Pp Total Cross Section Research Articles

Geometrical scaling at the pp collider (√s=540 GeV)

Models for high-energy elastic scattering can be easily discriminated at the CERN pp collider. In particular, the recent measurement of the pp total cross section, sigma ( square root s=540)=66+or-7 mb, combined with the dispersion relation estimates of the ratio rho identical to ReF(s, 0)/ImF(s, 0) approximately=0.15, already strongly constrains the predictions of geometrical scaling for the differential elastic cross section.

Comparison of small-angle pp̄ and pp elastic scattering at 52.8 GeV center-of-mass energy at the CERN intersecting storage rings

Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001⩽| t|⩽0.06 GeV 2 for center-of-mass energy 52.8 GeV at the CERN Intersecting Storage Rings (ISR). Using the known pp total cross section, a simultaneous fit to the pp̄ and pp differential cross sections yields the pp̄ total cross section; in addition, we obtain the ratio of the real-to-imaginary part of the forward nuclear-scattering amplitude and the nuclear-slope parameter for both pp̄ and pp. Our results show conclusively that the pp̄ total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the pp̄ and pp total cross section vanishes at very high energy.

Evidence of a rise in the antiproton-proton total cross section at the CERN intersecting storage rings

We measured the total cross section for p p scattering at s = 52.8 GeV at the CERN ISR, using the direct, total-rate method. The result obtained, σ tot ( pp ) = 44.70 ± 0.53 mb , shows that, in common with σ tot(pp), this cross section also starts to rise in the ISR energy range. We remeasured the total cross section for pp scattering at the same energy, obtaining σ tot(pp) = 43.26 ± 0.33 mb, and found for the difference, Δσ tot = σ tot ( pp ) − σ tot ( pp) , a value of 1.44±0.45 mb.

Measurement of the antiproton-proton total cross section and elastic scattering at the CERN intersecting storage rings

We measured the total cross section for pp scattering at √ s = 53 GeV at the CERN ISR. The method was based on the measurement of the total interaction rate and of the ISR luminosity. The result obtained, σ tot = 44.1 ± 2.0 mb, suggests that σ tot ( pp) starts increasing at ISR energies. A measurement of the pp differential cross section was also performed: the results show a change in the slope at | t| ≈ 0.1 GeV 2, similar to that observed in pp scattering.

Analysis of double diffraction dissociation in nucleon-nucleon collisions at the CERN ISR

Final results from combined measurements of single and double diffraction of protons neutrons into (N π) and (N ππ) final states are presented. The experiments were performed at the CERN Intersecting Storage Rings with the Split Field Magnet detector using proton and deuteron colliding beams. The general properties of the dissociating vertex in single and double diffractive reactions are essentially identical. Mass spectra and decay angular distributions are compared with the predictions of a dual resonant Deck model. Decay angular correlations and a strong slope-mass correlation are observed also in double diffraction. Detailed tests of factorization indicate its validity over the full range of all kinematical variables and in their correlations. A model-independent analysis gives strong support to the peripheral nature of diffraction dissociation, with double diffraction being concentrated in a narrow gaussian ring at the edge of the proton. Both the exclusive and the inclusive double diffractive cross sections display a marked increase over the ISR energy range. Both mechanisms yield comparable contributions to the peripheral increase of the total pp cross section, with an approximate saturation of the Pumplin bound.

Comment on the possibility of narrow structure inσtot(pp)at medium energy

The possibility that dibaryon resonant states, of the type proposed recently by MacGregor, might be detected as narrow peaks in the pp total cross section is discussed.

Charmed particles from two-gluon annihilation in proton-proton collisions

We estimate the cross section for charmed particle production in proton-proton scattering. An analysis of all possible sources of charmed particles reveals that the dominant mechanism at high energy involves the annihilation of constituent gluon partons. This process is as effective as the annihilation of constituent quark and antiquark partons in proton-antiproton scattering. Our unorthodox conclusion is that proton-proton collisions are practically as effective as proton-antiproton collisions for the production of charmed particles, or for the production of states involving heavier quarks. Gluon-gluon collisions may also produce light quark pairs. The possible relation between this process and the observed rising pp total cross section is discussed.

Measurement of the transverse spin dependence of the pp total cross section in the 1–3 GeV/ c region

The pp total cross section difference between pure transverse spin states was measured in the laboratory momentum range 1–3 GeV/ c. Significant differences were found and these differences show striking energy dependence. This structure is in disagreement with the predictions of simple exchange models.

The rise of the cross section and the Mandelstam diagrams

We evaluate multi-pomeron exchanges based on non-planar, Mandelstam-like diagrams of an underlying field theory. We take into account both the coupling of many pomerons to the external lines and the coupling of the pomerons among themselves in a scheme that can incorporate low-energy effects in a natural way. We express the total cross section in terms of one-two-three-pomeron exchange plus a term due to the triple-pomeron interaction. We have considered two possible values for the intercept: α 0 = 1.025, α 0 = 1. In both cases we can find agreement with the observed rise of the pp total cross section.

Lepton-hadron relation, average multiplicities of various charged secondary particles in pp scattering and some comments on the rising pp total cross-section at ISR energies

By applying a lepton-hadron relation, average multiplicities of charged (π, K) mesons and baryons-antibaryons in pp scattering have been found out which are in excellent agreement with experimental results. The proposed linkage between the rising total pp cross-section phenomenon and the antibaryon production has also been investigated and the result is found to be negative. The explanation of this rising pp cross-section phenomenon, in this model, is however attributed to the diffraction effects in which the black-core radius expands logarithmically with energy (R∼R0 lns) as suggested by Cheng, Walker and Wu.

Measurements of the total cross-section difference and the parameter CLL in pp scattering with longitudinally-polarized beam and target

We have measured the difference between the pp total cross-sections for parallel and anti-parallel longitudinal spin states at beam momenta of 3 and 6 GeV/ c. These results, combined with our previous measurements, at lower momenta, are useful in clarifying a striking structure appearing at around 1.5 GeV/ c. We have also measured for the first time, the spin-spin correlation parameter C LL ( t) in pp elastic scattering at 6 GeV/ c. We observe evidence for an exchange with A 1-like quantum-numbers.

? Production and the spin dependence of thepp total cross section

The general features of the spin dependence of the totalpp cross section for laboratory momenta ≧1 GeV/c may be accounted for by considering theπ- andρ-meson-exchange contributions toNΔ andΔΔ production.

Interaction of neutrons at high energies

A review is given of problems of the interaction of nucleons. The processes are discussed mainly at energies corresponding to the regions of the minimum and the rise of the total cross sections and to regions covered by the accelerators at Serpukhov and Batavia and the colliding-beam storage rings. Detailed consideration is given to np interactions, including the technique for performing experiments in neutron beams. This is done because accurate experiments in neutron beams have been carried out only recently, and the experimental features of these experiments are not widely known. The article discusses total cross sections, forward elastic scattering, backward elastic scattering (np charge exchange), and diffraction dissociation of nucleons. The equality of the total np and pp cross sections (observed experimentally in the energy range of the Serpukhov accelerator), and the near identity of elastic scattering in the diffraction region, mean from the point of view of the optical model that the distributions of nuclear matter in neutrons and protons in the peripheral regions are practically identical. The equality of the total cross sections is in agreement with the prediction of dual models involving degeneracy of the ρ and A2 trajectories. It is well known that in the np charge-exchange reaction there is also observed a longrange interaction which appears in the form of a very sharp peak at t≈0. The slope of the peak is ≈1/mπ2, where mπ, is the pion mass. The existence of this peak and also the simple kinematic law for variation of the cross section with energy: E–2(observed in experiments up to 30 GeV) are due to the dominant role of pion exchange in the charge-exchange reaction. On going to higher energies (the energy range of the Serpukhov accelerator) changes are observed in the energy behavior of the charge-exchange reaction: E–(1.5–1.6). Changes of this type were predicted in Regge models and are due to the increasing role of ρ and A2 exchanges at high energies. Recently careful studies have been made of the diffraction dissociation of nucleons at high energies (Serpukhov, Batavia, and colliding beams). These studies have revealed a number of features previously unobserved (at energies below 30 GeV), such as the backward peak in the distribution in cos ΘGJ in the Gottfried-Jackson coordinate system, the shift of the maximum in the mass spectrum toward higher masses, the approach of the cross section to a constant value at high energies, and other effects. All of the observed effects can be explained with the Deck mechanism if, in addition to one-pion exchange we take into account baryon exchanges and interference.

The rise of total cross sections and a critical pomeron

The framework of a Reggeon Field Theory with thresholds in rapidity is used to predict the rise of pp total cross section while maintaining the critical character of the pomeron.

Structure functions of proton and deuteron

RIORDAI~ et al. (i) have analysed the two structure functions of proton based on their measured result for scattered electrons at laboratory angles of 15, 18 19, 26 and 34 degrees from e-p reactions. The Bjorken (Bj) scaling and its degree of breaking have been tested extensively. They also tabulated the data for e-D interactions of similar experiments using the 8 GeV spectrometer. ATWOOD (3) has measured W1 functions of proton and deuteron for scattered electrons at 50 and 60 degrees and performed the analysis of proton W1 function. He used 1.6 GeV spectrometer in his experiment. By combining these two independent experiments the range of the Bj-variable is covered from 0.1 to 0.9 and from 0.1 to 0.8 for the structure functions F 1 and F~, respectively. The purpose of this paper is to look for the appropriate parametrization of structure functions of both proton and deuteron so as to satisfy the joined data of the above-mentioned experiments and several necessary requirements. These last conditions include the extrapolation of either Bj or Bloom-Gilman (BG) variables to their min-max values and other theoretical considerations. The minimum scale breaking obtains for the F~ function of the deuteron in case of the BG variable. The significance of our approach was discussed in connection with the relevant problems. As a by-product we also estimate the quark-proton reaction cross-section, following West 's approach (s). The best fit admits the zero quark mass, bu t with a large ehi-square. The u(d)-p cross-section thus determined seems to be supported by the observed pp total cross-section (4).

Multichannel eikonal model for pp elastic scattering and diffractive dissociation

A Regge eikonal model with an explicit mechanism for diffractive dissociation is compared in detail with the ISR data on pp total and differential cross sections for elastic scattering. The proton and its diffractive excitations are taken to be superpositions of “diffractive eigenstates” which scatter only elastically or non-diffractively. The eikonals for the scattering of these states are assumed to be dominated by a pomeron Regge pole with simple exponential residues. The data are consistent with a pomeron of near-zero slope and intercept 1.05 so that the characteristic features of the differential cross sections are due to absorption. The diffractive dissociation amplitudes needed to obtain agreement with the elastic data reproduce the basic features of the data on low-mass diffractive dissociation.

Multiplicity Distributions in Impact Parameter Space

A definition for the average multiplicity of pions as a function of momentum transfer and total energy in the high energy proton-proton collisions is proposed by using the n-pion production differential cross section with the given momentum transfer from a proton to other final products and the given energy of the latter. Contributions from nondiffractive and diffractive processes are formulated in a multi-Regge model. We define a relationship between impact parameter and momentum transfer in the sense of classical theory for inelastic processes and we obtain the average multiplicity of pions as a function of impact parameter and total energy from the corresponding quantity afore­ mentioned. By comparing this quantity with the square root of the opaqueness at given impact parameter, we conclude that the overlap of localized constituents is important m determining the opaqueness at given impact parameter in a collision of two hadrons. Experiments for high energy particle collisions revealed the structure deep inside the hadrons and the distributions of their constituents in impact parameter space. Typical phenomena which appeared in such investigations would be a scal­ ing behaviour in the structure functions for the deep inelastic electron-proton scat­ tering1J and the interesting results given by a geometrical analysis of the scattering amplitudes in an elastic PP collision. A recent work 2J showed that at extremely high energies each colliding hadron has, in the c.m. system, two interaction regions: (1) A highly absorptive core (pionization region) and (2) a partially absorptive fringe, where diffractive dissociation occurs, which has a large interaction radius and large transparancy, and which is responsible for the increase in the pp total cross section shown in ISR experiments. 3J In this paper we extend such a geometrical description to inelastic processes. That is, we propose a definition for the average multiplicity of pions produced at high energy PP collisions in impact parameter space and look at its behaviour as the impact parameter changes from zero to infinity, in other words as one goes from a violent collision to a peripheral one. For this purpose we first define the average multiplicity of pions as a function of momentum transfer and total energy in § 2. The n-pion production differential cross section with the given momentum transfer from a proton to other final products and the given total energy of the latter is defined in the multi-Regge formalism by Chew, Goldberger and Low. 4 J Nondiffractive and diffractive processes

Finite-Energy Sum Rules and Evidence for Rapid Rise of p and pp Total Cross Sections

An attempt is made to discriminate between a ln2s and a ln s rise of πp and pp total cross sections. The crossing-even forward amplitudes A are parametrized in terms of an asymptotic form Aa above the momentum ka, which is taken in the FNAL energy range. The amplitude Aa is determined by means of a set of finite-energy sum rules, and its uncertainties are estimated in relation to experimental errors of the total cross-section data used in the sum rules. The criteria of the discrimination are: i) Te imaginary part of the ln2s term of Aa is definitely positive; ii) the predicted quantities, the total cross section above ka and the real part of A, are consistent with the experimental data; iii) when the determination of Aa is repeated with ka increased, the result becomes stable. The ln2s rise proves to be much more favorable than the ln s rise for both πp and pp processes.

The contribution of Δproduction to the anomalous spin-dependence of low-energy pp scattering

The large spin-dependence of the proton-proton total cross section data for laboratory momenta less than 3 GeV/c is shown to be consistent with the interference between the K and p exchange contributions to A production. The recent measurements of the total cross section for proton-proton scattering from specific initial spin states in the momentum range 2 d p,,lb d 6GeV/c (de Boer et a1 1975, Krisch 1975) have presented certain problems for the conventional descriptions of the pp interaction in terms of t-channel exchanges. The quantity measured is the difference between the total cross section of incoming protons with spins perpendicular to the beam direction, in one case parallel (crTt) and in the other case antiparallel (G:~) This cross-section difference 6,,, changes magnitude rapidly with energy, and both Regge pole and cut models fail completely to reproduce this phenomenon (Leader and Wray 1975). It has been suggested (Wilkin 1975) that this dramatic change in spin-dependence at around pi,lb = 2 GeV/c should be associated with the opening up of the A production threshold which is the dominant contribution to the pp total cross section in this energy region. An examination of the pp elastic phase-shifts does indeed indicate that resonance-like behaviour can be seen in Im $2(0) at these energies (Kane and Thomas 1975), and it is then natural to associate such behaviour with the A production threshold. The question remains, however, whether it is possible for A production alone to produce such a large contribution to a,,,, . In this Letter we show that the spin effect 6,,, can be correctly described by a simple dynamical model for pp -+ NA and that this model is also consistent with our knowledge of the spin-averaged differential cross section for this process. The input to our calculation is taken to be n and p exchange in the t-channel. The n and p are assumed to couple as elementary particles to NN and NA. The type of coupling and coupling constants of the nNN, nNA and pNN vertices are well known and reasonably well determined and we use standard forms for these (Pilkuhn et a/ 1973). The pNA vertex is not so well known and we take our vertex function to be

Pp Total Cross Section Rise with a Renormalized Romeron

The single-loop Pomeron diagram connected through the generalized optical theorem to two-cluster production is used to construct an integral equation. The infinite class . of Pomeron loop diagrams taken into account by this equation effectively renormalizes the Pomeron singularity. A simple pole Pomeron·at IXo=l is renormalized by this procedure into a j-plane pole-doublet and leads to a rising pp total cross section. Single or double-particle diffrac:tive dissociation has been one of several mechanisms proposed to account for the observed proton-proton total cross section rise above PL=50 Ge V / c.u- 4> It is found, however, that quantitative predictions from either one are insufficient5'- 7' to explain this experimental feature, although numerical results vary according to the chosen functional form and strength at t=O of the triple Pomeron coupling.8'· 9' In this work we start from a bare Pomeron trajectory a ( t) = a 0 +a' t ex­ changed between two diffractively produced fireballs, and assumed to control the triple-Regge region. 10' An integral equ~tion is then constructed to sum the class of (bare) Pomeron loop-diagrams that correspond to diffractive production of an unrestricted number of fireballs. This equation is (approximately) solved and the contribution to the elastic amplitude of the resulting renormalized Pomeron is obtained and compared to pp total cross section data. One secondary term rvs- 1/ 2 is added to extend the description of data down to PL=10GeV/c. Proton-proton scattering may produce an event with at least one large repidity gap separating groups of particles. If the energy is larger than some certain threshold, a minimum separation in rapidity is ensured between the fireballs. The cross section for two fireballs with masses squared s1 and s2 is given in the Regge asymptotic limit by1n' 12'