Regge Contributions Research Articles

Secondary Regge contributions in charge exchange reactions at t = 0

Second order contributions to Regge-pole exchange are analyzed in πN and KN charge-exchange reactions at zero angle, using recent experimental data. Models involving secondary trajectory exchange, contributions from cuts and complex Regge dipoles are compared. The breaking of the ϱ − A 2 exchange degeneracy is found to be rather important for the residues; the second order corrections to pure ϱ and A 2 Regge-pole exchange are small, too small to account for the high-energy behaviour of the total cross section Δσ π = σ tot( π −p) − σ tot( π +p) measured at the Serpukhov accelerator. It seems impossible to distinguish between second-order corrections from secondary trajectory exchange and cuts, at t = 0. The cut contribution to ϱ exchange predicted by a simple absorption model is very small in the forward direction; this is confirmed by the fit.

Light cone commutator functions and truncated Fubini-Dasheb-Gell-Mann sum rules

Consequences of a proposed structure of light cone commutation functions are investigated. In the case of electroproduction, configuration space considerations are seen to discriminate between the different behaviors of the scaling function F 2( ω) consistent with the present data. A method for obtaining sum rules of the Fubini-Dashen-Gell-Mann type is then suggested which, by subtracting off the leading Regge contributions, are kept meaningful even in the case of “bad” commutators.

Comments on the Regge-pole model for the reaction [formula omitted

Difficulties of exchange models for the high-energy reaction KN→ K ∗ (890)N are examined in the light of new data. The new experimental results allow an analysis of the reaction K ± p→ K ∗± p independent of low-energy data which strongly influenced our previous analysis. Although consistent with significant exchange amplitudes for the leading trajectories ω and P′ (but not P) at small − t, the fast energy dependence of the high-energy (4–13 GeV/ c) K ± p→ K ∗± p data gives direct evidence for a very important secondary Regge contribution. This dominant low-lying isoscalar contribution remains a problem for the conventional exchange models and cannot be reproduced by a Reggeised absorption-cut model involving leading trajectories. Various models including secondary Regge poles previously used are constructed and the difficulties of some of these are pointed out. A typical Regge-pole model which can successfully reproduce the data on all charge modes is illustrated. This model has isoscalar contributions from the trajectories P′, a comparatively flat ω (without the cross-over zero) and a third vacuum Regge pole P″ introduced in πN elastic scattering.

Exchange Degeneracy andΣ−ΛSplitting

The hypothesis is made that the sum of the imaginary parts of the baryonic Regge contributions to exotic meson-baryon scattering amplitudes must vanish. This hypothesis is combined with the assumptions that all coupling constants satisfy exact $\mathrm{SU}(3)$ symmetry and that the $\ensuremath{\Sigma}\ensuremath{-}\ensuremath{\Lambda}$ mass splitting cannot be neglected, so that the $\ensuremath{\Sigma}$ and $\ensuremath{\Lambda}$ lie on different Regge trajectories. All possible partitions of the spin-parity-${\frac{3}{2}}^{\ensuremath{-}}$ $\ensuremath{\Lambda}'\mathrm{s}$ and $\ensuremath{\Sigma}'\mathrm{s}$ (belonging to an octet, singlet, and decuplet) into the two trajectories are considered. A set of consistency equations is derived, and all solutions are obtained. If the $\ensuremath{\Lambda}(1520)$ is the only odd-parity hyperon on the bottom [$\ensuremath{\Lambda}(1115)$] trajectory, and the $\ensuremath{\Lambda}(1690)$ and one or two $\ensuremath{\Sigma}'\mathrm{s}$ lie on the top trajectory, there is only one solution. In this solution, there is no odd-parity decuplet, the $\frac{F}{D}$ ratios of the couplings to mesonbaryon states of the ${j}^{P}={\frac{1}{2}}^{+} \mathrm{and} {\frac{3}{2}}^{\ensuremath{-}}$ trajectories are 1, and the singlet-octet mixing angle of the ${\frac{3}{2}}^{\ensuremath{-}}$ $\ensuremath{\Lambda}'\mathrm{s}$ is $\ensuremath{\theta}=invtan\ensuremath{\surd}\frac{1}{2}$. This solution is in approximate agreement with experiment.

Restrictions on SU(3) mixing implied by exchange degeneracy

It is shown that the hypothesis that the imaginary parts of exchanged Regge contributions must cancel in channels which contain no resonances implies restrictions on the way in which SU(3) may be mixted and broken in the vector and tensor meson nonets; for example, the mixing angle should satisfy tan 2ϵ = 1 2 .

Conspirators and Daughters in Unequal-Mass, Nonzero-Spin Scattering

The problem of satisfying the all unequal-mass kinematic constraints at $s=0$ for helicity amplitudes for two-body scattering of particles with spin is analyzed in a Regge model. The Mandelstam-Sommerfeld-Watson transformation is used to obtain the form of the Regge contributions. It is shown that a sequence of daughter trajectories spaced at $\ensuremath{\Delta}\ensuremath{\alpha}=1$ is necessary to keep the amplitude analytic at $s=0$. For ${\ensuremath{\mu}}_{m}=min(|{\ensuremath{\lambda}}_{a}\ensuremath{-}{\ensuremath{\lambda}}_{b}|,|{\ensuremath{\lambda}}_{c}\ensuremath{-}{\ensuremath{\lambda}}_{d}|)=0$, no further trajectories are needed; for ${\ensuremath{\mu}}_{m}\ensuremath{\ne}0$ and the reduced Regge residue finite at $s=0$, the kinematic constraint and analyticity require dauthters and a conspirator sequence of opposite parity starting at ${\ensuremath{\alpha}}_{c}={\ensuremath{\alpha}}_{\mathrm{Regge}}$. It is shown to be probable that, for a residue which vanishes as ${s}^{n} (n\ensuremath{\ge}{\ensuremath{\mu}}_{m})$ at $s=0$, only the daughter trajectories are needed.

Electromagnetic Mass Differences and Regge Phenomenology

We examine the electromagnetic mass differences of hadrons by a phenomenological analysis of the forward virtual Compton amplitude. In addition to the usual elastic contribution, we consider in detail the contribution from ${{A}_{2}}^{0}$ Regge exchange for $I=1$ mass differences and possible contributions from non-Regge behavior for this weak amplitude in the asymptotic region. In the approximation of neglecting the inelastic resonant spectrum in Compton scattering, the contribution of the pure Regge exchange to the subtraction term for any $I=1$ mass difference can be related to a ratio of the ${{A}_{2}}^{0}$ residue functions (hence independent of the target) and the relevant elastic form factors. This analysis suggests that a large Regge contribution requires comparable longitudinal and transverse electroproduction cross sections at high energy for small spacelike virtual photon mass. The tadpole model is also examined from the observation that certain linear combinations of $I=1$ mass differences with just the ${{A}_{2}}^{0}$ Regge pole removed can be formulated in terms of unsubtracted dispersion relations and are presumably satisfied by retaining just the elastic contribution. The $\frac{F}{D}$ ratio that we calculate in this way for the tensor-meson couplings to baryons agrees with that obtained from high-energy experiments. From a superconvergence relation it is argued that there is a fixed pole in the helicity-flip crossed-channel Compton amplitude at $J=0$, $I=1$, the experimental consequences of which are discussed.

ModifiedπNSuperconvergence and the Static Model

Recently, superconvergence relations have been proposed for certain scattering amplitudes with spin at fixed momentum transfer. Unfortunately, the kinematics and high-energy behavior of $\ensuremath{\pi}N$ scattering do not permit any such relations for this process. If, however, one assumes Regge-pole dominance at high energy, one can write superconvergence relations for certain amplitudes from which the leading Regge-pole contributions have been subtracted out. Assuming resonance dominance in the low-energy region, one has a sum rule relating these resonances to the Regge parameters. Comparison with experimental data in the forward direction shows that the Regge contribution is small and that the dominant resonances are the $N$ and ${N}^{*}$; the sum rule is then approximately satisfied. Completely ignoring the Regge poles and making certain additional assumptions leads to a relativistic version of the static model, which gives a relation, for instance, between the $N$ and ${N}^{*}$ coupling constants. This relation is quite well satisfied. In addition one may derive the Adler PCAC (partially conserved axial-vector current) self-consistency condition. These results are shown to be related to the vanishing of the equal-time commutator of the pion currents.