Sum rules for forward elastic photon scattering

Relations between integrals over forward elastic photon scattering amplitudes, forward elastic cross sections and total cross sections are derived from dispersion relations. A new photon-proton interaction sum rule is derived and evaluated.     

Sum rules for forward elastic pion-nucleon scattering

A number of energy weighted sum rules relating amplitudes and differential cross sections for forward elastic and charge exchange scattering to the total pion-nucleon cross section are derived from dispersion relations.     

Constraints on the asymptotic behaviour of total cross sections

We derive constraints on the asymptotic behaviour of total cross sections which follow from dispersion relations and measured real parts of the forward scattering amplitudes. For πN and pp scattering, these constraints are calculated using recent results from FNAL and Serpukhov. The relation to other methods is discussed.     

Dispersion-relation analysis of K+p scattering below 2 GeV/c

We have obtained K⁺p scattering amplitudes that fit a large body of data below 2 GeV/c, satisfy phenomenological partial-wave backward dispersion relations, and are consistent with forward dispersion relations for the spin-non-flip amplitude, and forward dispersion-relation sum rules for the K⁺p P-wave scattering lengths. This has been achieved by firstly making an energy-dependent phase-shift analysis of 1 660 pieces of K⁺p data below 2 GeV/c, using parameterised partial-wave dispersion relations, with the additional constraints of forward dispersion relations and P-wave scattering lengths obtained from forward dispersion-relation sum rules, and then checking the resulting solutions for consistency with backward K⁺p dispersion relations.     

Evaluation ofk ± p forward dispersion relations

Kaon-nucleon forward scattering amplitudes have been calculated from dispersion relations using recent experimental data on the total cross sections. In the unphysical region the analytical continuation of theK ^? p effective range theory has been done and for the asymptotic behaviour of the total cross sections a parametrization, suggested by the Regge-pole models, has been used. The calculated real parts of the scattering amplitude are compared with the existing experimental values, as found by the optical theorem and the extrapolation of the angular distribution to the forward direction.     

Forward pion-nucleus elastic scattering amplitudes

Values for the real part of the forward scattering amplitude have been obtained using dispersion relations from an analysis of pion-nucleus total cross sections for ⁴He, ⁶Li and ¹²C. The results are compared with measured values and those predicted by simple optical models. The dependence of the derived values for the forward scattering amplitudes on uncertainties in the measured cross sections is also discussed.     

The quark model and exchange degeneracy

The quark model and exchange degeneracy of leading Reggeon contributions to quark-quark scattering amplitudes are combined for deriving a number of relations on polarizations, the real parts of forward scattering amplitudes and total cross sections. The comparison of these relations with experimental data is discussed.The authors are grateful to Ya. I.Asimov, E. M.Levin and L. L.Frankfurt for their interest in this work.     

Crossing sum rules and high-energy bounds

Exact energy-averaged high -energy bounds for total ππ cross sections are given which do not depend on the d-wave scattering lengthes. Instead, the low-energy input is, essentially, the properties of the f^o meson. The starting points are rigorous sum rules for the physical absorptive parts, following from crossing and analyticity. Except at rather low energies, these bounds are much tighter than the best previous ones.     

Dispersion relation approach to the anomalous magnetic moment in gauge theories

The reason why the dispersion relations for the anomalous magnetic moment are not valid in gauge theories is explained. New sum rules are derived based on unitary bounds of scattering amplitudes. In gauge theories these sum rules give the correct values for the anomalous magnetic moment, while, in the case of conventional renormalizable theories which contain no massive vector bosons, they are identical with the usual dispersion relations for the anomalous magnetic moment.     

A new determination of the πN coupling constantf 2

The coupling constantf ² has been determined from forward dispersion relations for theπN helicity flip and no-flip amplitudes, using the recent information on total cross sections, phase shifts and charge exchange forward cross sections. The calculation gives also the values of the amplitudes and the first derivative at the crossing symmetry point.     

A method for the calculation of Coulomb interference and rescattering corrections to total cross sections in pure spin states

We propose a dispersion theoretic approach to the calculation of Coulomb interference and rescattering corrections to total cross sections in pure spin states. Both types of corrections can be carried out only if the real parts of the forward amplitudes are known, which in general is not the case. However, we show that under some assumptions the unknown real parts enter linearly, which together with analyticity leads to a uniquely solvable integral equation. Our approach is particularly useful in pp and pd scattering where corresponding measurements have been or will be performed. Some applications are discussed.     

Recent Applications of KN Forward Dispersion Relations and Sum Rules

Recent applications of kaon-nucleon forward dispersion relations, superconvergence relations, finite energy sum rules, derivative sum rules, and the Adler-Weisberger sum rule are reviewed. These dispersion relations and sum rules have been used for the determination of the KNA and KN coupling constants, the phases of the kaon-nucleon forward scattering amplitudes, and the Regge pole parameters, and have allowed tests of the PCAC hypothesis for strangeness-changing currents. They also provide important constraints which help to resolve ambiguities in the phenomenological analysis of the scattering data. A critical comparison of various methods which have been proposed is given, the theoretical predictions are compared with experiment when possible, and our present knowledge of the kaon-nucleon interaction parameters is summarized. Some new results are presented.     

Analyticity and quark-gluon structure of hadron total cross sections

The amplitudes of hadron-hadron forward elastic scattering at high energies are investigated on the basis of analyticity and crossing symmetry. A universal uniformizing variable for them is proposed, and the formulas for crossing-even and crossing-odd amplitudes are derived. The same parameters in these formulas determine the real and imaginary (total cross sections) parts of the amplitudes. The analysis of the parameters determined from experimental data clearly points to the quark-gluon structure of hadron total cross sections. The total cross sections for hyperon-proton scattering are predicted. They are consistent with experimental data and, in particular, with the new SELEX-collaboration measurement σ_tot(Σ^?p).     

p elastic scattering in the T-meson region

We have made improved measurements of 43.8 ± 0.8, 41.3 ± 0.4 and 39.3 ± 0.8 mb for the p elastic cross sections at 1.11, 1.33 and 1.52 GeV/c laboratory momenta respectively. Sharp forward peaks in the differential cross sections with broad secondary maxima agree with previous observations [3–6]. The forward differential cross sections are (11 ± 3)% above the optical point in agreement with real amplitudes extended from lower momenta using dispersion relations [7]. The elastic cross sections do not show any structure in the s-channel. Backward differential cross sections show the onset of a “third diffraction peak” but no evidence for other structure in agreement with earlier experiments [6, 13].     

重离子弹性散射中的角分散研究

简要评述了重离子弹性散射角分散研究的内容、 方法及物理意义。通过前角区重离子弹性散射产物微分截面的角分布测量,作出角分散图ln(dσ/dθ)\|θ2。 分析经典偏转函数, 从而在实验上确定了反应系统的核虹角。 在低能、 重靶的重离子反应系统中, 核虹角远小于擦边角。 晕核及弱束缚核比稳定核具有更小的核虹角和更大的核相互作用范围。 经典偏转函数的计算有助于提供一套光学势参数, 以便于拟合弹性散射产物的微分截面。 In terms of the angular dispersion plot of ln(dσ/dθ) versus θ2, which can be obtained from the angular distribution of the elastic scattering differential cross sections in heavy ion collisions, systematic analysis on the angular dispersions is made by using classical deflection function for the available experimental data on the target of 208Pb. Our systematic analyses bring about some important results. Firstly, there is an angular dispersion turning angle at forward angular range beyond the grazing angle. Secondly, the nuclear rainbow angle for such reaction systems can be determined by measuring differential cross sections of elastic scattering at forward angular range and analyzing the angular dispersion. Thirdly, analysis of angular dispersion may provide a way to determine a set of optical potential parameters by means of fitting the experimental data of elastic scattering differential cross sections. Finally, for the halo nuclei as the projectiles, there is an exotic behaviour, i. e., smaller angular dispersion turning angle.     

How crossing affects the analytic relationship between low energy ππ amplitudes and their asymptotic behaviour

Different physical assumptions about the asymptotic behaviour of ππ amplitudes are realised in the different number of substractions involved in fixed t dispersion relations for the various amplitudes and their inverses. The fact that each new dispersion relation must be consistent with s - t crossing leads to a number of conditions relating low energy ππ amplitudes to their high energy behaviour. These are discussed in detail. Such relationships supplement finite energy sum rules with which they are compared. The dispersive sum rules, crossing conditions, and finite energy sum rules we discuss are applied to recent phenomenological solutions to Roy's equations and shown not to narrow the presently accepted range of threshold parameters. These results are in marked contrast to the conclusions of other recent studies. To complete the study of finite energy sum rules we consider the behaviour of the isospin zero t-channel amplitude and estimate the asymptotic ππ total cross-section. We present evidence to suggest that the pomeron is late-developing in meson-meson scattering.     

Dispersion corrections to the forward Rayleigh scattering amplitudes around the L‐shell of tantalum and lead

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum and lead in the photon energy range 6.4–24.14 keV were determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoelectric cross‐sections. The photoelectric cross‐sections were extracted by subtracting the coherent and incoherent scattering contribution from the measured total attenuation cross‐section, using a high‐resolution, high‐purity germanium detector in a narrow‐beam good geometry setup. The real part of the dispersion correction to which the relativistic corrections calculated by Kissel and Pratt (S‐matrix approach) or Creagh and McAuley (multipole corrections) have been included are in better agreement with the available theoretical values than those values to which the relativistic corrections calculated by Cromer and Liberman (dipole corrections) are added. Copyright © 2006 John Wiley & Sons, Ltd.     

On the symmetries between neutrino and antineutrino-nucleon elastic scattering

Various symmetry relations developed between neutrino-neutron and antineutrino-proton elastic scattering cross sections are surveyed and an identity between scattering amplitudes and a symmetry between cross sections of these processes established by consideringCPT andG conjugation invariance of current matrix elements. A symmetry is obtained giving rise to a theorem on the nature of contribution of form factors to terms in the cross sections.     

Electronuclear sum rules

Generalized sum rules are derived by integrating the electromagnetic structure functions along lines of constant ratio of momentum and energy transfer. For non-relativistic systems these sum rules are related to the conventional photonuclear sum rules by a scaling transformation. The generalized sum rules are connected with the absorptive part of the forward scattering amplitude of virtual photons. The analytic structure of the scattering amplitudes and the possible existence of dispersion relations have been investigated in schematic relativistic and non-relativistic models. While for the non-relativistic case analyticity does not hold, the relativistic scattering amplitude is analytical for time-like (but not for space-like) photons and relations similar to the Gell-Mann-Goldberger-Thirring sum rule exist.