Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension condensates containing at least one pair. We extract the direct single-instanton contribution to the sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel. Received: 15 September 1997 / Revised version: 15 November 1997 / Published online: 26 February 1998     

Meson spectrum in a simple planar bootstrap model

A simple planar cluster-multiperipheral model with a finite-energy sum rule constraint is set up, and self-consistency is imposed. This dynamically generates a zero-parameter infinitely-rising vector-tensor Regge trajectory which is in good agreement with experiment.     

Representation of optical fields using finite numbers of bits

We consider the problem of representation of a finite-energy optical field, with a finite number of bits. The optical field is represented with a finite number of uniformly spaced finite-accuracy samples (there is a finite number of amplitude levels that can be reliably distinguished for each sample). The total number of bits required to encode all samples constitutes the cost of the representation. We investigate the optimal number and spacing of these samples under a total cost budget. Our framework reveals the trade-off between the number, spacing, and accuracy of the samples. When we vary the cost budget, we obtain trade-off curves between the representation error and the cost budget. We also discuss the effect of degree of coherence of the field.     

The non-ordinary Regge behavior of the $$K^*_0(800)$$ or $$\kappa $$κ-meson versus the ordinary $$K^*_0(1430)$$K0∗(1430)

The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the \(K^*_0(1430)\) Regge trajectory, finding the ordinary almost real and linear behavior, typical of \(q \bar{q}\) resonances. In contrast, for the \(K^*_0(800)\) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the \(f_0(500)\) or \(\sigma \) meson. The slope of these unusual Regge trajectories seems to scale with the meson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non-ordinary, predominantly meson–meson-like, interpretation for the lightest strange and non-strange resonances.     

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 poles in the collective model of the nuclear giant multipole resonances

Giant nuclear resonance states, of higher multipolarity than dipole, have recently been observed in hadron and electron scattering. They may possibly be described by the collective Goldhaber-Teller model as extended to the higher multipolarity case, and as generalized to include spin-isospin vibrations and spin waves. Based on such a model, we show that the multipole resonances, together with the conventional dipole resonances, can be generated by the motion of a few basic Regge poles through the complex angular momentum plane. This viewpoint unifies all the resonances with a given spin-isospin character but arbitrary value of the multipolarity, and suggests the existence of the higher-multipole resonances as a consequence of the existence of the dipole resonance. We also analyze these Regge poles in terms of collective surface waves (“creeping waves”) circumnavigating the nucleus, and we determine their phase velocities and attenuations. Finally, the giant resonances them selves are explained as a resonant reinforcement of phase-matched surface waves.     

散射幅的渐近行为和高能非弹性作用

假设当t<0时,真空Regge极点变为一对共轭复数,计算了高能道么正积分的弹性部分,结果亦得到应有一系列的支点。弹性积分不可能得到相应其他Regge极点的渐近项。把Regge表示推广应用到非弹性过程,得到有限粒子束的产生截面随(Ins)^-3下降。要使总截面趋于常数,则束数应达到Ins的数量级。     

Correspondances between the Symmetric Lund Model and the Dual Resonance Model

The Symmetric Lund Model is formulated in a manifestly forward-backward symmetric way and generalized to include transverse momenta and finite width resonances. It is shown to possess multiregge behaviour and inclusive-exclusive connection. It's characteristic exp (?area) damping factor is shown to occur also in dual amplitudes, if the Regge slope is given an imaginary part. The introduction of an infinite family of resonances described by a continuous mass spectrum is advocated; it realizes the synthesis of the Symmetric Lund Model with the Bowler and the Artru-Mennessier models, and improves the connection with the Dual Resonance Model.     

Split-width dual model

A crossing-symmetric amplitude with asymptotic Regge behaviour and second-sheet resonances with different widths for parents and each daughter is proposed. With a suitable choice of a function, ghosts and tachyons can be eliminated.     

Understanding the Meson States and Non-qq States

By studying the behavious of Regge trajectories of the boson resonances and comparing with the predictions from quark model, we understand more the existing scalar, tensor, pseudoscalar particles and non-quark-antiquark states. One can find some resonances are non-qq states.     

Resonance-reggeon and parton-hadron duality in strong interactions

By using the concept of duality between direct channel resonances and Regge exchanges we relate the small- and large-x behavior of the structure functions. We show that even a single resonance exhibits Bjorken scaling at large Q². Received: 30 October 2001 / Accepted: 16 November 2001     

Sum rules from boundary dispersion relations

Sum rules for inelastic reactions are derived from boundary dispersion relations. If sufficient data or a model is available for the amplitude in the direct channel, then these sum rules provide a means of studying the dynamics in the cross channel. The convergence of these sum rules is investigated, assuming they can be saturated with narrow-width resonances, and rough estimates of the coupling constants of cross-channel exchanges for the photoproduction of pseudoscalar mesons are obtained.     

Pion-induced ${K}^{* }$ production with ${{\rm{\Sigma }}}^{* }$ baryon off proton target

In this work, the reaction ${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$ is investigated with an effective Lagrangian approach. The contributions from the Born terms, including the s, t, and u channel, are considered, and the Regge model and the Feynman model are applied to treat the t -channel contribution. The existing experimental data can be reproduced with the best-fitted χ ² being 2.38 and 1.54 for the Feynman and Regge models, respectively. Moreover, it is found that the contribution from the t channel is dominant in the cross-section. The contribution of the u channel is mainly distributed at backward angles, and the contribution from the s channel is small and negligible. In the Feynman model, the contribution of the t -channel K exchange is much larger than the contribution of the ${K}^{* }$ exchange, while in the Regge model the contribution of the t -channel K exchange is comparable to that of the ${K}^{* }$ exchange. Prediction about the differential cross-section of the ${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$ reaction is also presented, which is helpful for clarifying the role of the Regge treatment. The current results suggest high-precision experimental measurements which can be performed at J-PARC and COMPASS.     

Regge poles for the superposition of central and quadratic spin-orbital potentials

The nature of the arrangement, the multiplicity, and the behavior of Regge poles are investigated when the quadratic as well as the central spin-orbital potentials are taken into account in the Schrodinger equation. It is established that in this case the appearance of additional poles that can be interpreted as bound states and resonances is possible in the domain Re >0. ForK ²> 0 the Regge poles can be arranged in both the first and fourth quadrants of the -plane.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 18–20, March, 1984.     

Hadron scattering in two-dimensional QCD: (I). Formalism and leading order calculations

Two-dimensional quantum chromodynamics in the 1/N_c expansion is explored as a model for hadronic interactions. In meson-meson scattering, order 1/N_c terms exhibit embryonic “Regge” behaviour, with the crossed channel factorization, signature and exchange degeneracy properties found in dual Regge models. “Regge” intercepts are additive in the quark quantum numbers exchanged, and have a lower limit for large quark masses. Residues also factorize in the direct channel. An analogue for fixed angle scattering is presented which has deviations from dimensional counting rules related to form factors and Regge intercepts.     

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。     

Resonance theory of elastic wave scattering from a cylindrical cavity

Resonant excitation of a fluid-filled cylindrical cavity in an elastic medium by an incident compressional wave is investigated on the basis of the resonance theory of nuclear scattering. It is shown that the scattering amplitude consists of a series of narrow resonances super-imposed upon, and interfering with, a broad background that corresponds to the scattering from an empty cavity. The resonances may be analyzed in a most enlightening fashion by studying them separately in each partial wave of the normal-mode series. They are seen to correspond to excitations of the eigenvibrations of the cavity fluid caused by a phase-match of “creeping waves”, similar to the “Regge poles” of nuclear physics.