of quarks. This leads to smaller rms radii for hadrons than those derived from e.m. formfactors, implying that the constituent quarks have formfactors. Predictions for hadron-neutron and strange and charmed hadron-nucleon scattering are derived.

Coulomb effects in hadron-nucleus and nucleus-nucleus collisions and the hadron-neutron amplitude

Coulomb effects in high energy charged hadron-nucleus collisions are studied in a formalism which is exact within the framework of multiple diffraction theory and takes into account the extended charge effects of the incident hadron and the bound protons. Several more approximate but simpler formulas are also considered and their accuracy discussed. Results are extended to include heavy-ion collisions in the optical limit of the Glauber theory and in the Chou-Yang model. Applications are made to the proton-deuteron elastic and elastic plus quasielastic scattering measurements below 70 GeV to extract the ratio of real to imaginary part and the slope parameter of the proton-neutron elastic scattering amplitude. The results are compared with those from dispersion relation calculations and from earlier analyses. Approximate analytic formulas derived for $p\ensuremath{-}d$ scattering give results almost identical to the more exact expressions. For nucleus-nucleus collisions the Coulomb effects are found to be important over a rather wide range of momentum transfers.NUCLEAR REACTIONS $d(p, p)$, $E=10\ensuremath{-}70$ GeV; calculated $\ensuremath{\sigma}(E, \ensuremath{\theta})$ in Coulomb-nuclear interference region; deduced $p\ensuremath{-}n$ scattering amplitude parameters. $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, $^{208}\mathrm{Pb}(p, p)$, $E=1.04$ GeV, $^{12}\mathrm{C}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$), $E=2.1$ GeV/nucleon; Coulomb effects, calculated $\ensuremath{\sigma}(\ensuremath{\theta})$.

A diffractive model including spin for pp elastic scattering at very high energy

In this paper we present a theoretical diffractive model for spin-dependent proton-proton scattering at very high energies using an extended version of the Chou-Yang model. The model describes a wide t range, but in this paper we use it for small t values. We obtain estimates of the ratio of spin-dependent to spin-independent amplitudes, β, consistent with a previous phenomenological analysis. Next we estimate the asymmetry, Σ, expected in a certain polarized inclusive process at high energy. We then compute the size of polarization effects in pp total cross-section measurements, using polarized beam and target at very high energy. Our estimates of the latter two quantities indicate that their measurement would not provide a sensitive test of pomeron factorization.

Proton-proton scattering, the Chou-Yang model, and proton form factors

Recent high-energy proton-proton elastic scattering angular distribution data for $0<\ensuremath{-}t\ensuremath{\le}5.3$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ are used with the Chou-Yang model to investigate the proton electromagnetic form factors. Comparisons with the measurements of the form factors are given. The use of the proton-proton data in the analysis reveals either the need for measurements at larger momentum transfers or possible inconsistencies when the model is applied at finite energies. Analytical fits to the angular distribution data are also presented.

Extension of the Chou-Yang model to multiparticle processes

A natural and essentially unique extension of the Chou-Yang model to multiparticle processes is presented. The multiparticle amplitudes are derived from the physical ideas of the original Chou-Yang approach. The beam and target particles are treated as extended, non-recoiling, Lorentz-contracted objects which interact and produce particles as they pass through each other. The resulting multiparticle amplitudes satisfy s-channel unitarity exactly. A minor modification allows us to include diffractive inelastic effects. When diffraction is included the connection with the electromagnetic form factor must be given up. The model is in good qualitative agreement with various features exhibited by the data. The model requires the total cross section to rise in a definite way. However, quantitative agreement at ISR energies is far from satisfactory. This is probably due to the “no-recoil” assumption inherent in the Chou-Yang model.

Shrinkage, complex poles and the Chou-Yang model

The shrinkage of the diffraction peaks is reproduced by the interference of a geometric pomeron and of complex poles representing S-channel threshold effects (like heavy pair production). Asymptotically, one recovers the Chou and Yang model. The shrinkage is expected to stop at P lab ⋍ 10 5 GeV/c . The total cross section σ T is conjectured to have a maximum of 45–48 mb (for pp) at about the same energy where the shrinkage stops. The asymptotic value of σ T would only differ from the maximum value by about 1 mb. The break structure at |t| ⋍ 1.2 GeV 2/c 2 seen at low energies for pp elastic scattering is explained in term of secondary Regge exchanges only. At high energies, the dip at | t| ∼ 1.3–1.4 GeV 2/ c 2 is given by the geometric pomeron. Because of the eikonalization procedure one obtains an intermediate | t| shrinkage and a dip displacement in good agreement with experiment.

Phenomenological Consequences of the Shielded Fixed-Pole Pomeron at Very High Energies

Phenomenological consequences of shielding-cut mechanism of Oehme type are investi­ gated within the framework of eikonal approximation. Under the assumption of the usual dipole form factor for the hadronic matter density, it is shown that eikonalization of the fixed-simple-pole Pomeron with two Arnold and Barnett's shielding cuts provides a simple and natural generalization of the Chou-Yang droplet model and yields a successful explana­ tion of all of the recent CERN-ISR results on p-p diffraction scattering. Our fit to the data is performed by using the only one adjustable parameter. Quantitative predictions about phenomenological features of elastic P'P scattering are also given at extremely high energies such as ISABELLE energies. On the basis of these observations, it is argued that the Pomeronic amplitude is well .described by an absorbing disc. at very high energies, the effective radius of which shows no appreciable . energy dependence and is approximately fixed at 1.0 fm, and the total magnitude of which slowly grows to an asymptotic value with increasing energy.

Test of a generalized Chou-Yang model at currently available high energies

The Chou-Yang model generalized to include energy dependence is shown to give a very good description of the CERN ISR $pp$ data. We show that in this type of model the height of the secondary maximum increases by roughly a factor of 2 over the ISR range. This feature, which can be experimentally checked, will distinguish models of this type from the usual Regge models where such an increase in bump height is not expected.

Shift of peaks and dips in elastic scattering in the Chou-Yang model

The effect of the logarithmic increase of total cross section of the $\mathrm{pp}$ interaction on the Chou-Yang model is investigated. It is found that (i) the positions of dips and peaks move inward towards smaller $|t|$ values as the energy increases and (ii) the height of the peaks increases logarithmically as a function of energy. Comparison with the model of Cheng and Wu is made.

A comment on the energy dependence of the Chou-Yang model

A comment on the energy dependence of the Chou-Yang model

Structures in the proton-proton elastic cross-section and two components of the pomeron

Two energy-dependent structures have been observed in proton-proton elastic cross sections at ISR energies-namely, the change of slope of the diffraction peak in the form of a break at t approx equal - -0.15 (GeV/c)/sup 2/ , and the dip at t approx equal - 1.3 (GeV/c)/sup 2/. Arguments are presented in favor of a unique explanation of both phenomena, under the assumptions that the central distribution of the protonic matter is given as in the Chou-Yang model with the form factor independent of the energy, and that the energy - dependent component of the pomeron has the form of a moving simple Regge behavior of the elastic pp scattering at 1480 GeV/c are calculated and compared with experiment, It is concluded that the results of the present work support the idea of two component of the pomeron with the central component independent of the energy. (LBS)

High-energy elastic proton-proton scattering and the Chou-Yang model

Abstract The Chou-Yang model with an empirical fit for G m p ( t ) isshown to be in remarkable agreement with recent high-energy proton-proton experiments. This result is compared with the Chou-Yang model employing dipole and Gaussian forms for G m p ( t ) , and also with the Glauber multiple-scattering-series approach, considering a three-quark model for the proton. We find the agreement of the Chou-Yang model with the data is considerably improved on taking a more accurate account of the electron-proton scattering data using an empirical fit for G m p ( t ).