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.     

K−p and pp elastic scattering at 10.1 GeV/c

The differential cross sections for K^?p and $\text{p}$p elastic scattering have been measured over the range of four-momentum transfer squared 0.18<?t<3.3 (GeV/c)². The K^?p data decrease smoothly as a function of ?t, whereas, the $\text{p}\text{p}$ data shows a break at ?t = 0.6 (GeV/c)² followed by a fast drop to ?t ? 1.6 (GeV/c)² where the differential cross section levels off and stays constant out to ?t = 3 (GeV/c)².     

Low-energy kaon-nucleon scattering in the I = 0 state

The KN system in the I = 0 state is studied with the method of Padé approximants. The treatment follows the lines of the previous work of the same authors on the I = 1 interaction. From the same Lagrangian, the unitary [1,1] Padé approximants for the scattering functions in the $\text{s, p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ waves are calculated at low energies in terms of a single coupling constant. The model predicts negative and rather strong s-wave scattering lengths and phase shifts, while the two p-waves are small and of opposite signs. The differential and total cross sections for elastic and charge-exchange processes in K⁺ scattering by neutrons and the differential polarization in K⁺n → K⁰p are compared with data extracted from experiments on K⁺ scattering by deuterons. The model predicts that the cross section in the I = 0 state decreases slowly with energy.     

Regge description of nucleon-nucleon polarisation

Recent polarisation data for pp and pn elastic scattering within the momentum range 6 to 45 GeV/c are economically described by a simple Regge model. A crucial feature of the model is the inclusion of a non-factorising pomeron which couples both to helicity flip and to non-flip. This allows an understanding of the observed t-dependent structure and rapid energy dependence of the pp polarisation. Predictions are made for pp and pn polarisation measurements at higher momenta. Fragmentary data on $\text{p}\text{p}$ elastic polarisation are compared to predictions.     

Elastic antiproton-deutron scattering below 1.0 GeV/c

We present differential cross sections for elastic $\text{p}$d scattering at beam momenta 0.735 and 0.940 GeV/c and momentum transfers in the range 0.04<|t|<0.5(GeV/c)². The $\text{p}$d elastic differential cross section is expressed in terms of a deutron form factor and the I=0 t-channel exchange $\text{N}$N amplitudes, enabling us to isolate the corresponding I=0 t-channel exchange cross sections.     

Elastic pp scattering in the cern sps energy region

The pronounced dip-bump structure with a sharp minimum at |t| = 1.5 (GeV/c)², recently observed in elastic $\text{p}$p scattering at P_L = 50 GeV/c at the CERN SPS, is explained by the quark multiple scattering model with a realistic wavefunction for the proton and the antiproton. It is predicted that a second dip will appear around |t| = 7 (GeV/c)² at P_L = 50 GeV/ c and at higher energies.     

A study of the Regge recurrence of the Δ(1236) produced in 10 GeV/c K+p interactions

Data are presented on a high mass $\text{I}\text{3}\text{2}\text{Δ}$ resonance produced in 10 GeV/c K⁺p interactions. The mass and width of the resonance, determined by a maximum likelihood fit to the pπ⁺ spectrum in the final state K⁺pπ⁺π^?, are 1895±15 MeV/c²230±50 MeV/c² respectively. The differential cross sections, dσ/dt, for the quasi two-body final states K¹(890)Δ(1236) and K¹(890)Δ(1900) are well described by the one pion exchange model. In addition the moments of the Gottfried-Jackson angular distribution of the pπ⁺ system agree with those computed from on-shell π⁺p elastic scattering data. We conclude that the two final states are produced mainly by π exchange and associate the structure observed in the moments up to NH(6,0) in the 1900 MeV region with the $\text{7}\text{2}{}^{\mathrm{+}}$ Regge recurrence of the Δ(1236). The dominant decay mode of the resonance is Δ⁺⁺(1900)→pπ⁺ but decays to pπ⁺π⁰ and nπ⁺π⁺ are also observed. Cross sections are determined for the production of the quasi two-body final states K¹(890)Δ(1236), K¹(890) Δ(1900), K¹(1420)Δ(1236) and K¹(1420)Δ(1900).     

Measurement of elastic scattering in antiproton-proton collisions at 52.8 GeV centre-of-mass energy

We measured the differential cross section for p?p and pp elastic scattering in the momentum-transfer range 0.01 <|t| < 1.0 GeV² at the CERN Intersecting Storage Rings with center-of-mass energy $\text{s}\text{= 52.8}\text{GeV}$. Fitting the differential cross section with an exponential [Aexp (bt)], we found $\text{b}\text{p}\text{p = 13.92 ± 0.59}\text{GeV}{}^{\mathrm{?2}}$ for |t| < 0.05 GeV², whilst for |t| > 0.09 GeV², $\text{b}\text{p}\text{p = 10.68 ± 0.26}\text{GeV}{}^{\mathrm{?2}}$. Using the optical theorem, we obtained for the total cross section $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{p}\text{p)= 44.86 ± 0.78}\text{mb}$ and, by integrating the differential cross section, we obtained for the total elastic cross section $\text{σ}{}_{\mathrm{<mtext>el</mtext>}}\text{(}\text{p}\text{p) = 7.89 ± 0.28}\text{mb}$. Calculations of σ_tot combining elastic-rate and total-rate measurements are also given. All of these measurements were also performed for pp scattering at the same energy, and the results for both reactions are compared.     

Proton-proton scattering and the pomeron

We describe various attempts to fit the data on pp and $\text{p}\text{p}$ elastic scattering and total cross sections, including the recent ISR data, with a variety of Regge pole and cut models. Only two types of model are able to explain the data over the whole energy range satisfactorily. The simplest of these has no cuts, but a pomeron pole with trajectory αp(0) = 1.06 + 0.25 t, and a non-shrinking “core” term at large |t|. The other has a flat trajectory, αp(t) = 1.06 for all t, and strong eikonal-model cuts which explain both the shrinkage at low |t|, and the lack of it at larger |t|. We also briefly review various speculations which relate the fact that αp(0) > 1 to the small triple-pomeron coupling.     

A comparison between pp and pp diffractive peaks at and beyond ISR energies

Although a substantial difference between pp differential cross section at ISR energies and $\text{p}\text{p}$ differential cross section at SPS energy has been reported, we demonstrate that both differential cross sections, at least up to |t| ～ 1.2 GeV², can be satisfactory accounted for within the usual eikonal model in which the diffractive component is crossing even. Thus at a given ultra high energy, there is no suggestive evidence for a difference between pp and $\text{p}\text{p}$ diffractive peaks.     

Elastic scattering of π±p, K±p,pp ANDprmpp AT 39 AND 44.5 GeV/c

The differential cross sections for elastic $\text{π}{}^{\mathrm{?}}\text{p, K}{}^{\mathrm{?}}\text{p}\text{,}\text{p}\text{p and}\text{π}{}^{\mathrm{+}}\text{p, pp}$ scattering at 39 and 44.5 GeV/c, respectively, have been measured in the interval of momentum transfer squared 0.15 ≤ ovbt| ≤ 2 (GeV/c)².     

Inclusive K1±(892) production in pp and π+p interactions

A study is presented of the inclusive production cross sections of K^1±(892) vector mesons in pp interactions at 12 and 24 GeV/c and in π⁺p interactions at 16 GeV/c. The K^1± inclusive cross section is ～0.9 mb for both pp at 24 GeV/c and π⁺p interactions at 16 GeV/c. For pp interactions, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{)}$ and $\text{σ(}\text{K}{}^{\mathrm{1?}}\text{)}$ are seen to rise with energy, showing a threshold behaviour. In both pp and π⁺p interactions, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{)}$ largely exceeds $\text{σ(}\text{K}{}^{\mathrm{1?}}\text{)}$ at these energies and this excess is interpreted as K¹⁺ production by beam and target fragmentations. The decays of K^1±0 yield ～30% of the K⁰ observed in the final states. The p_T² dependence of both K¹⁺ and K^1? cross sections is described by an exponential with slope of ～3.3 (GeV/c)^?2. The longitudinal momentum spectra for K¹⁺ in 16 GeV/cπ⁺p and 24 GeV/c pp interactions are similar in shape in the target hemisphere. The K^1? spectra are similar over the whole kinematic region when viewed in the quark c.m.s. and point to a central production mechanism. Comparing K¹⁺ and ρ⁰ production, striking similarities are found.     

A study of K+n charge exchange at 2–3 GeV/c

In an experiment with the 1.5 m bubble chamber at the Rutherford Laboratory, the reaction K⁺d→K⁰pp has been studied at beam momenta of 2.2, 2.45 and 2.7 GeV/c. The cross section for the reaction K⁺n→K⁰p has been estimated and found to be approximately twice that of the line-reversed reaction $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^0\text{n}$ at comparable energies. An SU(3) sum rule, due to Barger and Cline, has been tested and found not to be valid in this momentum range. The differential cross section for K⁺n→K⁰p has also been measured and a determination made of the imaginary to real ratio of the forward amplitude, using the optical theorem. Implications of these, and other results, for various Regge models are briefly discussed.     

On studying energy dependences of π− p elastic scattering cross sections in the 33–55 GeV/c range

The π^? p differential elastic scattering cross sections have been measured for eight momenta in the 33–55 GeV/c range. The energy dependence of the slope and of the total elastic scattering cross sections has been determined experimentally. The results are compared with the known data. The experimental data are compared both with the Regge pole model and with the quasi-potential one.     

Differential cross sections and analyzing powers for pd elastic scattering below 1.0 MeV

Differential cross sections for the elastic pd scattering were measured at seven energies between 0.4 and 1.0 MeV for scattering angles from θ_c.m. = 44.5° to 149.2°. A mixture of D₂ and Kr was used as target gas and the pd differential cross sections were determined relative to those of pKr scattering with a statistical error of $\text{Δσ}\text{σ}$ ～5 × 10^?3. Analyzing powers for $\text{p}$d scattering were measured at 0.8, 0.9 and 1.0 MeV with a statistical error of ΔA_y ～5 × 10^?4.     

Shielded fixed-pole Pomeranchon model for high energy total and differential cross sections

A Regge model with a fixed-pole Pomeranchon and its associated shielding cut is used for π^±p, K^±p and pp scattering at small t and from 6 GeV to NAL and ISR energies. No additional parameters are associated with the cut. The model produces rising total cross sections and anti-shrinkage or non-shrinking diffraction peaks for some s and t. Good fits to total cross sections and to Serpukhov and ISR pp slope parameter data are obtained, and predictions about cross sections and shrinkage at NAL energies are made.     

Elastic pd scattering at 5.55 GeV/c incident momentum

Based on 150 000 photographs taken at the ZGS with the 30 inch deuterium-filled chamber we present an analysis of the elastic $\text{p}$d scattering reaction. Due to unrecoreded small deuteron recoils we were only able to measure the elastic cross section in the four-momentum region |t| > 0.03 (GeV/c)². Extrapolation towards small |t| by two different methods gave us two compatible estimates of the total elastic cross section. The differential cross section was analyzed by means of the Glauber formalism both with and without the effects due to the D-wave part of the deuteron wave function. The differential cross sections of np at 5.4 GeV/c and $\text{pn}$ deduced from our data were compared and exhibit a crossover phenomenon.     

Does the Pomeron have two components?

Experimental total and differential elastic cross sections are in remarkable agreement with the ansatz that the Pomeron contribution satisfies the relation $\text{P(π}\text{p}\text{) = (}\text{1}\text{2}\text{)P(}\text{Kp}\text{) + (}\text{1}\text{3}\text{)P(}\text{pp}\text{)}$ weaker than the quark model relation $\text{P(π}\text{p}\text{) = P(}\text{KP}\text{) = (}\text{2}\text{3}\text{)P(}\text{pp}\text{)}$ and following from the assumption that the Pomeron has a second component satisfying the relation $\text{P(π}\text{p}\text{) = 2P(}\text{KP}\text{) = (}\text{4}\text{9}\text{)P(}\text{pp}\text{)}$. Sum rules obtained from this ansatz are satisfied to an accuracy of 1% by total cross section data from 6 to 200 GeV/c where the quark model relation has a consistent discrepancy of 15%. They are satisfied to better than 20% for differential cross section data at 3, 3.6, 5, 6 and 42 GeV/c over a range of t where cross sections change by several orders of magnitude and the ratio of Kp and pp amplitudes varies from $\text{2}\text{5}$ to 5 and violates the simple quark model prediction of $\text{2}\text{3}$ by large factors in both directions.     

Measurement of the differential cross section and of the polarization parameter in pp elastic scattering at 200 GeV/c

Data are given for the polarization parameter and for the differential cross section in pp elastic scattering at 200 GeV/c, in the range $\text{0.5 ??t ? 4.0}\text{GeV}{}^2$. The polarization changes sign in the dip region, as already observed at 150 GeV/c.     

Hadron production at transverse momenta from 0.5 up to 2.2 GeV/c in proton-proton collisions at 70 GeV

The cross sections for π^±, K^±, p, and $\text{p}$ production in pp collisions have been measured at transverse momenta from 0.48 up to 2.21 GeV/c at 70 GeV. The data are compared with results obtained at lower and higher proton energies and also with the quantum chromodynamics parton model (QPM) calculations. Common behaviour of the cross sections of the form $\text{g(p}{}_{\mathrm{\perp }}\text{)?(x}{}_{\mathrm{\perp }}\text{)}$ in the energy range above 200 GeV does not take place at lower energies. Qualitatively QPM fits the data and the best agreement is for π⁺/π^? and K⁺/π⁺ ratios.