Quark distributions in QCD sum rules: Unexpected features and paradoxes

Some very unusual features of the hadron structure functions, obtained in generalized QCD sum rules, like the surprisingly strong difference between longitudinally and transversally polarized ρ-meson structure functions and the strong suppression of the gluon sea in the longitudinally polarized ρ meson, are discussed. The text was submitted by the authors in English.     

Excitation of spin-isospin dipole mode in nuclei

The excitation of spin-isospin dipole mode in the region of nuclei from¹⁶O to nickel isotopes is discussed. The results of calculation of this mode in (e, é) reaction are systematized. It is shown that the concentration of transition strength takes place in all nuclei considered in the energy region of 20–26 MeV.     

Quark distribution in light nuclei

The distribution of quarks in light nuclei is given using the quark cluster wave function. An analytic expression for the nucleus⁴He is obtained. The distribution so obtained is compared with the one obtained using a different theoretical formulation called mapping.     

Strength of spin-isospin transitions in A = 28 nuclei

The relations between the strengths of spin-isospin transition operators extracted from direct nuclear reactions, magnetic electron scattering, and processes of semileptonic weak interaction are discussed.     

Magic numbers in exotic nuclei and spin-isospin properties of the NN interaction

The magic numbers in exotic nuclei are discussed, and their novel origin is shown to be the spin-isospin dependent part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in terms of meson exchange, G-matrix, and QCD theories. In neutron-rich exotic nuclei, magic numbers such as N = 8, 20, etc. can disappear, while N = 6, 16, etc. arise, affecting the structure of the lightest exotic nuclei to nucleosynthesis of heavy elements.     

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.     

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.     

Polarizability sum rules in QED

The well founded total photoproduction and the, assumed substraction free, longitudinal photoproduction polarizability sum rules are checked in QED at the lowest non-trivial order. The first one is shown to hold, whereas the second one turns out to need a subtraction, which makes its usefulness for determining the electromagnetic polarizabilities of the nucleons quite doubtful.     

Optical Thomas-Reiche-Kuhn sum rules

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.     

Meson baryon sum rules

The PCAC consistency condition, the Adler-Weisberger sum rule and the dispersion superconvergent sum rule have been saturated with resonance contributions only. Strangeness-changing currents and strangeness-conserving currents have been considered and compared. The results obtained also support PCAC for the strangeness conserving current. While in theπN case PCAC and the Adler-Weisberger sum rule are almost saturated with the famous N ₃₃ ^* resonance only, in the KN caseY ₁ ^* (1385),Y ₀ ^* (1405) andY ₀ ^* (1520) seem to be sufficient. The superconvergent sum rule works very well in the case ofπN scattering, including the contribution of twelve resonances. For KN scattering it can be neither established nor disapproved.     

Spatial-dispersion and relativistic effects in the optical sum rules

We describe a procedure to take into account the spatial dispersion of the optical excitations in the susceptibility sum rules. We show that this implies that relativistic corrections of the same order must be considered. The final result is a decrease of the total oscillator strength equal to the ratio of the average electron kinetic energy with mc². We propose experiments with synchrotron radiation sources on crystals of heavy elements to observe the described effect. Received 5 June 2001     

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.