High energy predictions for ¯pp andpp elastic scattering and total cross sections

Predictions for thes behavior at high energies are made for¯pp andpp: the differential elastic scattering cross section dσ/dt vs.t, the squared 4-momentum transfer; the total elastic cross sectionσ _el; the nuclear slope parameterB; the curvature parameterC; ?, the ratio of the real to the imaginary portion of the forward scattering amplitude; and the total cross sectionσ _tot. A hybrid approach is employed in order to gain reliable predictions. The energy dependence of? andσ _tot is fixed by fittingpp and¯pp experimental data for? andσ _tot from 15 GeV toS¯ppS energies, using analytic amplitudes. The other quantities are found using the Chou-Yang model, where the total, cross section is fixed from the fit.     

Measurement of the total cross section difference ΔσT(pp) in the energy range from 0.43 to 2.4 GeV

The SATURNE II polarized proton beam and the Saclay frozen spin polarized proton target were used to measure the total cross section difference Δσ_T = −2σ_{1 tot} at 26 energies between 0.43 and 2.4 GeV. Here Δσ_T is the total cross section difference for transverse beam and target spins parallel and antiparallel, respectively, and σ_1tot is one of spin-dependent terms in the total cross section σ_tot. The energy dependence of Δσ_T below 1 GeV shows similar structures as for Δσ_L. An additional minimum appears at about 1.3 GeV, which involves a structure in singlet spin partial waves.     

The complete O(ɛ2) reggeon field theory scaling law dσel/dt and its applications at collider energies

We give the complete asymptotic reggeon field theory (RFT) scaling law for the elastic cross section in O(?²), extending previous results to include the 3-pomeron cut. This provides the most detailed realistic test of this theory. Numerically we find the encouraging result that the small-t SPS collider data for dσ_el/dt are in agreement with these new asymptotic RFT predictions. However, ISR data are not compatible with this theory, either in s or t dependence. Previous positive ISR results were largely due to the existence of a j = 1 fixed cut which is not present here. Our results, coupled with the observation that critical RFT fits to σ_tot require large non-leading terms, imply that a lower bound for the RFT asymptotic scale in single renormalized propagator processes (σ_tot,dσ_el/dt) lies around SPS-collider energies. The asymptotic scale for multi-propagator processes (the rapidity plateau, ab→aX reactions, multiplicity distributions etc.) is expected to be well beyond the SPS collider. A possible global RFT picture is them that perturbation theory (including finite rapidity scale effects due to the excitation of new quantum numbers) is applicable through ISR and up to the SPS collider, consistent with recent observations. The critical RFT can become the relevant diffractive theory for σ_tot and dσ_el/dt at larger t at and above the SPS collider. Predictions for dσ_el/dt at larger t at the SPS collider are given in this paper and we urge experimentalists to test them.     

Measurements of elastic scattering in alpha-alpha and alpha-proton collisions at the CERN intersecting storage rings

We measured the elastic scattering of $\text{αα}\text{at}\text{s}\text{= 126}\text{GeV}$ and of αp at $\text{s}\text{= 89}\text{GeV}$. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV². At small |t| = 0.05?0.07 GeV², this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α_tot(αα) = 250 ± 50 mb and an integrated elastic cross section σ_e1(αα) = 45 ± mb. Another method of estimating σ_tot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV², and for 0.05 < |t| < 0.18 GeV² behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σ_tot(αp) = 130 ± 20 and σ_e1(αp) = 20 ± 4mb. Results on pp elastic scattering at $\text{s}\text{= 63}\text{GeV}$ agree with previous ISR experiments.     

Complex Regge poles and high energy scattering data

For the high energy data on σ_tot^pp the proton-proton total cross section, and on ?, the ratio of real to imaginary part of the forward elastic amplitude, including the recent ISR results, an excellent fit is obtained with P, P', ω Regge poles plus a pair of complex conjugate Regge poles. The complex poles describe the possible oscillatory behavior of the quantities σ_tot^pp and ?. The physical meaning of these complex poles and extrapolation to future measurements of the above quantities are discussed.     

<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Antiproton-proton cross sections at 200 and 900 GeV c.m. energy

Data on antiproton-proton cross sections at the c.m. energies 200 and 900 GeV are presented. The data were obtained at the CERN antiproton-proton Collider operated in a new pulsed mode in which the same beams were accelerated and decelerated between beam energies of 450 and 100 GeV. The properties of the machine determine the ratio of the luminosities at the two energies to about 1% and thus an accurate measurement of the ratioR of the inelastic cross sections could be made. We findR (=σ ⁹⁰⁰/σ ²⁰⁰)=1.20±0.01±0.02, where the first error is statistical and the second systematic. Interpolating existing data to estimateσ _ine1(200 GeV) this measurement ofR leads toσ _ine1(900 GeV)=50.3+0.4+1.0 mb. Using an extrapolated value ofσ _e1/σ _tot we estimate the total cross section at 900 GeV to be 65.3±0.7±1.5 mb. Both the inelastic and total cross sections are compatible with a ln² s dependence. Comparisons are made with different fits to the total cross section energy dependence.     

ω Meson photoproduction from deuterium at 3.9 GeV photon energy

Measurements are presented of the cross sections for ω meson photoproduction from deuterium at an average photon energy of 3.9 GeV. The cross section for the coherent process γd → dω is found to be 1.4 ± 0.5 μb and that for the incoherent process γd → npω is 3.3 ± 0.7 μb. The forward differential cross section for γd → dω is estimated to be (dσ/dt)_t=0 = 54 ± 20 μb/GeV². This result indicates that the value of the A₂ exchange amplitude in ω photoproduction from hydrogen is less than that predicted from the measurements of the difference between the total hadron photoproduction cross sections from neutrons and protons. We note that the world data tend to show that the A₂ exchange amplitude is more consistent with zero than with the value needed to explain these differences. Measurements are also presented of the ratio of the coupling constants of the photon to the ? and ω mesons which tend to favour the vector dominance model proposed by Das, Mathur and Okubo with exact SU(3) symmetry at infinite energies.     

Cross sections for semihard interactions in hardronic collisions beyond the leading order of perturbative QCD

An estimate of cross sections which correspond to semihard interactions such as gluon (mini) jet production is presented. It takes into account recent results concerning gluon distributions in the small x region beyond the leading log Q² approximation and rescattering corrections in the hadron-hadron channel. The estimated cross sections are at very high energies significantly smaller in their magnitude than a simple integration of the two-jet inclusive cross section might imply yet they are still expected to constitute a substantial part or σ_tot in the TeV energy regime.     

Differential cross section and vector analysing power of the p pol p → {pp} s π0 reaction at 353–700 MeV

The reaction p _pol p → {pp} _s π⁰ was studied with the ANKE spectrometer at COSY-Jülich using a polarized beam with energies 353, 500, 550 and 700 MeV. The proton pairs {pp} _s were detected at low excitation energy E _pp < 3 MeV, where S-wave dominates. The angular dependences of vector analysing power A _y and differential cross section dσ/dΩ of the reaction have been obtained for the most of the angular range at 353 MeV and forward angles at the higher beam energies. The partial wave amplitude analysis, done with the 353 MeV results, is important for Chiral Perturbation Theory tests at this energy. The data at higher energies detalize the energy dependence of dσ/dΩ(0°) obtained earlier. It allows to learn about the dynamics of the Δ(1232) resonance excitation in two-nucleon systems.     

High-mass diffraction and Regge behavior of total cross sections

We consider a modified two-component model of particle production in which diffractive excitation into high mass states gives a contribution to K^±p, π^±p and pp total cross sections of sufficient magnitude and with the proper associated threshold to be a possible explanation of deviations of σ_tot from Regge pole model fits at Serpukhov energies. We present tests of the model. for K⁺p scattering by extrapolating σ_tot to National Accelerator Laboratory energies and by calculating the high mass diffraction contribution to the forward peak in inclusive reactions. The consistency of this scheme is discussed in relation to the pomeron intercept and the form of the triple-pomeron coupling.     

Universality of the rate of growth of all hadron-nucleon total cross sections in the range 10 to 1500 GeV/c

The energy dependence of total cross section of hadron-nucleon collisions has been studied in terms of two components: the first component decreases with increasing energy of the incident hadron whereas the second component increases like ln s. The coefficient of ln s is found to be the same within 5% for p^±p, π^±p and K^±p collisions. The rate of growth of the rising component i.e., dσ /d(ln,s), of inelastic cross sections, deduced from σ_tot and σ_el, of pp and πp are found to be the same within 1.5 standard deviations; an attempt has been made to understand this near equality from factorization of the pomeron.     

A new “parametrization” of the differential cross section for elastic scattering

A new parametrization of the differential cross section for elastic scattering is proposed. The parametrization incorporates correct analytic properties of the differential cross section and is based on optimized polynomial expansions of an analytic function. It is, in principle, valid for all energies and all angles. The parametrization has been tested for pp, $\text{p}\text{p}$, pd, π^± and K^±p elastic scattering at high energies and small angles. The results of the new fits are compared with those of the old ones. It has been found that with the same number of parameters one obtains practically the same values of χ². However, the new values of physical quantities, such as slope, α and (dσ/dt)₀, in most cases differ considerably from those obtained by the old parametrization. In particular, it has been found that the slope of the differential cross section for pp, $\text{p}\text{p}$, pd and K^±p elastic scattering increases continuously as the forward direction is approached.     

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

We measured the total cross section for $\text{p}$p scattering at $\text{s}\text{= 52.8}\text{GeV}$ at the CERN ISR, using the direct, total-rate method. The result obtained, $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{p}\text{p}\text{) = 44.70 ± 0.53}\text{mb}$, 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, $\text{Δσ}{}_{\mathrm{<mtext>tot</mtext>}}\text{= σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{p}\text{p}\text{) ? σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{pp}\text{)}$, a value of 1.44±0.45 mb.     

Elastic and inelastic φ photoproduction

The differential cross section of the reaction (γp → pφ) has been measured in the t range 0 ? t ? 0.4 GeV² and for photon energies from 3.0 to 6.7 GeV. In particular for the small t region the measurement accuracy was better than 10%. We obtained for the slope parameter B in an exponential parametrization of the differential cross section dσ/dt = Ae^?Bt values of $\text{B ? 6 ± 0.5}\text{GeV}{}^{\mathrm{?2}}$ which are significantly larger than the slopes obtained by most other experiments at higher t values. This indicates a t dependence of B particularly in the small t region.An energy dependence of the optical point (dσ/dt)_t=0, observed in our measurements, has been explained as a kinematic effect due to the VDM relation. A fit of our measurements is in excellent agreement with all other published values of (dσ/dt)_t=0(γp → φp), this implies that σ_tot(φp) must be essentially energy independent in this energy range.Spin density matrix elements of the φ have been evaluated and an analysis of the helicity amplitudes has been carried out. This analysis confirmed s-channel helicity conservation. Moments of spherical harmonics of the $\text{K}\text{K}$ angular decay distribution have been computed for 10 MeV $\text{K}\text{K}$ mass-bins from threshold to 1.3 GeV. The mass dependence of the normalized moments is generally smooth. Contributing amplitudes have essentially only even moments. The moment 〈Y₂⁰〉/〈Y₀⁰〉 changes sign above the φ mass.Differential cross sections for the inelastic φ production γp → φX have been evaluated for the first time both with respect to t?t_min and M_K. The integrated inelastic cross sections are comparable in size with the elastic ones. The slopes of the differential cross sections dσ/dt appear to become flatter with increasing M_X.     

K +-meson production inpBe interactions atT p=2.9 GeV

The production ofK ⁺ andπ ⁺ mesons and protons inpBe collisions atT _p=2.9 GeV has been studied at the ITEP proton synchrotron. Ejectiles with a momentum ofp=545 MeV/c were observed under an emission angle ?=17°. The detectors which have been developed for the identification of kaons out of a six orders of magnitude more intense background of pions and protons are described. A cross-section ratio d²σ _K ⁺/dΩdp: d² σ _p /dΩdp: d²σ _p /dΩdp of (1±0.34):(85±1):(31±1) has been measured. Normalization with existing pion data yields an invariant differential cross sectionE·d³σ _K ⁺/d³ p=(3.1±1.2) mbGeV^?2c³sr^?1 and a total cross section of σ_tot(pBe)=(3.7±1.5) mb. These cross sections are compared with existing data and theoretical predictions. TheA dependence ofK ⁺ production in the few-GeV range is analyzed.     

The nonelastic projectile break-up cross section from particle-gamma coincidence measurements for the 6li + 40ca reaction at 156 mev

The cross sections for nonelastic break-up modes have been studied for the ⁶Li + ⁴⁰Ca reaction at E_Li = 156 MeV. Gamma-ray spectra from target-like residual nuclei were measured in coinci- dence with beam-velocity projectile fragments and a value for the nonelastic break-up cross section σ^b.u_non = 582 ± 110 mb has been found. Together with results of inclusive charged-particle measure- ments we infer for the total break-up cross section σ^b.u_tot = 930 ± 115 mb comprising about 50% of the total reaction cross section. The nonelastic contribution of the break-up reaction appears to be less than predicted by the DWBA break-up theory. This result is directly evident from the differential cross sections by comparing inclusive and exclusive results.     

Topics in the S-matrix theory of massless particles

We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low-energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering, and two-photon exchange between neutral systems. These zeros make two-body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two-body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find σ_tot <s^? (where ? is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely.