Comment concerning the evaluation of the Cabibbo-Radicati sum rule

The Gilman-Schnitzer evaluation of the Cabibbo-Radicati sum rule is discussed. It is argued that the SU(2) generalization of the ΔNπγ contact5 term has to be included in the evaluation. Doing so considerably decreases (15% rather than 8% discrepancy) the agreement of the sum rule with the data.     

Inelastic sum rule for high-energy hadron scattering and nucleon-nucleon correlations

We have considered the influence of short-range dynamical and statistical correlations on the elastic and summed inelastic scattering of high-energy hadrons from light nuclei. Our calculations are based on the complete multiple scattering series of Glauber. The correlation effects are discussed on the example of the inelastic sum rule for p-¹⁶O scattering.     

Longitudinal sum rule for inelastic electron scattering and nucleon-nucleon correlations

We have considered the influence of short-range dynamical and statistical correlations on the inelastic scattering of electrons from light nuclei. The correlation effects are discussed on the example of the longitudinal sum rule for the ¹⁶O and ¹²C nuclei. A remarkable increase in the sum rule, caused by the short-range correlations at medium momentum transfers (100–200 MeV), is pointed out.     

The relativistic Coulomb sum rule for electron scattering in the independent-particle model

The problems associated with including relativistic effects in the non-energy-weighted Coulomb sum rule for electron scattering are discussed. A new formulation of the sum rule is proposed, and this sum rule is calculated under a variety of conditions within the framework of the independent-particle model. Ambiguities due to model dependence were found to be small, and the simple factor Z, the atomic number, was found to be a good approximation to the calculated values of the sum rule. This provides a basis against which correlations or more exotic effects can be measured.     

X-ray magnetic circular dichroism sum rule correction for the light transition metals

Distinguishable L₂ and L₃ edges and a clear separation into j _3/2 and j _1/2 excitations are necessary for the application of L_2,3 edge X-ray magnetic circular dichroism (XMCD) sum rules, which provide element-specific information about spin and orbital magnetic moments. This separation is present for the heavy transition metals (TM), like Co and Ni, due to their large L_2,3 spin–orbit splitting. However, for the light TM, the 2p spin–orbit splitting is strongly reduced and quantum mechanical mixing of j _3/2 and j _1/2 excitations is present. This mixing reduces the observed XMCD related spin and magnetic dipole term contributions and prevents the direct application of XMCD spin sum rules. A large number of 2p?→?3d absorption spectra have been fitted nearly perfectly by a simple and phenomenological model, which takes into account lifetime effects and provides quantitative information about jj-mixing at the light TMs. On the basis of this mixing coefficient, sum rule correction factors have been determined. The proposed model results in renormalized magnetic projected XMCD spin moments, verified for different compounds of V, Cr, and Mn. A comparison with complementary methods gives consistent results. This or a similar fitting procedure and the estimated correction factors can be used in the future as a light element XMCD spin renormalization technique.     

A QCD sum rule study of the light scalar mesons

We examine the interpretation of the light scalar meson nonet as bound states of the scalar diquark and the scalar antidiquark using the QCD sum rule approach. Our results are obtained by means of the operator product expansion (OPE) including operators up to dimension 8. They show no evidence of the coupling of the tetraquark states to the light scalar meson nonet.     

Spin-orbit sum rule for electric multipole transitions in nonresonant inelastic x-ray scattering

The sum rule for the branching ratio of dipole-excited core-valence transitions in isotropic x-ray absorption spectroscopy is extended to electric multipole transitions. The derived sum rule not only shows that the branching ratio is linearly related to the expectation value of the angular part of the spin-orbit operator in the valence states, but also shows a strong dependence on the rank of the multipole. The spin-orbit dependence vanishes in the weighted sum over the branching ratios. The effect can be an important diagnostic tool for high-energy spectroscopies.     

New sum rules for polarized deep inelastic scattering

Relations between the structure functions g₁ and g₂ of polarized DIS are derived in the leading perturbative QCD approximation, starting with the sum rules for twist-3 parton correlation functions which follow from gauge invariance and the equation of motion of the quark fields. For the first moments they coincide with the approximate relations proposed earlier by Wandzura and Wilczek as well as Bukhvostov, Kuraev and Lipatov.     

Superposition rule for light scattering by a composite particle

A superposition rule for light scattering by composite particles is presented that expresses the scattering amplitude of a composite particle as a superposition of that of the host particle and those of the shadowed inclusions. The superposition rule is derived for a soft composite particle but also provides insight into light scattering by a general composite scatterer. Favorable comparison with an exact numerical method demonstrates the usefulness of the rule in analyzing light scattering by composite particles such as biological cells.     

QCD sum rule study of the masses of light tetraquark scalar mesons

We study the low-lying scalar mesons of light u, d, s flavors in the QCD sum rule. Having all possible combinations of tetraquark currents in the local form, QCD sum rule analysis has been carefully performed. We found that using the appropriate tetraquark currents, the masses of σ, κ, f₀ and a₀ mesons appear in the region of 0.6–1 GeV with the expected ordering. The results are compared with that of the conventional currents, where the masses are considerably larger.     

New sum rules forππ scattering using Roskies’ amplitudes

On the basis of crossing symmetry a new set of exact relations involving theππ partial wave amplitudes have been derived, using Roskies’ amplitudes.     

Third-frequency-moment sum rule for electronic multilayers

The authors establish the third-frequency-moment sum rules for the density-density reponse matrix of electronic multilayer structures modeled as an array of N parallel two-dimensional (2D) electron-plasma monolayers. Layer densities and spacings between adjacent layers need not be equal. Contact is made with previously established sum rules for the isolated 2D electron liquid and type-1 infinite superlattices. The case of the equal-density bilayer is considered and its third frequency-moment-sum-rules for the in-phase and out-of-phase inverse dielectric functions are formulated.     

Longitudinal sum rule for the general dielectric function

The sum rule is derived without assuming any translational or point symmetry. Within the self consistent field approximation, for the case of finite translational symmetry, a more direct proof is given.     

A universal sum rule for hadronic elastic scattering with applications to the Tevatron,RHIC and LHC

Under the assumption that at high energies total absorption prevails so that the imaginary part of the scattering amplitude dominates, we present a sum rule for all hadronic elastic differential cross-sections. We find that the dimensionless quantity , at asymptotic energies. A comparison with experimental data from ISR and Tevatron confirms a trend towards its saturation and some estimates are presented for LHC. Its universality and further consequences for the nature of absorption in QCD based models for elastic and total cross-sections are explored.Received: 15 August 2004, Revised: 27 April 2005, Published online: 8 July 2005     

New approach to axial coupling constants in the QCD sum rule

We derive new QCD sum rules for the axial coupling constants by considering the correlation functions of axial-vector currents in a one-nucleon state. The QCD sum rules tell us that the axial coupling constants are expressed by nucleon matrix elements of quark-gluon composite operators which are related to the sigma terms and the moments of parton distributions. The results for the isovector axial coupling constants and the eighth component of the SU(3)(f) octet are in good agreement with experiment.     

Understanding light scalar meson by color-magnetic wave function in QCD sum rule

In this paper, we study the 0⁺ nonet mesons as tetraquark states with interpolating currents inspired by the color-magnetic wave function. This wave function is the eigenfunction of an effective color-magnetic Hamiltonian with the lowest eigenvalue, meaning that the state depicted by this wave function is the most stable one and is the most probable to be observed in experiments. We perform an OPE calculation up to dimension-eight condensates and find that the best QCD sum rule is achieved when the current inspired by the color-magnetic wave function is a proper mixture of the tensor and pseudoscalar diquark-antidiquark bound states. Compared with previous results, to sigma(600) and kappa(800), our results appear better, due to larger pole contribution. The direct instanton contributions are also considered, which yields a consistent result with previous OPE results. Finally, we also discuss the h￠ \eta{^\prime} problem as a possible six-quark state.     

Electric dipole sum rule for light even-even nuclei via Brueckner-Hartree-Fock (BHF) wave functions

We present calculations of the enhancement factor κ in the electric dipole sum done by the use of solutions of the Brueckner-Hartree-Fock (BHF) equations. Results are given for ⁴He, ¹²C and ¹⁶O for various realistic nucleon-nucleon potentials.