Regge Amplitude Research Articles

Renormalization of hadronic diffraction and the structure of the pomeron

A phenomenological renormalization scheme for hadronic diffraction is proposed, which unitarizes the triple-pomeron Regge amplitude while preserving its M 2 and t dependence. Predictions for pp p p single diffractive, double diffractive and double pomeron exchange cross sections are presented and compared with experimental results. A new interpretation of hard and deep inelastic diffractive data emerges in which the momentum sum rule is obeyed by the constituents of a pomeron described as a mixture of quark and gluon color singlets in a ratio dictated by asymptopia.

Regge pole model with K*?K** exchange and absorption for the $$\bar \Lambda \Lambda $$ reaction

The strangeness production process ¯pp→\(\bar \Lambda \Lambda \) is studied in theK—K Regge pole approach with exchange degeneracy and absorption. An improved parametrization of the Regge amplitude is adopted. The absorption is approximated by distortion factors for initial and final states. An overall good description of cross section and spin observables is achieved down to very low energies.

Superstring Regge amplitudes and emission vertices

We calculate (super) string high-energy amplitudes with external leading Regge trajectories in terms of new emission vertices with continuous spin and off-shell momenta. Such vertices are constructed as quasi-local operators from the short-distance product of primary fields and used to calculate the four-graviton Regge amplitude, relevant to gravitational scattering at planckian energies.

Possible absorptive corrections in hard-scattering processes at very high energies

Absorptive effects in hard-scattering processes, which can possibly originate from multiparton final-state interactions, give rise to a vanishingly small logarithmic correction to the parton → parton + parton splitting process, if simulated by Regge amplitudes. When this effect is iterated, within the leading logarithmic approximation of quantum chromodynamics, it may be promoted to a small power correction to the structure (or fragmentation) functions and be observable at very high energies.

Triple Pomeron coupling and pion inclusive scattering

A characteristic rise in the cross section near x = 1 has been reported for the single particle inclusive reaction π−p → π−X at Fermilab energies. Factorizable Regge amplitudes are used with a well-established analysis of the pp → pX peak to construct a parametrization of the triple-Regge couplings with αP(0) > 1 and to give a triple-Regge description of the meson + proton → meson + X cross section. Good agreement with the π−p → π−X data at 147 GeV/c is obtained and the peak is dominated by the triple-Pomeron component. This approach provides a reliable method for obtaining an estimate of the non-diffractive component. The inelastic diffractive cross section rises with energy and is found to account for most of the observed rise in σtot(π±p). The procedure is extended to K±p → K±X.

Construction of multi-Regge amplitudes by the Van Hove-Durand method

The Van Hove-Durand method of deriving Regge amplitudes by summing Feynman tree diagrams is extended to the multi-Regge domain. Using previously developed vertex functions for particles of arbitrary spins, single-, double-, and triple-Regge amplitudes incorporating signature are obtained. Criteria necessary to arrive at unique Regge-pole terms are found. It is also shown how external spins can be included.

Reggeization of scalars and dual model structure of Yang-Mills theory

When the Regge amplitudes are required to satisfy the kinematical constraints on helicity amplitudes the scalars can Reggeize both in scalar QED (in agreement with findings of Cheng and Lo) and in non-Abelian gauge theories. For the SU(2) Yang-Mills model with spontaneously broken symmetry we exhibit a Reggepole structure reminiscent of the dual model.

Analysis of backward πN scattering data at 3.5 GeV/ c

The pion-nucleon backward scattering data at 3.5 GeV/ c are fitted with two Regge-type models which were first used at 6 GeV/ c: a good description of the data is obtained; however the parameters differ significantly from those at 6 GeV/ c. A simultaneous fit at 3.5 and 6 GeV/ c can be made with N α and N γ Regge amplitudes, if the non-Regge terms are fitted with separate sets of parameters at each energy.

Reggeon amplitudes for heavy hadrons

The simple Regge power law ${(\frac{s}{{s}_{0}})}^{\ensuremath{\alpha}(t)}$ leads to enormous suppression factors in reactions involving heavy hadrons. We point out that the location of the heavy hadronic resonances introduces a dynamical threshold ${s}_{1}$ in the Regge amplitude ${[\frac{(s\ensuremath{-}{s}_{1})}{{s}_{0}}]}^{\ensuremath{\alpha}(t)}$. This effect, which is due to the dual nature of the Reggeon, removes most of the large suppression.

Crossing relations for infinitely rising trajectories: An asymptotic expression of local duality

Asymptotic crossing relations for the Regge amplitudes are proposed as a model-independent expression of local duality. They allow local duality to be formulated solely in terms of Regge trajectories without any violation of unitarity or neglect of resonance widths. The crossing relations connect the direct- and crossed-channel Regge-pole amplitudes for the elastic scattering of two equal-mass particles as $s\ensuremath{\rightarrow}\ensuremath{\infty}$ in a given domain of the real $\mathrm{st}$ plane. The main purpose of this paper is to determine the type of domain in which such crossing relations will possess nontrivial solutions that are both self-consistent and in keeping with the known properties of the Regge trajectories and residues. An extensive and systematic study of all domains involving large, positive $s$ and values of $t$ in some interval [${t}_{1}, {t}_{2}$] along the positive $t$ axis is presented. We consider both intervals of fixed length and intervals whose length is increasing with $s$. Only one type of interval is found that is satisfactory, namely, intervals consisting of values of $t$ that are increasing in proportion to $s$, i.e., for any given $s$, $t\ensuremath{\in}[\frac{s}{{r}_{1}}, s]$ for some ${r}_{1}>1$. The reasons are the following. It is the only type of interval (1) in which we can provide an existence proof for the solutions to the crossing relations, the proof being valid for asymptotically parallel trajectories; (2) for which the generalization to unequal-mass scattering encounters no obvious inconsistencies; and (3) for which the residues calculated from the crossing relations have an asymptotic form of the type found in the Veneziano model. Furthermore, we can prove the validity of the proposed crossing relations over this type of interval if the modified $s$-channel background integral ${B}_{s}^{\ensuremath{'}}$ satisfies the bound $\mathrm{ln}|{B}_{s}^{\ensuremath{'}}|<\frac{\ensuremath{\surd}2a{s}^{p}}{p}$, where $\mathrm{Re}\ensuremath{\alpha}(s)\ensuremath{\rightarrow}a{s}^{p}$ as $s\ensuremath{\rightarrow}\ensuremath{\infty}$ for $p>0.802$. The analogous proof for any of the other types of domains considered requires the bound $\mathrm{ln}|{B}_{s}^{\ensuremath{'}}|<N\mathrm{ln}s$ for some $N$, which is a much stronger bound. The proof to which we refer assumes only that the contributions of Regge branch cuts to the scattering amplitude are negligible compared to the contributions of Regge poles, ${\ensuremath{\alpha}}_{n}(s)$, for $s$ positive and sufficiently large. In the indicated domain, the crossing relations imply certain homogeneous integral equations that the residues must satisfy. Although a complete solution is not given, we show that as $s\ensuremath{\rightarrow}\ensuremath{\infty}$ the residues behave as $\mathrm{exp}(\ensuremath{-}\ensuremath{\gamma}a{s}^{p})$, where $\ensuremath{\gamma}$ is a logarithmic function of ${r}_{1}$ and $p$. From the expression for $\ensuremath{\gamma}$ we obtain the upper bound $\ensuremath{\gamma}<\mathrm{ln}(3+2\ensuremath{\surd}2)\ensuremath{-}\frac{\ensuremath{\surd}2}{p}$ (for $p=1$, $\ensuremath{\gamma}<0.348$). The constant analogous to $\ensuremath{\gamma}$ in the Veneziano model is 0.38. We add that if the crossing relations proposed here are not valid, then either the background integrals must generate the crossed-channel Regge terms or the background integrals in concert with the direct-channel Regge terms must do so.

Rigorous lower and upper bounds for the slope parameter

It is proved within the framework of axiomatic field theory that the logarithmic derivative of the absorptive part of the scattering amplitude with respect to momentum transfer is bounded from above by (15 log s) [4√t(2 − √t)] for a sequence of s→+∞, and from below either in the s-channel by const. × s −5 log −4 s or in the u-channel by const. × u −5 log −4 u for at least one sequence of s or u →+∞, respectively. In the particular case of the s− u even-symmetric amplitude, a stronger lower bound is obtained; namely, const. × s −5 log −4 s for at least one sequence of s→+∞. Here s, t, and u are the usual Mandelstam variables, and all bounds are obtained in the forward and the unphysical regions: 0⩽ t<4 (in units of pion mass). It is observed that the Regge amplitude β( t) s α( t) of high-energy scattering gives the same energy dependence as the above upper bound, and, furthermore, that the slope of the Regge trajectory is bounded from above by 15 [4√t(2 − √t)] for 0 < t < 4 .

Regge amplitudes through solution of S-matrix equations

This work is a first step in a program for construction of meson–meson scattering amplitudes with analyticity, crossing symmetry, and unitarity. The construction is to be carried out by solving a nonlinear integral equation for the partial wave amplitude a (l,s) at complex l and physical s. The program is intended to overcome the difficulties encountered in the traditional approach based on the Mandelstam iteration of double-spectral functions. An important initial step is to analyze nonrelativistic potential scattering from this autonomous S-matrix viewpoint, in which the Schrödinger equation is replaced by a nonlinear equation for the partial wave amplitude. In the present paper, it is demonstrated that the partial-wave equation has a locally unique solution, provided the potential is of a suitably restricted Yukawa type. This result indicates the feasibility of a pure S-matrix approach to dynamics. In the present report, the potential is so restricted in strength as to preclude bound states or resonances. The extension of the method to the case of strong potentials will be pursued in a later publication.

A phase corrected regge pole model for π− p → π0n

We assume that the imaginary part of the Regge amplitude is given by the standard Regge pole model, but that the real part is given by fixed- t dispersion relations. We compare the results of calculations using this method with those of the Regge pole model for π − p → π 0n in the intermediate energy range 3 ⩽ p lab ⩽ 18 GeV/ c where we find good fits to the data. The magnitude of the ϱ′ contribution needed is in better agreement with measurements of ϱ′ → 2 π couplings than in conventional Regge pole models.

Amplitude analysis of A 2 exchange at 6 GeV/ c

An analysis of experimental data on π − p → η n and K − p → K o n reactions is performed, which enables us to exhibit the A 2 amplitudes. There is strong evidence that the A 2 spin-flip amplitude behaves like a Regge amplitude, exchange degenerate with the ϱ spin-flip one.

Evaluation of [formula omitted] d-waves for −25 μu2 ⩽ t ⩽ 4 μ2

A Froissart-Gribov projection of πN phase shifts and Regge amplitudes is used to evaluate the ππ→ N N scattering length at t=4 μ 2, and partial waves for −25 μ 2 ⩽ t < 4 μ 2. The new value of the scattering length is 15% higher than a previous estimate made in the narrow width resonance approximation. The values for the partial waves are confronted with previous estimates, and lower bounds. As a result, the latter become saturated near t=0, but less restrictive near t=4 μ 2.

Multiple Scattering Effects on the Composite Model forKNand $\bar{K}N$ Elastic and Charge-Exchange Processes

The K± N elastic and charge-exchange scattering up to several Ge V /c is i~vestigated by using the multiple scattering theory. In the present ·treatment it is assumed that hadrons are composed of quarks and when a hadron collides with another hadron . the conventional Regge poles are exchanged between constituent quarks of each hadron. The hadron-hadron scattering amplitudes are then written in terms of the Regge amplitudes. The multiple scattering effect is calculated to second order. The dip-bump and break observed in differ­ ential cross sections are explained by the interference between the single and the double scattering terms.. However the multiple scattering effect for spin-flip amplitude is neglected to fit the cross sections of K-p charge exchange process. The polarization and spin rotation parameters are also ~alcu1ated.

Model independent analysis of the structure in pp scattering

An empirical study of the structure at t≈−1.1 in dσ dt (pp → pp), in terms of two exponential amplitudes plus interference, gives the following results. The steeper exponential shows standard Regge shrinkage, corresponding to a trajectory α ≈1+0.3 t. The other exponential slope stays constant; the overall energy dependence of this amplitude is approximately s −1 for 10–30 GeV, leveling off possibly to a constant at ISR. The relative phase is about 2.1 rad at the lower momenta, becoming 2.5 at ISR. These results suggest a simple physical picture, in which a relatively unstructured shrinking Regge amplitude interferes with an even-signature non-Regge background. This interpretation predicts that the interference minimum in dσ dt is deepest at an intermediate momentum near 175 GeV where measurements will soon be made at NAL.

Strong Interactions at Large Transverse Momentum

The models of Blankenbecler, Brodsky, and Gunion for inclusive and exclusive reactions at large transverse momentum are examined in a covariant framework. The discussion of inclusive reactions is much less model-dependent than that of exclusive reactions, but it is argued that for both the rather specific assumptions of Blankenbecler, Brodsky, and Gunion should probably be relaxed. One can argue that, for inclusive reactions, there may be a connection between the power-law falloff in transverse momentum and the behavior of the structure functions for electroproduction and electron-positron annihilation at $\ensuremath{\omega}=1$ and $\ensuremath{\omega}=0$. The relation of large transverse-momentum inclusive amplitudes to Regge amplitudes at small transverse momentum is also discussed. For the exclusive process it is shown that a more detailed calculation suggests that the angular dependence is different from that calculated by Blankenbecler, Brodsky, and Gunion.

A Colliding-Regge-Cut Representation of the Dual Absorption Amplitude

A colliding-Regge-cut representation of the dual absorption model is proposed for the non-Pomeron amplitude at high energies, in the case of logarithmically s-dependent interaction radius. It is argued that our model is free from ghost divergence and compatible with a set of assumptions; (i) dominance of peripheral partial waves at intermediate and high energies, (ii) logarithmic shrinkage of the Regge amplitude at intermediate and high energies and (iii) approximate s-independence of effective radius at intermediate energies.

Continuous moment sum rules and Regge amplitudes for pion-nucleon scattering

Using continuous moment sum rules and phase-shift data as the only input, Regge-parametrized amplitudes for pion-nucleon scattering are derived. These amplitudes can to great accuracy reproduce high-energy differential cross section and polarization data. They also agree in detail with other model amplitudes and reproduce fairly well the pion-nucleon s-channel helicity amplitudes at the energies where a complete analysis of pion-nucleon scattering has been performed. It turns out to be important that the integration of the amplitude over the unphysical range is treated with care.