QCD sum rule for nucleon in nuclear matter

We consider the two-point function of nucleon current in nuclear matter and write a QCD sum rule to analyse the residue of the nucleon pole as a function of nuclear density. The nucleon self-energy needed for the sum rule is taken as input from calculations using phenomenological N N potential. Our result shows a decrease in the residue with increasing nuclear density, as is known to be the case with similar quantities.     

Exchange currents and nucleon magnetic moments

We investigate the effect of gluon and pion exchange currents on the magnetic moments of the nucleon using the constituent quark model. We also study the effect of scalar exchange currents connected with the confinement and sigma exchange potentials. We conclude that although individual exchange currents are quite large, the total exchange current contribution is relatively small, due to a cancellation of gluon, pion, and scalar exchange currents.Lecture presented at the Indian-Summer School on Interaction in Hadronic Systems, Praha (The Czech Republic), 25–31 August 1993.I would like to thank my colleagues Dr. E. Hernandez and Prof. K. Yazaki, for their collaboration in this field.     

Test of sum rules in nucleon transfer reactions

The quantitative consistency of nucleon transfer reactions as a probe of the occupancy of valence orbits in nuclei is tested. Neutron-adding, neutron-removal, and proton-adding transfer reactions were measured on the four stable even Ni isotopes, with particular attention to the cross section determinations. The data were analyzed consistently in terms of the distorted wave Born approximation to yield spectroscopic factors. Valence-orbit occupancies were extracted, utilizing the Macfarlane-French sum rules. The deduced occupancies are consistent with the changing number of valence neutrons, as are the vacancies for protons, both at the level of <5%. While there has been some debate regarding the true "observability" of spectroscopic factors, the present results indicate that empirically they yield self-consistent results.     

Current quark-mass dependence of nucleon magnetic moments and radii

A calculation of the current quark-mass dependence of nucleon static electromagnetic properties is necessary in order to use observational data as a means to place constraints on the variation of Nature’s fundamental parameters. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined quarks and nonpointlike diquarks, is used to calculate this dependence. The results indicate that, like observables dependent on the nucleons’ magnetic moments, quantities sensitive to their magnetic and charge radii, such as the energy levels and transition frequencies in hydrogen and deuterium, might also provide a tool with which to place limits on the allowed variation in Nature’s constants.     

QCD sum rule determination of the axial-vector coupling of the nucleon at finite temperature

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, g_A(T). We find that g_A(T) is essentially independent of T, in the very wide range 0≤T≤0.9 T_c, where T_c is the critical temperature. While g_A at T=0 is q²-independent, it develops a q² dependence at finite temperature. We then obtain the mean square radius associated with g_A and find that it diverges at T=T_c, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.     

SUSY magnetic moments sum rules and supersymmetry breaking

It was recently shown that unbrokenN=1 Susy relates, in a model independent way, the magnetic transitions between states of different spin within a given charged massive supermultiplet. We verify explicitly these sum rules for a vector multiplet in the case of massless and massive fermions. The purpose of this analysis is to provide the ground for the broken susy case. We study the modifications of these results when an explicit soft Susy breaking realized through a universal mass for all scalars is present. As a by-product we provide a computation of theg — 2 of theW boson in the standard model which corrects previous evaluations in the literature.     

Energy-weighted sum rule for magnetic excitations in the random phase approximation

The formulas for the energy-weighted sum rule are obtained within the Random Phase Approximation (RPA) in the case of multipole excitations of atomic nuclei induced by the magnetic external field of the general form. The results are compared with the formulas known from the literature and with direct calculations of the moments of the strength function within the RPA.     

Ground state baryon magnetic moments and nucleon axial vector coupling

Ground-state baryon magnetic moments and nucleon axial vector coupling are calculated usingqcd inspired configuration mixing and relativistic corrections. Unlike earlier attempts, we incorporate a natural mass scale for quarks, taken as one third the nucleon mass for up and down quarks, and the strange quark mass suggested by the Lipkin’s sum rule. In the parameter-free non-relativistic limit, we find a fairly good fit, which improves upon including relativistic corrections.     

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.     

Pion mass dependence on nucleon magnetic moments in the extended linear sigma model

The dependence of the nucleon magnetic moments on the pion mass is studied in the framework of the extended linear sigma model. The field equations have been solved in the mean-field approximation. A remarkable agreement is observed in comparison with other models.     

QCD sum rules and electromagnetic polarizabilities of a nucleon

We investigate the electromagnetic polarizabilities of a nucleon using the method of QCD sum rules. The diagrams in the operator product expansion are taken into account up to dimension 6. We find that the polarizabilities of a nucleon can be expressed by means of three new kinds of susceptibilities of quark condensates which represent the response under weak external electromagnetic fields. Estimating the susceptibilities with the QCD sum rules itself based on the formalism by Balitsky et al., we see that good agreement is obtained for the neutron electric polarizability.     

The nucleon structure functions in deep inelastic scattering off deuterium: nuclear shadowing and the Gottfried sum rule

The perturbative QCD is applied to calculation of nuclear shadowing correction to the deuterium structure functionF ₂ ^D (x) atx«1. This correction is shown to be numerically large. It is emphasized that the neglect of nuclear shadowing leads to underestimating of the neutron structure functionF ₂ ⁿ (x) and, as a result, to gross overestimating of the Gottfried integral \(\int_0^1 {\left[ {F_2^P (x) - F_2^n (x)} \right]} dx/x\)      

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 Bayesian analysis of the nucleon QCD sum rules

QCD sum rules of the nucleon channel are reanalyzed, using the maximum-entropy method (MEM). This new approach, based on the Bayesian probability theory, does not restrict the spectral function to the usual “pole + continuum” form, allowing a more flexible investigation of the nucleon spectral function. Making use of this flexibility, we are able to investigate the spectral functions of various interpolating fields, finding that the nucleon ground state mainly couples to an operator containing a scalar diquark. Moreover, we formulate the Gaussian sum rule for the nucleon channel and find that it is more suitable for the MEM analysis to extract the nucleon pole in the region of its experimental value, while the Borel sum rule does not contain enough information to clearly separate the nucleon pole from the continuum.