The parity of regge cuts

The exchange of two reggeons of naturalities η_a and η_b will in general produce a J plane cut in amplitudes of both naturalities ± η_aη_b. We show that the amplitudes of naturality ? η_aη_b are suppressed, and this suppression grows with the energy, regardless of the particular model used for the vertices coupling the reggeons to the external particles. In consequence, for cuts where the two reggeons are any of ?, A₂, f, ω, or the pomeron, the natural-parity cut (if it is present) will dominate over the unnatural parity. We also show that cut vertices which contribute to both naturalities satisfy the conspiracy condition at t = 0 by suppressing both contributions equally. Away from t = 0, the η = + η_aη_b contribution can recover from this suppression. This behaviour is of importance in, for example, the pion-pomeron cut.We compare these conclusions with experiment.     

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 model for Regge cuts with pole enhancement

It is argued that, since hadronic processes show Regge shrinkage even at large ∣t∣, Regge-cut discontinuities must be enhanced in the region of J near the Regge poles (as suggested by some recent theoretical work on the weak-coupling solution to the “infrared problem” in the reggeon calculus) so that the dominant Regge-cut contribution (at current energies) does not come from the region of the discontinuity near the branch point (as it does in eikonal and absorption models). In particular we show that this hypothesis works well for π^?p→π⁰n. However, there is less shrinkage in photoproduction processes at large ∣t∣, and we find that in γp→π⁰p (and related processes) there is no pole enhancement of the cuts. We connect this fact with the absence of t-channel unitarity constraints for electromagnetic processes and more speculatively with the possibility that a scaling behaviour due to Regge cuts develops at large ∣t∣ as the mass of the external particle is decreased.     

The content of unitarity constraints on a pomeron pole of intercept one

We present a consistent picture of a pomeron pole with intercept one, together with its cuts, which evades the decoupling arguments. We use the reggeon cut discontinuity formulae to introduce Gribov's reggeon calculus as an exact solution of multiparticle t-channel unitarity. We show how, within the calculus, two-pomeron iterations of a singular kernel can be responsible for the zero in the triple-pomeron vertex. Using the concept of a bare pomeron pole as a multiperipheral production process which is subsequently renormalised by other effects, we apply the reggeon calculus analysis to inclusive cross sections. We find that the inclusive sum rule decoupling arguments are avoided because of the addition of enhanced absorptive corrections to the conventional Regge pole contributions. However, we show that in this picture the combined pole and two-pomeron cut contribution to the total cross section factories to order (ln s)^?2.We also show that, when the correct helicity structure of the pomeron is taken into account, the s-channel unitarity condition for pomeron scattering amplitudes does not lead to any serious decouplings.     

Asymptotic-planarity prediction of a pomeron-like unnatural parity trajectory

The asymptotic-planarity argument that explains the pomeron as a cylinder-shifted f, when applied to unnatural parity, predicts near t = 0 a high-lying small-slope H trajectory, with the corresponding I = 0, 1⁺, C = ? meson mass near 1 GeV. H couplings near t = 0 will be close to pure SU₃ singlet.     

An estimate of exchange contributions to the reaction γγ→ρ0ρ0 near threshold

The large cross section for γγ→ρ⁰ρ⁰ below and near the nominal ρ⁰ρ⁰ threshold cannot be accounted for byt-channel exchange contributions as estimated using a factorisation model.     

Fine structure of the diffraction cone: Manifestation of <Emphasis Type="Italic">t</Emphasis>-channel unitarity

We show that the deviation from exponential behavior of the diffraction cone observed near t = ?0.1 GeV² both at the ISR and the LHC (so-called break) follows from a two-pion loop in the t-channel, imposed by unitarity. By using a simple Regge-pole model we extrapolate the “break” from the ISR energy region to that of the LHC.     

The subtraction constant in π± electroproduction

A method is proposed for dealing with the subtraction constant required in fixed-t dispersion relations for π^± electroproduction. The method requires a knowledge of the t-channel cut contribution (evaluated at the subtraction points s₀), which can be determined at k² = 0 using a gauge invariance sum rule. Estimates by this and other methods show that it is small (compared with the pion pole contribution) for ?t ? 1 GeV², and in particular it is irrelevant to determinations of the pion form factor using high-energy forward π⁺ data.     

Factorization and the couplings of the vacuum trajectory

The decoupling theorems associated with an isolated factorizable pomeron pole of unit intercept are re-examined. It is found that the coupling of three such poles, Γ(t, t, 0), need not vanish, precisely at the point t = 0. This is demonstrated by summing only over states in the appropriate unitarity sum, and sum rule, which are consistent with the M², s/M² → ∞ limit. The triple-Regge region then makes a constant contribution to σ_total, insteadsb of the ln lns result obtained if the isolated pole is assumed to couple also to states such that s/M² = constant. The physical implications regarding factorization and the pole-cut relationship are discussed. The relationship between higher order optical theorems (Mueller discontinuities) and particular terms in the unitarity sum for the two → two absorptive part A₂₂ is exploited. Consistent contributions to the triple-Regge region contribute constant vertex corrections to pure pole behaviour in A₂₂. There is no cut contribution and the magnitude of the vertex corrections reflects the relative amount of diffractive production. The analysis is extended to multiple fireball production where pure multipole structures emerge. The series naturally terminates if the diffractive component is sufficiently small. The implications for the behaviour of the total cross section at machine energies are discussed.     

A study of ππ → NN partial-wave amplitudes using hyperbolic dispersion relations

We investigate $\text{ππ →}\text{N}\text{N}$ partial-wave amplitudes, using a spin separation method based on hyperbolic dispersion relations. Partial-wave amplitudes with J ? 3 are dominant in the pseudophysical region between the ππ and $\text{N}\text{N}$ thresholds, but we find clear evidence for J = 4 and J = 5 contributions from regions near and above the $\text{N}\text{N}$ threshold. We isolate J = 2 and J = 3 partial waves and determine the couplings of f₀(1270) and g (1680). Knowing the high-spin contributions, we are able to eliminate thse and to study s- and p-waves. We find evidence for small p-wave contributions above the ?, having the same sign as the ? contributions. We develop methods for determining the I = J = 0 ππ scattering length a₀⁰ and find a₀⁰ = 0.30 ± 0.15.     

The electromagnetic interaction in chiral perturbation theory

We investigate electromagnetic effects in the framework of chiral perturbation theory. Using a completely independent method, we confirm Urech’s results for the divergences of the one-loop functional in the electromagnetic sector. We perform a one-loop analysis of allP _t2 (P=π, K, η) and theK _t3 form factors $f_ + ^{K^ + \pi ^o } (0),f_ + ^{K^o \pi ^ - } (0)$ , including a systematic treatment of theO(e ² p ²) contributions in the mesonic part. We illustrate our results by several numerical estimates.     

Importance of longitudinal contributions to backward inelastic electron scattering

Coulomb contributions of multipolarity 2 are calculated for backward (θ = 180°) inelastic electron scattering by our improved DWBA code. General features are studied such as nuclear charge (Z) dependence, energy transfer dependence, momentum transfer dependence as well as the angle dependence near θ = 180°, with the help of a simple model for the transition charge density. We compare these features with PWBA and other simple approximations. We show, as a specific example, that the C2 contribution is comparable to the M1 and E2 multipole form factors for inelastic scattering to the rotational excited states of ¹⁸¹Ta.     

Integral relation for the t-dependence of the It = 1 ππ absorptive part

We derive a sum rule relating the I_t = 1 ππ absorptive part Δ(s, t) to integrals over total cross sections. We show how it can be used to estimate the t-dependence of this absorptive part and in particular its zero. A recent low energy ππ phenomenological analysis seems to imply a zero near t = ?0.2 GeV² for large s.     

Čebyšev mixing and harmonic oscillator models

We exhibit a simple variable pitch helix model which shows that the “chaotic” behavior of ?eby?ev iterations is an illusion of dimensional projection. As a consequence the stroboscopic images of the motion of a simple harmonic oscillator, recorded at the times 2ⁿt (n = 0, 1, 2, …), reproduce the mixing. This power law of time evolution may be used to generate other types of mixing transformations.     

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.     

Two and three pion-cut contributions to nucleon-nucleon scattering

Examining information from NN forward scattering in terms of discrepancy functions, we show that the 2π cut contributions as calculated via dispersion methods from πN scattering are in perfect agreement with NN scattering. Furthermore, we demonstrate the need for 3π cut contributions which are quantitatively well described by a nucleon exchange model. Finally, in addition to the 2π and 3π cut contributions, we determine the coupling constants of the ω and A₁ to be: g_Vω²/4π = 8.1 ± 1.5, g_Tω/g_Vω = 0.14 ± 0.20 and g_A1²/4π = 7.3 ± 3.0. The coupling of the η turns out to be zero.     

A measurement of polarization in π−p→ K°Λ° at 5 GeV/c

We have measured the Λ° polarization in π^?p→ K°Λ° at 5 GeV/c, using a data sample of 3709 events. The polarization is positive for small t, passes through zero near t = ?0.3 (GeV/c)², and becomes large and negative at larger t, consistent with a value of ?1.0 for t between ?0.7 and ?1.6(GeV/c)².     

Scaling law in the electrodisintegration of deuterons around 1 (GeV/c)2

Starting from ?t around 1 (GeV/c)², the electrodisintegration cross section of the deuteron near the threshold is shown to follow a scaling law when the contributions from the nucleon form factors are properly treated.     

A measurement of the KL0p → KS0p reaction between 4 and 14 GeV/c in the range 0.1 ⩽|t|⩽ 2 GeV2

We present experimental data on the K_L⁰p → K_S⁰p reaction between 4 and 14 GeV/c in the range 0.1 ? |t| ? 2 GeV². This experiment has been performed at the CERN PS, using spark chambers and a large aperture magnet. The results show a break of slope at t = ?0.3 GeV². The ω trajectory deduced from the data has an intercept α(0) = 0.5 and a slope α′ = 0.88. A comparison with various models shows that the non-flip amplitude is dominant.