Bounds on elastic absorptive parts

We reduce the general problem of obtaining bounds on elastic absorptive parts of a scattering amplitude subject to unitarity restrictions and any number of constraints involving partial wave amplitudes linearly to a form where it can be directly applied to any such problem. A series of bounds on absorptive parts for positive momentum transfer square t, within the Lehmann-Martin ellipse, is derived. These involve a knowledge of the first few momentum transfer derivatives of the absorptive part in the forward direction, i.e., t = 0. Upper and lower bounds on the higher t-derivatives of the absorptive part at t = 0 are also given.     

Stringent upper bounds on π−p charge-exchange differential cross sections

Unitary bounds on (dσ/dt) for π^?p charge-exchange reactions in terms of the π^?p elastic amplitudes are obtained. No assumptions have been made regarding the spin and helicity structure of the problem. Computation of the bounds at various energies reveal the severe restrictions unitarity places on a rapid rise of the spin-flip amplitude at near-forward angles. The near saturation of the bounds at some angles suggests that such bounds are of potential use in restricting the choice of elastic amplitudes fitting a given set of elastic observables.     

Unitary bounds on elastic absorptive amplitudes involving total cross section,forward slope and curvature

We obtain rather tight unitarity upper and lower bounds on the absorptive part A(s, t) of elastic amplitudes with given total cross section, slope and curvature at t = 0 and compare them with experiment.     

Measurement of coherent elastic and inelastic deuteron-proton scattering at s = 2800 GeV2

Data on coherent elastic and inelastic deuteron-proton scattering are presented. The measurements were made at the CERN ISR with a single arm spectrometer, at s = 2800 GeV² and momentum transfer squared (?t) in the range 0.15 to 0.42 GeV².The data are compared with elastic and inelastic diffractive proton-proton scattering data taken with the same apparatus at the same s and t values. The t dependence of the elastic dp → dp differential cross section is compared to simple predictions based on Glauber theory. The differential cross sections for pp → pX and dp → dX are also compared for M_X² → 280 GeV², where M_X denotes the mass of system X recoiling against the measured proton and deuteron.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Analysis of t-b-W and t-t-Z couplings from CLEO and LEP/SLC data

We update the constraints on anomalous dimension four t-b-W and t-t-Z couplings by using CLEO b→sγ and LEP/SLC precision Z-pole data. It is found that the data imposes very stringent bounds on them. Moreover, the 2σ pull from SM predictions of A_LR(hadrons), A_b and A_FB(b) have little chance of being explained by the strongly constrained anomalous couplings.     

Searching for effects of neutrino magnetic moments at reactors and accelerators

The sensitivity of the νe elastic scattering experiments to possible effects of nonzero neutrino magnetic moment (μ) is analyzed and the optimal experimental condition under which such effects are relatively enhanced are found. New, somewhat more restrictive than the previously derived bounds on μ, are obtained on the basis of existing data by the use of selfconsistent statistical analyses: μ_νe < 1.52 × 10^?10e/2m_e and μ_νμ < 1.19 × 10^?9e/2m_e. These bounds are expected to be improved approximately by an order of magnitude in experiments planned to be performed in the near future.     

Eikonal description of nucleon-nucleon polarizations

Nucleon-nucleon elastic polarization data are analyzed within an eikonal framework in the range 6?plab?45 GeV/c and |t| 2.5 GeV/V². The isovector component is found to be dominated by a nearly exchange degenerate ρ-A₂ contribution while the isoscalar part requires both a lower lying Regge-pole exchange and an asymptotic pomeron contribution.     

The diffraction pattern of pp elastic scattering and the composite structure of the proton

The consequences of the quark-glue structure of hadrons for pp elastic scattering are examined in a simple model where the glue is taken to be the active constituent in normal (low p_T) hadronic collisions. Earlier work based on the study of pp inelastic diffraction led to the conclusion that the glue-glue elastic amplitude t_g is approximately Gaussian in the glue-glue impact parameter b_g, with maximum opacity at b_g = 0. A slight refinement of this approximation, in which t_g is almost maximally opaque over a small b_g interval and is Gaussian at larger b_g, is now shown to account for the remarkable diffraction structure observed in pp elastic scattering at ISR energies. A very simple form is obtained for the form factor describing the impact parameter distribution of the glue inside a proton relative to the proton itself.     

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.     

Soft π−p and pp elastic scattering in the energy range 30 to 345 GeV

Differential cross sections for π^?p and pp elastic scattering have been measured at incident momenta ranging from 30 to 345 GeV and in the t range 0.002 (GeV/c)² ? |t| ? 0.04 (GeV/c)². From the analysis of the data, the ratio ? (t = 0) of the real to the imaginary parts of the forward scattering amplitude was determined together with the logarithmic slope b of the diffraction cone.The results on the real parts confirm the validity of the forward dispersion relations at high energies. Using the dispersion relations, it was shown that the experimental data on ?_{π?p(t = 0)} require a continuous rise of the total πp cross sections, at least up to the energy of 2000 GeV, thus revealing a close similarity in high-energy behaviour of πp and pp interactions.The results on the slope parameters from this experiment together with the analysis of the available world data demonstrate that the existing experimental data are consistent with the hypothesis of a universal shrinkage of the hadronic diffraction cone at high energies. The value of the asymptotic shrinkage parameter α_p^′ was found to be independent of the kind of the incident hadron and of the momentum transfer in the t range |t| ? 0.2 (GeV/c)² : 2α_{p^′ = ± 3 (GeV/c)^?2}.     

The even signatured,isoscalar exchange amplitudes at 6 GeV/c

An analysis of experimental data on KN elastic reactions and regeneration experiments leads to the I_t = 0 even signatured amplitudes. The results are similar to those obtained through amplitudes analysis of πN scattering. Spin conservation seems to be favoured rathere than helicity conservation. Predictions of the spin rotation parameters R^± and of the polarisation for the regeneration experiment are given.     

Photoproduction of Φ-mesons at small t-values

The reaction γ + p → Φ + p has been measured using a spark chamber spectrometer and a tagged photon beam in the energy range from 4.6 to 6.7 GeV. Approximately 3500 photoproduced elastic Φ-events have been collected in the t-range between t_min and t = ?0.4 (GeV/c)². Cross sections and t-distributions are presented.     

Constraints on the K_{l_3} form factors from analyticity and unitarity

The K?? form factors are investigated at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using as input the values of the form factors at t?=?0, and at the Callan?CTreiman point in the scalar case, stringent constraints are obtained on the slope and curvature parameters of the Taylor expansion at the origin.     

An investigation of unitarity at ISR energies

We analyse the unitarity equation in impact-parameter space using recent ISR data (at s=930 GeV²) on σ_T, dσ/dt (elastic) and d²σ/dtdM² (diffractive) as input. The assumption of s-channel helicity conservation for the diffractive process leads to a diffractive overlap function which is central. Unitarity then restricts single diffraction to satisfy 2σ_d?5.8 mb. The assumption of t-channel helicity conservation, on the other hand, gives the interesting result that diffractive processes are peripheral in b-space if the diffractively produced state has high spin. Unitarity in this case gives no significant bound on 2σ_d. For both cases, non-diffractive processes are peripheral.     

Bounds on the Kℓ3 scalar form factor from low-energy Kπ phase shift

Upper and lower bounds on the scalar form factor of K_?3 decay are calculated using the analytic properties of the form factor, the experimental low-energy S-wave Kπ phase shift, and an estimate of the propagator Δ(t) of the divergence of the strangeness changing current at zero momentum. We release the condition given by the soft-pion theorem on $\text{?(m}{}_{\mathrm{<mtext>K</mtext>}}{}^2\text{)}$ that we considered in a previous work. For this reason the new bounds are less restrictive. However they are sufficiently strong to be inconsistent with some experimental data irrespective of the fit used for Kπ scattering.     

The pomeron in elastic meson-baryon scattering

We show that a pomeron (P) trajectory with α_P(t) ≈ 1.07 + 0.22t provides a simple and satisfactory fit to π^±p and K^±p elastic scattering data (as well as pp and $\text{p}$p considered in an earlier publication) for |t| < 1.2 GeV², including the rising total cross sections. The destructive term needed to explain the diffraction minimum in pp may be explained as a weak P ? P cut effect provided that the Gribov vertices are given suitable structure, and the prediction is then made that similar minima should be observed in meson-baryon scattering at FNAL somewhere in the region 1.5 < |t| < 2.5 GeV². The P ? P cut does not seem to be related (at least directly) to the unitarization effects which must eventually make σ_tot ～ log²s (but not until s > 10⁸GeV²). Thus the “effective” J-plane singularity structure, at currently available energies seems to be much simpler than it can be asymptotically.