s-and t-channel helicity conservation of pion induced nucleon diffraction dissociation at 3.9 GeV/c and the implications of a two-component model

A study of schannel and t-channel helicity conservation has been carried out on a prism plot separated sample of 3.9 GeV/cπ^±p → π (Nπ)_dd diffraction dissociation events. s-channel helicity conservation is found to be strongly violated while t-channel helicity conservation is found to be mildly violated. These results are similar to that found at 11.7 GeV/c. We explain these violations on the basis of a “two-component model” of which the first component is a single exchange amplitude. We postulate that this amplitude is the generalization of the pomeron exchange amplitude which may conserve s-channel helicity. The second component of the model is a double exchange mechanism which strongly violates s-channel helicity. The predictions of this model agree with the experimental data.     

Production properties of A1 in πp interactions at 5.45 GeV/c

The production of the peripheral 3π mass enhancement in the A₁ region is described. The differential cross section and its variation with 3π mass is studied and the spin density matrix elements are given for the t-channel and s-channel helicity frames. As observed in π⁻p interactions t channel but not s channel helicity is conserved. A Deck type double Regge trajectory exchange amplitude gives good fits to the experimental distributions. Its use is supported by the equality of ?_{0 0} for the A₁ and ?00 for the ? in the t-channel, as noted by Donohue.     

Rho production by virtual photons

The reaction γ_Vp → pπ⁺π^? was studied in the W, Q² region 1.3–2.8 GeV, 0.3–1.4 GeV² using the streamer chamber at DESY. A detailed analysis of rho production viaγ_Vp→?⁰p is presented. Near threshold rho production has peripheral and non-peripheral contributions of comparable magnitude. At higher energies (W > 2 GeV) the peripheral component is dominant. The Q² dependence of σ(γ_Vp→?⁰p) follows that of the rho propagator as predicted by VDM. The slope of dσ/dt at 〈Q²〉 = 0.4 and 0.8 GeV² is within errors equal to its value at Q² = 0. The overall shape of the ?⁰ is t dependent as in photoproduction, but is independent of Q². The decay angular distribution shows that longitudinal rhos dominate in the threshold region. At higher energies transverse rhos are dominant. Rho production by transverse photons proceeds almost exclusively by natural parity exchange, σ_T^N ? (0.83 ± 0.06) σ_T for 2.2 < W < 2.8 GeV. The s-channel helicity-flip amplitudes are small compared to non-flip amplitudes. The ratio R = σ_L/σ_T was determined assuming s-channel helicity conservation. We find R = ξ²Q²/M_?² with ξ² ≈ 0.4 for 〈W〉 = 2.45 GeV. Interference between rho production amplitudes from longitudinal and transverse photons is observed. With increasing energy the phase between the two amplitudes decreases. The observed features of rho electroproduction are consistent with a dominantly diffractive production mechanism for W > 2 GeV.     

Properties of ψN scattering

Extracting ψN scattering from photoproduction requires vector meson dominance and diffractive assumptions. We observe that (i) kinematic corrections to standard vector dominance formulas are important; (ii) both threshold and high energy behaviors of σ_t(ψN) support the diffractive assumption; (iii) q²-dependence in the γψ coupling could imply larger ψN cross sections; (iv) in any case σ_t is bounded through the slope of dσ/dt and σ_el/σ_t remains small.     

Elastic photoproduction of ϱ0 mesons at HERA

The cross section for the elastic photoproduction of ϱ⁰ mesons (γp → ϱ⁰p) has been measured with the H1 detector at HERA for two average photon-proton centre-of-mass energies of 55 and 187 GeV. The lower energy point was measured by observing directly the ϱ⁰ decay giving a cross section of 9.1 ± 0.9 (stat.) ± 2.5 (syst.) μb. The logarithmic slope parameter of the differential cross section, dσ/dt, is found to be 10.9 ± 2.4 (stat.) ± 1.1 (syst.) GeV⁻². The ϱ⁰ decay polar angular distribution is found to be consistent with s-channel helicity conservation. The higher energy cross section was determined from analysis of the lower part of the hadronic invariant mass spectrum of diffractive photoproduction and found to be 13.6 ± 0.8 (stat.) ± 2.4 (syst.) μb.     

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.     

Measurement of elastic ω photoproduction at HERA ZEUS Collaboration

The reaction γp →ωp(ω → π⁺π^?π⁰ and π⁰ → γ γ) has been studied in ep interactions using the ZEUS detector at photon-proton centre-of-mass energies between 70 and 90GeV and ∣t∣ < 0.6GeV², where t is the squared four momentum transferred at the proton vertex. The elastic ω photoproduction cross section has been measured to be σ_{γp → ωp} = 1.21 ±0.12 ±0.23 μb. The differential cross section dσ_γp→ωp/d¦t¦ has an exponential shape e^?b∣t∣ with a slope b =10.0 ± 1.2 ± 1.3 GeV^?2. The angular distributions of the decay pions are consistent with s-channel helicity conservation. When compared to low energy data, the features of ω photoproduction as measured at HERA energies are in agreement with those of a soft diffractive process. Previous measurements of the ρ⁰ and ? photoproduction cross sections at HERA show a similar behaviour.     

Unitarity bounds for inelastic diffraction

Unitarity in the s-channel is invoked to derive an upper bound for the inelastic diffractive cross-section as a function of impact parameter. The application of this bound to high-energy proton-proton scattering strongly suggests that inelastic diffraction should be peripheral in the impact parameter space.     

An impact parameter description of single and double diffraction dissociation

An s-channel impact parameter model of inelastic diffraction dissociation is constructed which describes quantitatively the momentum transfer distributions of both pion and nucleon induced reactions. It is stressed that the impact parameter profile is peripheral and is approximately the same for all helicity amplitudes. From the fits to the data, the concept of a universal limiting strength (ULS) for each amplitude is deduced and its consequence for other diffractive processes, and the approximate TCHC hypothesis are discussed. Finally, detailed predictions are presented the momentum transfer distributions in the double diffraction process NN → (Nπ)(Nπ), and compared with a simple t-channel picture of diffraction dissociation.     

Factorization in high energy hadron collisions

The concept of factorization is discussed for elastic diffraction scattering and diffraction dissociation of hadrons at high energy. In addition to the usual definition in terms of the t-channel, a natural definition of factorization in the s-channel is proposed and compared with the former. It is shown that s-channel factorization of all diffractive processes is consistent with the assumption that elastic scattering is identical to the shadow of the diffraction dissociation processes.     

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.     

On helicity conservation in the reaction π−p → A1p at 4.45 GeV/c

Helicity conservation in the reaction π^? p → pA₁ at 4.45 GeV/c has been studied using 50 cm and 55 cm liquid hydrogen bubble chambers. In the Jackson and the helicity frames the dependence of the ? matrix elements on the four-momentum transfer squared to the proton (t) for A₁ maximum decay has been calculated. The obtained data are in a good agreement with t-channel helicity conservation. The t-channel dependence of the ? matrix elements in the mentioned frames is in good agreement with that calculated using the Regge π-pole exchange model (it is suggested that the A₁ maximum nature is explained by a kinematical effect of the Deck type).     

A spin dependent droplet model for high energy pion-nucleon elastic scattering

The Chou-Yang droplet model of hadron-hadron diffractive scattering is reinterpreted in a way that allows the spin structure of the amplitudes to be incorporated. The model is developed in the particular case of pion-nucleon elastic collisions, in which theA ⁽⁺⁾ andA′⁽⁺⁾ amplitudes are related respectively to theF ₂ andF ₁ Dirac form factors of the nucleon. A version of the model, which does not conserves-channel helicities, is first considered and its predictions compared with the high energy π±p elastic data, including polarization. Finally an interpretation of asymptotic helicity conservation is provided in terms of the model.     

Measurement of elastic J/ψ photoproduction at HERA

The reaction γ p → J/ψ p has been studied in ep interactions using the ZEUS detector at HERA. The cross section for elastic J/ψ photoproduction has been measured as a function of the photon-proton centre of mass energy W in the range 40 < W < 140 GeV at a median photon virtuality Q ² of 5 × 10^?5 GeV². The photoproduction cross section, σ_{γp→ J/ψp}, is observed to rise steeply with W. A fit to the data presented in this paper to determine the parameter δ in the form σ_{γp→ J/ψp} α W ^δ yields the value δ = 0.92±0.14±0.10. The differential cross section dσ/d ¦t¦is presented over the range ¦t¦< 1.0 GeV² where t is the square of the four-momentum exchanged at the proton vertex. dσ/d ¦t¦falls exponentially with a slope parameter of $4.6pm 0.4_{-0.6}^{+0.4} {? GeV}^{-2}$. The measured decay angular distributions are consistent with s-channel helicity conservation.     

Scale of corrections to the t-channel pole approximation in quasielastic pion knockout from a nucleon by high-energy electrons

An investigation of a dominant role of the simplest t-channel pole diagrams in pion electroproduction on nucleons for quasielastic-knockout kinematics at an electron energy of a few GeV is completed-namely, the competition between the t-channel pion and rho-meson pole amplitudes, on one hand, and the s-channel pole amplitude (tree diagram), on the other hand, is considered. When the virtual-photon mass is sufficiently large [Q ²>2(GeV/c)²], the last amplitude does not make significant contributions to relevant cross sections, either the longitudinal (dσ _L/dt) or the transverse (dσ _T/dt) one. At Q ²=0.7(GeV/c)², the term associated with the interference between the t-channel pion-pole amplitude and the s-channel pole amplitude is still noticeable in the longitudinal cross section. The vertex functions g _ρ NN(t) as obtained from the cross section for the quasielastic knockout of rho mesons and from the cross section for pion photoproduction are compared. Their disagreement must give impetus to a further development of the gauge-invariant theory of pion photoproduction.     

Is a subtraction really necessary in the isospin even πN dispersion relation?

It is shown that the assumption of anunsubtracted fixed-t dispersion relation for the isospin evenπN amplitudeA ⁺ is compatible with all data. The prediction for the subtraction function agrees reasonably well with independent determinations. The assumption has the consequence that the ratio of thes-channel helicity flip and non flip amplitudes vanishes in the high energy limit.     

Interpretations of the differential cross-sections for pp → π−π+

The differential cross-sections for $\text{p}$p → π^?π⁺ in the momentum range 0.8 to 2.4 GeV/c (centre-of-mass energy 2.02 to 2.57 GeV) are analysed in terms of the possible existence of s-channel resonances. The systematics of the dip structures and the s-dependence of dσ/dt are presented.     

Axial vector meson production

Recently available differential cross section and density matrix information on π^?p → B^?p at 4 GeV/c are successfully described in terms of t channel exchanges and s channel absorptive effects. The s channel helicity amplitude which is dominant at small |t| (zero net helicity flip ω exchange) is found to have a zero at ?t = 0.2 GeV². SU(3) and higher symmetries are used to predict cross sections for further axial vector meson production processes, in particular non-diffractive A₁ production. The importance of these processes with regard to Regge phenomenology and meson spectroscopy is emphasized.