Two body reactions and the quark model

A simple quark model for two-body hadronic amplitudes is presented and applied to pp ($\text{p}\text{p}$) and K^±p elastic scattering. Hadronic processes are described in terms of quark-quark scattering, using Glauber theory to take into account the effects of multiple scattering. Exchange degenerate Regge poles are introduced at the quark level. A predictive model for Regge cuts is obtained. It has some features in common with the dual absorption model in its correlation of dip structure and shrinkage in elastic processes with the exoticity of the s-channel but also significant differences, for example in the interpretation of the $\text{p}\text{p}$ dip. The qualitatively different structure in the pp differential cross section is also reproduced. It breaks exchange degeneracy in a well-defined way and in doing so offers an explanation of the differences between pp and K⁺p total cross sections. The difference in their differential cross sections is a natural consequence of the model and structure similar to the pp structure is predicted to appear in the K⁺p differential cross section in the region t ≈ ?2(GeV/c)².     

Single diffraction dissociation at the CERN SPS collider

The reaction $\text{p}\text{p}\text{→}\text{p}\text{X}$ was studied at a centre-of-mass energy $\text{s}\text{= 540}\text{GeV}$ by measuring the momentum spectrum of the antiproton. Data are presented in the four-momentum transfer range 05 < ?t < 1.2GeV². The shape of the mass distribution of the system X shows a diffractive component as already observed at lower energies. The differential cross section scales approximately with energy when compared to the ISR data.     

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.     

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.     

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.     

On the QCD perturbative predictions for the signal ofW± production in hadronic collisions

Evidence for the intermediate bosons in high energy pp and p?p collisions as signal in the cross section of large p_T charged lepton pp, $\text{p}\text{p}\text{→}\text{W}{}^{\mathrm{\pm }}\text{+}\text{X}$, W^±→?^±ν_? is considered for CM energy range $\text{s}\text{=100?800}\text{GeV}$. Besides the usual Drell-Yan term which gives a very sharp peak in the lepton p_T distribution, the first order QCD contribution is included thus producing the intermediate boson with transverse momentum and smearing the lepton distribution. Scaling violation of the structure functions is incorporated and compared with the case when it is absent.     

QCD predictions for beauty production in π p and pp collisions

The total cross sections for beauty production in πp, pp and $\text{p}$p collisions are calculated within perturbative QCD. It turns out that the cross sections are around several nanobarns at presently available energies. For the future $\text{p}$p colliders, the total cross section reaches several millibarns.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

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.     

A two-component model definition of two-body nucleon diffraction dissociation in πp → π(Nπ)reactions at 3.9 GeV/c and comparison with other experiments

Four low-mass “diffractive like” reactions π^±p → π^±(pπ⁰) and π^±p → π^±(nπ⁺) have been studied at 3.9 GeV/c incident pion momentum. These channels have been studied in the framework of a two-component model and we have proposed a definition of the diffraction dissociation amplitude. The following three features of the data are discussed: (1) an apparent violation of the predictions of isospin invariance for the cross section ratios, (2) the marked anisotropy of the s-channel helicity distributions and (3) the absence of the cross-over effect in the differential cross sections. The predictions of a two-component model previously used to explain the low mass $\text{I =}\text{1}\text{2}\text{(}\text{N}\text{π)}$ enhancement [1] and s- and t-channel helicity non-conservation [2] are seen to be in agreement with these observations. Predictions are also made for higher energy incident pions and incident K, p, and $\text{p}$ projectiles. These predictions are compared with available data including recent results at Fermilab and ISR energies.     

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.     

The charge exchange pp → nn at 5.0 and 7.76 GeV/c near the forward direction

The differential cross section for the charge exchange $\text{p}\text{p}\text{→}\text{n}\text{n}$ has been measured with high statistics at 7.76 GeV/c and at 5.0 GeV/c. The 7.76 GeV/c data show a very narrow [Δt ? 0.01 (GeV/c)²] forward peak superposed on a slow exponential fall-off.     

A measurement of e+e− → pp for (1975 ⩽ s ⩽ 2250) MeV

The $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{p}$ cross section has been measured in the energy interval (1975 ? 2E ? 2250) MeV for |cosθ| < 0.7. The measurement is based on ～ 100 events, thus improving by a factor 3 on the previous existing statistics in this energy interval. The form factor |G|² is given as a function of energy under the assumption |G_E| = |G_M|. We also give the first measurement of the differential cross section, averaged over the energy interval, and estimate the ratio G_M|/|G_E| from it.     

pp interactions at 303 GeVc: Analysis of diffraction excitation in the reaction pp → pX

The properties of the diffractively excited system observed at low missing mass in the inclusive pp → pX reaction at $\text{303}\text{GeV}\text{c}$ are presented. For diffraction excitation with |x| > 0.9, the cross section, σ_D=(5.6±0.8) mb, the mean charged multiplicity depends on the mass of the diffractive system approximately at 〈n_c〉 ≈ 0.6M_x + 2, and the slope of the momentum transfer distribution with |t| < 0.5 GeV² is 7.5±0.8 GeV^?2.     

Interference of QCD and weak interactions and the detection of vector bosons by hadronic jets: pp and pp collisions with polarized and unpolarized beams

Two-jet and single-jet cross sections and spin asymmetries are studied in polarized and unpolarized proton-proton and antiproton-proton collisions at collider energies $\text{s}\text{= 200}\text{to}\text{1000}\text{GeV}$. It is found that the interference terms between strong (QCD) and weak interactions strongly influence the parity violating weak cross section; especially, the vector boson peaks in pp cross sections and parity violating asymmetries are masked almost completely at the lower part of the energy range considered. In $\text{p}\text{p}$ collisions the vector boson peaks survive and a measurement of parity-violating asymmetries of double- and single-jet cross sections should lead to clear signals of the vector bosons.     

K1(890) production in K−p → NKπ at 16 GeV/c

Results on $\text{K}{}^1\text{(890)}$ production in K^?p → NKπ reactions at 16 GeV/c are presented. Total cross sections, differential cross sections and density matrix elements are determined. It is found that: (i) The cross section for K^1?(890) p is consistent with containing two components, one due to natural parity exchange, falling slowly with increasing energy, the other, due to unnatural parity exchange, vanishing rapidly with increasing energy. For $\text{K}{}^{\mathrm{<mtext>1</mtext><mtext>o</mtext>}}\text{(890)}\text{n}$, the cross section decreases steadily as the energy increases. (ii) Natural spin-parity exchange dominates in the K^1?(890) p channel, the unnatural exchange contribution being approximately (5±4)%. In $\text{K}{}^{\mathrm{<mtext>1</mtext><mtext>o</mtext>}}\text{(890)}\text{n}$, natural spin-parity exchange is only about (30±10)%. (iii) The reacton $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^{\mathrm{1?}}\text{(890)}\text{p}$ is dominated (95±5)% by isoscalar exchange. (iv) The effective trajectory involved in the I = 0 natural parity exchange is consistent with the ω-f trajectory. (v) Interference terms between exchanges with positive (f, π^o,…) and negative (?^o, ω,…) C-conjugation amount to (23±12) μb at 16 GeV/c.     

Exclusive reactions in pp interactions at 32 GeV/c

The cross sections of several exclusive reactions in $\text{p}\text{p}$ interactions are given. In the channels $\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{and}\text{p}\text{p}\text{→}\text{p}\text{p}\text{2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}$ which dominate the interactions, the single and double diffractive dissociations are analysed and compared to the results obtained with K^±p interactions at the same energy, pp and $\text{p}\text{p}$ interactions at other energies. The test of factorization at the p → pπ⁺π^? vertex is well verified. The process $\text{p}\text{p}\text{→ Δ}{}^{\mathrm{++}}\text{Δ}{}^{\mathrm{++}}$ is studied and the cross sections of $\text{Δ}{}^{\mathrm{++}}\text{,}\text{Δ}{}^{\mathrm{++}}\text{, ?}{}^0\text{and}\text{f}{}^0$ production are also given.     

Measurement of the cross sections for reaction π−p → Xo n in the momentum range up to 50 GeVc

The cross sections for the reaction π^?p → X^on, X^o → 2_λ are measured at 32.5 and $\text{48}\text{GeV}\text{c}$ momenta. The cross spectrometer of γ-quanta is used to select events of reaction, whose cross section is only about 0.05 μbarn. The cross section energy dependence has the power form ($\text{≈ p}{}^{\mathrm{?1.11\pm 0.12}}$. conclusion on U(6) symmetry of quark model is made when comparing the differential cross sections at zero angle for the reactions π^?p → X^o and π^?p → η^o. The angle of octet-singlet mixing for pseudo-scalar mesons β = ?(20.6 ± 2.2)° is defined.     

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.     

The reaction pp→pπ−π+p at 25 and 40 GeV/c

The reaction $\text{p}\text{p}\text{→}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{p}$ has been studied at 25 and 40 GeV/c at the Serpukhov proton synchroton using the CERN-IHEP spectrometer. The differential cross section has been determined as a function of four-momentum transfer to the proton (0.05–0.30 (GeV/c)²) and $\text{p}\text{ππ}$ mass (up to 2.2 and 2.6 GeV/c²). At both energies there is a broad low-mass maximum with an enhancement at 1.6–1.8 GeV/c². The cross section in a given mass band falls rapidly with |t|, with an exponential slope that decreases with increasing mass. In both the background and the 1.7 GeV/c² peak there is a strong $\text{Δ}{}^{\mathrm{??}}\text{π}{}^{\mathrm{+}}$ component. Possible spin-parity (J^P) contributions to it are discussed. Throughout the range 1.5–2.2 GeV there is at least one state of $\text{J ?}\text{3}\text{2}$ and there is interference between states of opposite P, |ΔJ| ? 1. At the peak there is a $\text{J ?}\text{5}\text{2}$ component. There are striking parallels between this reaction and the boson reactions π^?p→π^?π^?π⁺p and K^? → K^?π^?π⁺p.