On the Regge-pole description of nucleus-nucleus scattering

The properties of the Regge poles of theS-matrix for scattering of strongly-absorbed nuclear particles are considered. Simple formulae are obtained for describing the Regge trajectories in terms of the nuclear radius, the quasi stationary levels in the combined nuclear-Coulomb-potential and the widths of these levels. The predictions of these formulae are compared with the Regge trajectories obtained previously, for a Woods-Saxon potential, and with those required to fit¹⁶O-¹²C backward scattering.     

Relativistic potential scattering

Relativistic potential scattering by a superposition of Yukawa potentials is reexamined. In particular high-energy asymptotic expansions are obtained for the wave-functions and the Regge trajectories. Finally the behaviour of the Regge poles is discussed.     

Confining potentials and Regge poles

A study is made of scattering models which are described by a set of two coupled Schrödinger equations, containing a confining and a nonconfining potential. The partial wave amplitudes are compared with those of conventional potential scattering. Notably the behavior of Regge poles and Regge trajectories is compared.     

Determination of Regge trajectories in a bootstrap model of pion-pion scattering

A simple expansion is used for calculating the zero-energy intercepts of the leading Regge trajectories of the pion-pion scattering amplitude. The results agree well with those of other determinations.     

Continuous-parameter sum rules

Using Laplace transform and Regge high-energy behaviour, continuous-parameter sum rules are found for strong interaction amplitudes. The finite-energy version of these sum rules is discussed and equations for the Regge parameters obtained. Forward πN scattering is considered as an example and numerical values are found for the parameters of and ′ trajectories. A mathematical appendix on the incomplete gamma function is added.     

Regge oscillations in integral cross sections for proton impact on atomic hydrogen

The integral cross sections for elastic scattering and spin exchange for proton impact on atomic hydrogen show several oscillations in the energy range 0.01-1.0 eV that cannot be associated with resonances or the glory effect. A complex angular momentum analysis using computed Regge trajectories shows that each peak of the oscillatory structure is predominantly associated with at most three trajectories. In this way, the peaks are related to the L=0 bound states of H+ 2. The complex angular momentum theory for integral cross sections that we introduce shows that such oscillations are a general feature of potential scattering.     

Bound states in N = 8 supergravity and N = 4 supersymmetric Yang-Mills theories

We present a study of possible bound states in N = 8 supergravity. We find evidence for the existence of multiplets of two-body bound states and expect that many-body bound states may exist as well. Our study is based on a calculation of Regge trajectories in the two-body scattering amplitudes of the lagrangian field theory. We also study Regge trajectories in N = 4 Yang-Mills theory and find evidence for a possible spin zero, SU(4) and gauge singlet, massless bound state. If such a state actually exists and supersymmetry is not broken, it may be a member of a supersymmetric multiplet which includes the graviton.     

Regge-eikonal model for high energy elastic diffractive nucleon-nucleon scattering with a minimum number of reggeons

A phenomenological Regge-eikonal model with nonlinear monotonic parameterizations for Regge trajectories in which their asymptotic behavior in the perturbative region is taken into account explicitly is proposed. It is shown with the example of elastic proton-(anti)proton scattering that in the kinematic region \(\sqrt s \) > 23 GeV, 0.005 GeV² < ?t < 3 GeV², the diffraction pattern is mainly determined by only three Regge trajectories.     

Are the ϱ- and A2-Trajectories Linear?

We analyse in this paper to what extent the rise of the real part of Regge trajectories is due to contributions from baryon-antibaryon thresholds and to what extent it is connected with the presence of a linear term. It is shown that sewing the trajectory from the scattering to the resonance region results in “switching off” the linear term; the remaining contributions of various thresholds guarantee the necessary linearity of the trajectories.     

Crossing symmetric amplitude with Regge poles

We obtain a representation for a pion scattering amplitude that incorporates analyticity in the Mandelstam variables, and meromorphy in the right half of the l-plane. Full crossing symmetry and elastic unitarity in the three elastic regions are built into the equations; and we show how to derive the expected Regge asymptotic behavior as one Mandelstam variable tends to infinity, while another is held fixed at any real or complex value. Moreover, we demonstrate that the inelastic unitarity bound is respected by the partial wave amplitudes, even though the Regge trajectories are allowed to rise indefinitely.     

Possible phenomenological implications of the new trajectories on the pion trajectory

We discuss possible phenomenological consequences of the new Regge trajectories recently discovered in the conventional dual model (CDM) and the Neveu-Schwarz model (NSM). The contributions of the new trajectories to the scattering amplitude dominate at large enough momentum transfers in the multi-Regge limit and it is shown that the β_π trajectory of the NSM should be the most easy to detect experimentally.     

Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange

We derive simple equations in terms of definite signature partial waves for the quark scattering and annihilation amplitudes in the double logarithmic approximation of QCD. We apply the method of isolating the softest virtual particle in the graphs which is based on gauge invariance and unitarity. Besides the particle Regge trajectories and corresponding cuts, there are further singularities in the angular momentum plane generated by perturbative double logarithmic contributions and which may be of phenomenological relevance. We also consider amplitudes with external currents and discuss how to include ultraviolet single logarithms and non-perturbative contributions.     

Exchange-degenerate Regge trajectories: A fresh look from resonance and forward scattering regions

The exchange degeneracy of the mesonic and Regge trajectories, dominant at moderate and high energies in hadron elastic scattering, is analyzed from two viewpoints. The first one concerns the masses of the resonances lying on these trajectories; the second one deals with the total cross sections and the ratios of the real to the imaginary parts of the forward amplitudes of hadron and photon induced reactions. Neither set of data supports exact exchange degeneracy. Received: 23 June 2000 / Revised version: 13 November 2000 / Published online: 23 January 2001     

Threshold Behaviour of Simple and Double Regge Pole Trajectories

The threshold behaviour of simple and double Regge pole trajectories is studied. It is shown that for a number of cases two particle unitarity gives rise to moving J-plane zeros, colliding at threshold with Regge poles. Conditions are found for which Regge trajectories near the threshold S = S₀ have square-root behaviour independent of the value of α(S₀).     

Particle trajectories and quarkonium potentials

We examine the compatibility of potential models for quarkonium with conventional Regge trajectories, exploring in particular questions of linearity and the existence of daughter trajectories. Using, for practical calculations, an effective power behaved potential, it is found that linearity of Regge trajectories is not a universal characteristic. It occurs only in a specific range of the effective quark mass, namely in the ordinary mesons. The Regge slope is in fact a decreasing function of the effective quark mass. Linearity of the ? trajectory requires the ?′ to have a mass 1.62 GeV. Altogether our results bring support to the use of quarkonium potentials in the whole range of constituent quark masses. It is argued that relativistic and non-perturbative vacuum effects give an overall shift to the masses of light mesons but do not affect much mass splittings.     

费米子Regge轨迹的解析性和阈行为

从π介子核子散射振幅出发,根据Mandelstam表示和么正条件,对于奇异量子数为零、重子数为1的费米子Regge轨迹,求得了下列结果:(1)位置参数α(s)的解析性,只有右方物理割而无左方动力割,但是左方有从s=0到-∞的运动学割。(2)当s<0时α(s)取复数值,并且还有一条同它成复共轭(在s<0范围内)的Regge轨迹。这一对轨迹它们的J-宇称相同,但是空间宇称相反。02时,α(s)为实数。不同宇称的轨迹对s的依赖不同。(3)讨论了费米子Regge迹在阈能(W₀=M+μ)附近的行为。凡是与共振态、束缚态有关的Regge轨迹,α(W₀)≠0。求得了在阈附近的表示,定性方面同玻色子轨迹相同。(4)还有一大类Regge轨迹,它们同共振态、束缚态无关,α(W₀)=0。这类轨迹在能量趋近阈能时,有无穷多个极点趋于ReJ=0(即我们在费米子情况下得到Gribov-Pomeranchuk极点凝聚现象),这类轨迹当能量由阈下趋于阈时,从J平面左半平面共轭成对趋于ReJ=0;当能量从阈上趋于阈时,成对地从第一和第三象限趋于ReJ=0。所有这些极点实数部分Reα→0比虚数部分Imα→0快一或二个数量级。J平面原点是一个凝聚点,这类“非动力”的Regge轨迹阈行为,无论对玻色子、费米子,以至非相对论势散射,定性都相似(只是凝聚的轴线和点不同)。它们实际上是s矩阵在阈的普遍性质的反映。     

Asymptotic properties of regge trajectories and elastic pseudoscalar-meson scattering on nucleons at high energies

A phenomenological Regge-eikonal model featuring nonlinear monotonic parametrizations of vacuum Regge trajectories, where their asymptotic behavior in the perturbative sector is taken explicitly into account, is proposed for describing the elastic diffractive scattering of light pseudoscalar mesons on nucleons. In analyzing available experimental data on angular distributions, it is shown that, at collision energies in the region √s > 13 GeV, the diffraction pattern of the processes π ^± p → π ^± p and K ^± p → K ^± p at low momentum transfers can be described qualitatively by using the same phenomenological approximations to vacuum Regge trajectories as in the case of nucleon-nucleon scattering. This fact is indicative of the possibility of explicitly relating Regge phenomenology of various hadron-hadron processes to fundamental results obtained within QCD.     

Glueball spectrum and Pomeron in the Wilson loop approach

Using a nonperturbative method based on the asymptotic behavior of Wilson loops, we calculate the masses of glueballs and the corresponding Regge trajectories. The only input is the string tension fixed by the meson Regge slope, while perturbative contributions to spin splittings are defined by standard α_s values. The masses of the lowest glueball states are in a perfect agreement with lattice results. The leading glueball trajectory, which is associated with the Pomeron is discussed in detail, and its mixing with f and f′ trajectories is taken into account.