Inclusive Differential Cross Sections Research Articles

Light-particle emission in the reaction of 93Nb + 14N at 132, 159 and 208 MeV

Nonequilibrium light-particle emissions have been investigated in the reaction 93Nb + 14N at 132, 159 and 208 MeV by measuring inclusive differential cross sections of p, d, t, 3He and α. The experimental data were analyzed in terms of three models: (i) an extended exciton model, (ii) a coalescence model, and (iii) a moving thermal source model. The angle-integrated energy spectra of the protons were well described by the extended exciton model in which projectile nucleons were assumed to be transferred to the target one by one, but those of composite particles were not. On the other hand, the composite particle spectra (except for α at forward angles) were successfully described by the coalescence model using spectra consistent with those for the protons. Extracted coalescence radii P 0 were about 140 MeV/ c for d and t, and about 220 MeV/ c for α. The light-particle spectra were also fitted by the moving-source model assuming isotropic emission from a source moving with approximately half of the beam velocity and with much higher temperature than that of the compound nucleus. Extracted temperatures followed the systematics of a recent compilation for the various reactions. A discussion of these analyses is given.

The “subthreshold” production of antikaons in relativistic nuclear collisions

By use of simplified multiple collision model we calculate the inclusive differential cross section for antikaons produced in relativistic nucleus collisions at bombarding energies per nucleon below the threshold for production from free nucleon nucleon encounters. The primordial spectrum obtained is in qualitative agreement with experimental data for the reaction Si + Si at 2.1 GeV/nucleon. The inclusion of the rescattering and absorption of the antikaons significantly influences the shape of the primordial spectrum but does not substantially alter the degree of agreement with the experimental data.

The inclusive production of kaons in relativistic nucleus-nucleus collisions based on transport theory

We assume that in relativistic heavy-ion reactions positive kaons (K +) are produced in sequences of independent baryon-baryon collisions. The basic inputs into our calculation of the K + inclusive differential cross section thus are the baryon momentum distributions after a number n of collisions. These functions are, to a very good approximation, determined by their first and second moments which in turn are calculated by use of a transport theoretical approach. We compare our results with experimental data obtained from the reaction Ne + NaF at 2.1 GeV nucleon . This comparison is first made under the assumption that the kaons, once produced, escape from the participant region without further interactions. In this case, the observed K + total production cross section is reproduced quite well, but the corresponding differential cross sections are not. The inclusion of the K + elastic scattering on the surrounding baryons leads to a much better agreement with the experimental data. We also calculate the K + total production rate as a function of the bombarding energy per nucleon. At all energies, the number of kaons produced by multiply scattered baryons is seen to exceed by far that obtained from nucleons which scatter for the first time. The K + total production cross section remains sizeable in our approach even far below the threshold energy. For a very heavy system like Pb on Pb we estimate a cross section of 10 mb even 800 MeV below threshold.

Transport theory applied to Kaon production in high-energy nucleus-Nucleus collisions

The inclusive differential cross section for K +-meson production in the reaction Ne+NaF at 2.1 GeV per nucleon is calculated within a simplified multiple scattering approach based on sequences of independent baryon-baryon collisions. The momentum distributions of the baryons needed for the K + spectra are determined by use of the almost analytical, parameter-free model of transport theory. The scattering of the produced kaons by the surrounding baryons is taken into account and found to be essential for a reasonable agreement with the experimental data.

Parametrisation of hadron inclusive cross sections in p-p collisions extended to very low energies

To parametrise the inclusive differential cross sections of charged hadrons produced in p-p collisions at the CMS energy, square root s<or approximately=10 GeV, where the radial-scaling limit is not reached, a new variable xT=T*/T*max is introduced, where T* is the kinetic energy of a hadron produced in the CMS. The ratio of the low-energy inclusive differential cross section to that of its corresponding radial-scaling limit is found to be explicitly independent of pt and approaches unity monotonically and quickly from above for increasing square root s. The authors have succeeded in parametrising the inclusive differential cross sections for hadrons including pi +or-, kappa +or-, p and p, and the expressions obtained are applicable at energies from the ISR down to those near the production thresholds.

Charged particle and neutral kaon production ine + e − annihilation at PETRA

The mean charged multiplicity as well as its distribution has been measured as a function of c.m. energy in the reactione+e−→hadrons. Fragmentation models are compared with the data. After applying radiative corrections the mean charged multiplicity is measured to be 8.4±0.3±0.6 at 12 GeV, 13.1±0.3±0.6 at 30 GeV and 13.6±0.3±0.6 at 35 GeV. The ratio of mean charged multiplicity to the dispersion ( /Dch) is almost constant in the energy range studied, indicating KNO scaling of the charged multiplicity. The inclusive differential cross sections(dσ/dx p ) shows scaling violation in the highx p region (x p >0.15). The absolute value of the scaling violation is consistent with the result of 2nd order QCD calculations. The production of neutral kaons has been investigated by identifying the decayK S 0 →π+π−. The production probability for a strange quark relative to that of au ord quark in the fragmentation, γ s , has been determined to be 0.27±0.03±0.05 averaged over c.m. energies from 12 to 35 GeV. Momentum spectra for neutral kaons are presented and are compared with model predictions.

Absorbed Mueller-Regge model for backward inclusive proton production in positive pion-proton collisions

The inclusive production of protons in the backward direction in the reaction π++p→p+X is considered in a parameter-free Mueller-Regge model with absorption corrections. A large dip in the inclusive differential cross-section, similar to that predicted by us for the inclusive reaction π-+p→π0+X and later found experimentally, is predicted. The inclusive differential cross-sections for fixedu and for fixedMX2/s are given.

Tests of models for inclusive production of energetic light fragments at intermediate energies

Several models of light fragment emission are confronted with data from electron and proton induced reactions. The data appear to favor a mechanism, called the snowball model here, in which there is a single collision of the projectile and a few collisions of the secondary nucleons which then form the observed fragment. The parameter of the model is determined by fitting new isotopically separated inclusive differential cross section data.NUCLEAR REACTIONS Statistical, knockout, and coalescence models, light fragment emission, electron and proton induced reactions.

Effect of Singular Gauge Fields on Inclusive Differential Cross Sections

A classical, static non-Abelian gauge-field configuration with singularities along a line is exhibited and its effect on cross sections for massless fermion creation computed. It is shown that, while the effect of such a configuration on inclusive processes is negligible at high energy, its contribution to certain differential processes can be substantial, even to the point of dominating over the nominally leading, perturbative results.

Determination of quark-nucleon inclusive cross section from leptoproduction of hadrons in nuclear targets

The $A$ dependence of hadron leptoproduction from nuclear targets is interpreted as a measurement of inclusive inelastic and possibly also quasielastic quark-nucleon cross sections. The formulas which allow us to extract these cross sections from the data are derived and discussed. Numerical estimates indicate that the measurement of the total inelastic quark-nucleon cross section is perfectly feasible. Measurement of differential inclusive cross sections of the reaction quark + nucleon\ensuremath{\rightarrow}quark + anything is possible as well but requires experiments with rather high statistics. Implications of our calculations for the process of heavy-lepton pair production from nuclear targets are also briefly discussed.

Proton-nucleus interactions at 640 MeV accompanied by backward emission of energetic protons

Spectra of protons of energies between 50 and 145 MeV emitted from carbon have been measured at angles from 105° to 160° with respect to the 640 MeV proton beam. The measurements have been carried out both inclusively and in coincidence with protons emitted at forward angles up to ±40° with energies from 255 MeV to 330 MeV. This energy interval has been chosen in accordance with the kinematics of quasifree scattering on two-nucleon groups. Inclusive differential cross sections at 140° and coincidence cross sections at the angle pair (− 12°, 122°) have also been measured with Be, Al, Cu and Pb targets. The data have been compared with the predictions of several models.

Relation between scaling of semi-inclusive and inclusive reactions

On the basis of the scaling law for the semi-inclusive differential cross section proposed by Dao et al. and the two-component mechanisms for production phenomena, we demonstrate that Feynman scaling for the inclusive differential cross section is good for the $x\ensuremath{\ne}0$ region, but it is not valid at $x\ensuremath{\simeq}0$. Our results are quite in accord with high-energy data for $\mathrm{pp}$ collisions.

Some remarks on the high-energy behaviour of inclusive differential cross sections in QCD

Differential cross sections in QCD of quasi-exclusive processes, in the sense as introduced by Block and Nordsieck, are shown by an explicit perturbative calculation in lowest order to go as dσ/dt ∼ s2 at fixed t. This phenomenon is entirely traced back to the emission of massless quanta.

Higher-orderεterms in the triple-Regge region

Using the epsilon expansion of Reggeon field theory, we evaluate the exponent which governs the behavior of the inclusive differential cross section in the triple-Regge region at second order. It is found that the first-order result is modified by contributions coming from g/sup 4/ terms connecting three Pomeron lines, and that only diagrams with one or two Pomeron lines attached to the external particles are important at asymptotic energies.

Effective-gluon model description of inclusive meson production inπ±pandppcollisions

The recently introduced effective-gluon (EG) model is applied to inclusive meson production at large transverse momentum (p/sub t)/from ..pi../sup + -/p and pp interactions. In the EG model the dependence of the inclusive differential cross section on p/ sub t/ and center-of-momentum energy ..sqrt..s is characterized by a single universal constant B = 18 GeV/sup 2/; this constant is obtained by fitting to the inclusive data for pp ..-->.. cX with c = ..pi../sup + -/..pi../sup 0/, K/sup + -/p, and p-bar. Since the EG model requires that the inclusive differential cross sections for ..pi../sup + -/p ..-->.. X/should be characterized by the same constant B, the dependence of these cross sections on p/sub t/and ..sqrt..s should follow from the previous analysis of pp ..-->.. cX without the introduction of any additional parameters. The only new information required is the form of the momentum distribution function for partons in the incident pion. Several models for this function are considered and it it shown that all of the alternatives lead to approximately the same predictions. Comparison of theory and experiment indicates that the EG model description of the recent Fermilab data of Donaldson et al. is good to approximately 15--20 %more » per data point over a range of more than 10/sup 5/ in the magnitude of the inclusive cross section.« less

Relativistic quantum transport theory approach to multiparticle production

The field-theoretic description of multiparticle production processes is cast in a form analogous to ordinary transport theory. Inclusive differential cross sections are shown to be given by integrals of covariant phasespace distributions. The single-particle distribution function F(p, R) is defined as the Fourier transform of a suitable correlation function in analogy with the nonrelativistic (Wigner) phase-space distribution function. Its transform F(p, q) is observed to be essentially the discontinuity of a multiparticle scattering amplitude. External-field problems are studied to exhibit the physical content of the formalism. When q=0 one recovers the single-particle distribution exactly. The equation of motion for F(p, R) generates an infinite hierarchy of coupled equations for various distribution functions. In the Hartree approximation one obtains nonlinear integral equations analogous to the Vlasov equation in plasma physics. Such equations are convenient for exhibiting collective motions; in particular it appears that a collective mode exists in a φ^4 theory for a uniform infinite medium. It is speculated that such collective modes could provide a theoretical basis for clustering effects in multiparticle production.

Electron-Positron Annihilation into Hadrons

The structure functions W1 and W2 in the inelastic electron and charged pion scattering are obteined in the standard ABFST multiperipheral model with the triple-Pomeron coupling. W1 is zero in our model and νW2 consists of two components the first of which shows the Bjorken scaling behavior, while the second breaks this property. From the crossing relation the inclusive differential cross section for the electron-positron annihilation into a charged pion and anything is obtained. The ratio of the cross section for the electron-position annihilation into hadrons to that for their annihilation into the muon pair contains term which increases logarithmically with incident energies. The average charged pion multiplicity tends to a constant at high incident energies, which is equal to 4 in agreement with the experimental value 4.3 ±0.6 at 5 GeV of center-of-mass energy.

Equivalent exclusive and inclusive multiperipheral descriptions

It is shown that for each exclusive model satisfying a multiperipheral principle, there is an inclusive model satisfying a multiperipheral principle which predicts the same values for all exclusive and inclusive differential cross sections. The converse statement is also true. The relation between these models is thus one to one: formal expression is given for the transformation between one model and the other. These expressions have the form of the nonrelativistic Lippman-Schwinger equation. The proof is given first for multi- Regge models having poles and cuts as the J plane singularities. It is then generalized to models with multiparticle thresholds. The physical origin of such thresholds is discussed. Also treated are the further generalizations of the proof to models having N quantum number channels and to models having any general multiperipheral structure. (auth)

Inclusive reactions in the pionization limit

We discuss the inclusive differential cross section (IDCS) in the pionization limit via Gribov-Feynman graphs and Mueller's generalized optical theorem. Considering first the infinite energy limit in which the Gribov-Feynman graphs degenerate to reggeon graphs, we obtain the usual results for the leading and non-leading behaviour. It is recognized, however, that a number of ambiguities pertaining to energy scales, signs, and relative magnitudes of leading and non-leading contributions are unresolved in this naive theory. It is not possible, for instance to predict whether the approach to a scaling limit, if its exists, will be from below or above. In the second half of the paper, a more detailed discussion is presented with the emphasis on the finite energy behaviour. Several of the earlier ambiguities are resolved and some understanding of the ISR data is achieved. Two conclusions reached are that the data exhibits threshold rather than limiting behaviour and that the relevant energy scale is (η ▪) 1 4 rather than (η ▪) 1 4 as suggested by the more naive theory based on reggeon graphs.

Multi-reggeon effects for inclusive reactions in the pionization region

We determine the non-leading behaviour of the inclusive differential cross section (IDCS) in the pionization region by considering a number of Gribov-Feynman graphs which are related to the IDCS through Mueller's generalized optical theorem. We find in addition to “normal” regge cut dependence, (ln s) −1, a dependence of the form s (const)p 2 2⊥ ( ln s) −1 which has no analogy in two-body scattering.