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).     

Inclusive Single Particle Distributions from the Dual Fermion Model

Inclusive single particle distributions are calculated from the discontinuity of a phenomenological 4π NN amplitude obtained from the Neveu-Schwarz-Ramond dual fermion model. In contrast to former calculations using the conventional Veneziano B₆-function we get a correct triple Regge behaviour at x ≈ 1 with correct pole position in the t-channel which is able to reproduce the data. The pomeron, not contained in the dual Born amplitude, is taken into account phenomenologically in the NN channel. Other pomeron contributions are subtracted from the data. We compare the inclusive pion distributions of the model in the beam fragmentation and central region with experimental data for reactions π + N → + X at 8 and 16 GeV/c.     

Deuteron photodisintegration within the Quark-Gluon Strings Model and QCD motivated nonlinear Regge trajectories

We investigate deuteron two-body photodisintegration within the framework of the Quark-Gluon Strings Model with nonlinear baryon Regge trajectories. Special attention is paid to the use of QCD motivated Regge trajectories of the logarithmic and square-root form. We find that the recent experimental data from TJNAF in the few-GeV region can be reasonably described by the model. Angular distributions at different γ-energies are presented and the effect of a forward-backward asymmetry is discussed. Predictions for the energy dependence of dσ/dt at higher energies and different Θ_c.m. are presented, too. Received: 12 March 2001 / Accepted: 19 March 2001     

Dual analytic model of generalized parton distributions

A model for generalized parton distributions (GPDs) in the form of ∼(x/g ₀)^{(1−x)ᾶ(t)}, where ᾶ(t) = α(t) − α(0) is the nonlinear part of the Regge trajectory and g ₀ is a parameter, g ₀ > 1, is presented. For linear trajectories, it reduces to earlier proposals. We compare the calculated moments of these GPDs with the experimental data on form factors and find that the effects from the nonlinearity of Regge trajectories are large. By Fourier transforming the obtained GPDs, we access the spatial distribution of protons in the transverse plane. The relation between dual amplitudes with Mandelstam analyticity and composite models in the infinite-momentum frame is discussed, the integration variable in dual models being associated with the quark longitudinal-momentum fraction x in the nucleon. The text was submitted by the authors in English.     

Backward pion-nucleon scattering

A global analysis of the world data on differential cross-sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3GeV is performed in a Regge model. Including the N_a\ensuremath N_{\alpha} , N_g\ensuremath N_{\gamma} , D_d\ensuremath \Delta_{\delta} and D_b\ensuremath \Delta_{\beta} trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable u , in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3GeV. Our analysis suggests a G₃₉\ensuremath G_{39} -resonance with a mass of 2.83GeV as member of the D_b\ensuremath \Delta_{\beta} -trajectory from the corresponding Chew-Frautschi plot.     

Proton-proton scattering above 3 GeV/c

A large set of data on proton-proton differential cross sections, analyzing powers and the double-polarization parameter A_NN is analyzed employing the Regge formalism. We find that the data available at proton beam momenta from 3GeV/c to 50GeV/c exhibit features that are very well in line with the general characteristics of Regge phenomenology and can be described with a model that includes the $ \rho$ \rho , $ \omega$ \omega , f₂, and a₂ trajectories and single-Pomeron exchange. Additional data, specifically for spin-dependent observables at forward angles, would be very helpful for testing and refining our Regge model.     

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。     

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.     

最大解析性原理与Regge轨迹的若干性质

根据最大解析性原理,本文研究了Regge轨迹的某些性质。证明了与各粒子对应的Regge轨迹在阈能以下是能量的单调增加函数,当t→±∞时,每一轨迹的渐近极限是相同的。特别当-t₀p (0)应满足不等式1/t₀<α′_p(0)<1/4,其中t₀由α_p(t=-t₀)=0决定。     

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.     

Bare Reggeons in asymptotic free theories

Conformal symmetry is used to investigate the Regge asymptotics for the six dimensional scalar φ³ model and the QCD vacuum exchange amplitude. Resulting angular momentum cuts change into series of poles by scale breaking due to renormalization. The Regge pole trajectories are calculated for large momentum transfer.     

Regge analysis of the ππ scattering amplitude

The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the ππ scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the ππ amplitude (Pomeron, f and ρ), using factorization, phenomenological parametrizations of the πN and NN total cross sections at high energy, and a set of sum rules which connect the high and low energy properties of ππ scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with ℓ≤4. The uncertainties in our result for the Regge parameters are sizable, but in the solutions of the Roy equations these only manifest themselves above the K[`]KK\hspace {0.03cm}\overline {\rule [0.7em]{0.6em}{0em}}\hspace {-0.8em}K threshold.     

Regge behavior of DIS structure functions in scalar theories

The Bethe-Salpeter formalism is used to incorporate the valence Regge behavior into the total DIS amplitude. For a special case of scalar quarks with massless scalar exchange, the model is solved both analytically and numerically and exact scaling is found for the valence quark contribution F ₂(x) ∼ (1/x) ^l(0)−1 which mimicks the ρ-trajectory term. The solution solves a long-standing problem by showing that the coefficient in the Regge pole expansion is indeed fine-tuned to give the expected scaling. The method allows for generalization to the region of nonzero momentum transfer and calculation of the DVCS amplitude. The text was submitted by the authors in English.     

Experimental limits on the lowest possible mass horizontal gauge boson in SU(2) H

A unified picture of both soft and hard hadronic collisions is suggested. The basis idea is to use Regge trajectories of the type $$\alpha (t) = \alpha (0) - \gamma ln (1 + \beta \sqrt {t_0 - t} )$$ in dual models with Mandelstam analyticity. The idea is applied to elastic proton-proton scattering to derive kinematical boundaries of the asymptotic (Regge-t _R and scaling-S _sc.,t _sc.) regimes, to fix the angular dependence in the scaling-and thet-dependence in the Regge domain of the scattering amplitude and to interpolate between the two asymptotic domains.     

高能散射与αqRegge轨迹

我们引进一个具有真空量子数的新的Regge轨迹α_q,α_q(0)=α_p(0)=1,但α′_q(0)≠α′_p(0)。在高能非交换过程中α_q和α_p同时参与贡献且相互干涉,其结果和一个等效的Regge轨迹α_e相当,唯α_e的斜率α′_e(0)与过程有关,这与单一α_p轨迹的结论有本质的区别。根据我们的看法,由不同过程测得的α′_e(0)将有不同数值,这点和最近的实验是相容的,并且预期将来K-N散射所测的α′_e(0)亦将另取他值。α_q轨迹的存在将不改变高能相关过程总截面的关系,但使高能核子极化度随能量增大较缓慢地衰减。     

Sister trajectories in the dual resonance model

The existence of a Regge tranjectory γ = α/3 ? 1 in the eight-point amplitude of the Dual Resonance Model set of demonstrated. It is suggested that the three presently known trajectories α, β and γ are part of an infinite set of “sister” trajectories, the expected properties of which are discussed.     

Phenomenological description of the reaction K−p→K10(890)(π−p) using a dual fermion model

Using the Neveu-Schwarz-Ramond model as a starting point, attempts have been made to construct a phenomenological dual amplitude for the reaction $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^{10}\text{(890)(π}{}^{\mathrm{?}}\text{p}\text{)}$. The amplitude contains trajectories of both natural and unnatural spin-parity in the exchange channel as well as N_α, N_γ and Δ trajectories in the production channel. Furthermore, it has the correct Regge behaviour in both meson and fermion channels. Reasonable agreement between the predictions and the data with respect to differential cross sections and density matrix elements has been found.