Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order α _s corrections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.     

Photo-absorption sum rules σ<Subscript>–1</Subscript> in different environments (Atoms,nuclei, nucleons)

Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ_–1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the “CS-conjugated” triton and ³He.     

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.     

Approach to Perturbative QCD Results in Transition Amplitudes of Nucleon Negative-Parity Resonances

The scaling behaviors of the nucleon resonance transition amplitudes from perturbative QCD (PQCD) are utilized to parametrize the amplitudes of the first negative-parity nucleon resonance S₁₁(1535). Our analysis indicates that the constraints of the transition amplitude for the S₁₁ resonance at the limit Q²→∞ by QCD sum rule calculations are not applicable at a moderate Q² range of 2.5 ～ 4 GeV² compared with the present available data if the contribution of S₁₁ is dominant in the Q² limit.     

Bound-state perturbation method via SVZ sum rules in quantum mechanics

The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.     

Equal time commutators of spatial components of axial charges and corresponding sum rules

We derive a set of sum rules by saturating the equal-time commutator of integrated space components of axial currents between nucleon states at rest. The relation of these sum rules to the SU(6) results is discussed.     

Study of spin sum rules (and the strong coupling constant at large distances)

We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.     

Structure change of 156Yb at high-spin states

High-spin states of 156Yb have been studied via the 144Sm(16O,4n)156Yb fusion-evaporation reaction at beam energy 102 MeV. The positive-parity yrast band and negative-parity cascade have been extended up to higher-spin states, respectively. The characteristics of the negative-parity sequence above the 25- state may related to the excitation from the nucleon in the Z = 64, N = 82 core. The E-GOS curve for the positive-parity yrast sequence in 156Yb indicate that this nucleus may undergo an evolution from quasivibrational to quasirotational structure with increasing angular momentum. The Cranked Woods-Saxon-Strutinsky calculations by means of Total-Routhian-Surface (TRS) methods has been made to understand this structure change.     

On contribution of instantons to nucleon sum rules

The contribution of instantons to nucleon QCD sum rules is obtained. It is shown that this contribution does provide stabilization of the sum rules and leads to formation of a nucleon as a bound state of quarks in the instanton field.     

Odd-even nuclei in the A ≈ 100 nuclear region

Extensive calculations for the odd-neutron Ru-Pd isotopes and odd-proton Tc-Rh isotopes for both positive- and negative-parity states within the proton-neutron interacting boson-fermion model are presented. The results on energy levels, electromagnetic properties and spectroscopic strengths of one nucleon transfer reactions are compared with experiments. A general good agreement is obtained.     

Sum rules for the structure parameters of the nucleon

Based on the parton model and some commonly used assumptions, a class of sum rules is obtained which relates the structure parameters of the nucleon such as the proton charge radius with the quantities which can be most directly connected with the experimental observables in the hard massive photon limit, that is, the deep inelastic nucleon structure functions.     

A computation of Adler's β sum rule II

We improve our previous calculation of Adler's β sum rule by including the Born contributions to the πN states. The result is that the sum rule is only balanced if the weak axial nucleon form factor g_A(q²) and the strong pion-nucleon form factor have roughly the same q² dependance.     

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.     

The second moments of quark and gluon distribution functions in hadrons

The second moments of guark and gluon distribution functions in the nucleon and pion are calculated on the basis of the QCD sum rule method. The results obtained are in good agreement with the experimental data.     

Meson fields, exchange currents and progenitor sum rules

The theory of the integrated photoabsorption cross section and the dipole sum rule is reviewed. A new progenitor sum rule, in which meson fields appear explicitly, is derived from a field theory of interacting pions and nucleons. The relation of this sum rule to previous results obtained in a potential theory is elucidated, and the role of neutron-proton correlations in nuclear ground states is discussed in terms of their effect on the dipole sum rule. The inclusion of ρ-mesons (again in an oversimplified theory) and their contribution to progenitor sum rules is also mentioned.     

Experimental verification of the GDH sum rule

Sum rules involving the spin structure of the nucleon like those due to Bjorken, Ellis and Jaffe and the one due to Gerasimov, Drell and Hearn offer the opportunity to study the structure of strong interactions. At long distance scales in the confinement regime the Gerasimov-Drell-Hearn (GDH) Sum Rule connects static properties of the nucleon like the anomalous magnetic moment κ and the nucleon mass m, with the spin dependent absorption of real photons with total cross sections 0gs_3/2 and σ_1/2:

Here 3/2 and 1/2 identify relative spin orientation of the photon and the nucleon parallel or anti-parallel respectively in the nucleon rest frame; denotes the fine-structure constant and ν the energy of the photon. Hence the full spin-dependent excitation spectrum of the nucleon is related to its static properties. The sum rule has not been investigated experimentally until recently. For the first time this fundamental sum rule is verified by the GDH-Collaboration with circularly polarized real photons and longitudinally polarized nucleons at the two accelerators and . The investigation of the response of the proton as well as of the neutron allows to perform an isospin decomposition. Data from the resonance region up to the onset of the Regge regime are shown. The “sum” on the left hand side of the GDH Sum Rule can be generalized to the case of virtual photons. This allows to establish a Q² dependency and to study the transition to the perturbative regime of QCD. This is the subject of several experiments e.g. at for the resonance region and of the experiment at for higher Q². Moreover, this paper covers the status of theory concerning the GDH Sum Rule, the different experimental approaches and the results for the absorption of real and virtual photons will be reviewed.     

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.     

Gottfried sum rule and the shape ofF 2 ⌍ -F 2 ⌍

The recent experimental determination of the Gottfried sum rule of deep inelastic scattering provides strong evidence that SU(2) flavor symmetry is broken by the sea quark distributions of the nucleon. Two mechanisms have been suggested to explain the data: Pauli blocking and non-perturbative contributions to the sea arising from the pion cloud surrounding the nucleon. We investigate the effects of these two mechanisms on several standard parametrizations of the quark distribution functions and find that each mechanism has different effects on the shapes of these distribution functions. The best agreement between the experimental data and the modified quark distributions occurs when both mechanisms are taken into account using a softπNN form factor and a small Pauli correction.     

夸克的横向性分布与核子张量荷

夸克的横向性分布的一次矩定义了核子张量荷. 核子张量荷也可用张量流算符在核子态的矩阵元定义,由此用量子色动力学求和规则、有效理论和模型计算了核子张量荷. 对研究核子性质及强子物理的自洽非微扰途径问题也作了简要讨论. The first moment of quark transversity distribution defines the tensor charge of nucleon. The tensor charge of nucleon can also be defined as the forward matrix element of the tensor current in the nucleon state，which is used to study the nucleon’s tensor charge in terms of quantum color dynamics(QCD) sum rule approach， the effective theory and model. A consistent nonperturbative approach to study nucleon property and hadronic physics is also discussed.