Spin Dependent Quark Forces and the Spin Content of the Nucleon

The spin crisis of the nucleon is that the quark spin contribution is only a small fraction of the nucleon spin. A relativistic Dirac equation approach is followed assuming three low mass current quarks in the nucleon described by a (1/2⁺)³ configuration. If the lower component contribution to the normalization of the quark wave function is about 0.18, then the axial charge of the nucleon can be reproduced. However including the same lower component to every quark wave function is not enough to resolve the spin crisis. The net u quark spin z component is predicted as 1.0 and the net d quark spin z component is predicted as –0.25, both in disagreement with experiment. These predictions can be brought into agreement with experiment if flavor independent but spin dependent forces are assumed between the quarks. The strength of the spin dependent force found by empirically fitting the nucleon spin data is shown to be comparable to the spin dependence that can explain the -nucleon mass difference. The spin content of the ⁺ is then predicted using the interactions that reproduce the spin content of the proton.     

Transition magnetic moments of J~P=3/2~+ decuplet to J~P=1/2~+ octet baryons in the chiral constituent quark model

In light of the developments of the chiral constituent quark model(χ~(CQM)) in studying low energy hadronic matrix elements of the ground-state baryons, we extend this model to investigate their transition properties.The magnetic moments of transitions from the J~P=3/2~+ decuplet to J~P=1/2~+ octet baryons are calculated with explicit valence quark spin, sea quark spin and sea quark orbital angular momentum contributions. Since the experimental data is available for only a few transitions, we compare our results with the results of other available models. The implications of other complicated effects such as chiral symmetry breaking and SU(3) symmetry breaking arising due to confinement of quarks are also discussed.     

Flavor mixing in the low energy hadron dynamics: Interplay of theSU f (3) breaking and theU A (1) anomaly

We extend our previous investigation about the flavor mixing or the OZI violating process in the light quark systems with the use of the generalized Nambu-Jona-Lasinio model incorporating theU _A (1) anomaly. The OZI breaking effects newly studied in the meson sector include the and meson decay constants, their couplings with nucleon as well as the masses and the mixing property of the scalar mesons. As for the baryon sector, we reexamine the strangeness content of the proton and the -N sigma term _N by taking into account the interactions between the constituent quarks. It is found that the short-range spin-spin interaction between the quarks gives anO(10 MeV)-enhancement for the theoretical value of the sigma term. Anomalous quark contents of other octet and decuplet baryons (hyperons) are also examined. It is shown that the axial anomaly induces the anomalous quark contents which are not expected in the naive quark model, while the short-range interaction between the quarks acts to suppress (enhance) the quark contents of the decuplet (octet) baryons. All the results indicate that the following picture holds systematically:m _s is so large that (i) the strangeness mixing induced by the anomaly is considerably suppressed and that (ii) the naive chiral perturbation does not work in the strange sector even in the tree level of the meson fields (largeN _c limit). The spin problem of nucleon, which is another subject related to the flavor mixing, is also examined with the use of our effective model.This paper is a modified version of the paper SUNY-NTG-89-49, RYU-THP-89-2 (August 1989)     

Spontaneous violation of chiral symmetry in QCD vacuum is the origin of baryon masses and determines baryon magnetic moments and their other static properties

A short review is presented of the spontaneous violation of chiral symmetry in QCD vacuum. It is demonstrated that this phenomenon is the origin of baryon masses in QCD. The value of nucleon mass is calculated, as well as the masses of hyperons and some baryonic resonances, and expressed mainly through the values of quark condensates—, q = u, d, s,—the vacuum expectation values (v.e.v.) of quark field. The concept of v.e.v. induced by external fields is introduced. It is demonstrated that such v.e.v. induced by static electromagnetic field results in quark condensate magnetic susceptibility, which plays the main role in determination of baryon magnetic moments. The magnetic moments of proton, neutron, and hyperons are calculated. The results of calculation of baryon octet β-decay constants are also presented. The text was submitted by the author in English.     

Particle masses,force constants,and Spin(8)

From a number of qualitative conjectures, the constantsm _e ,c, , and a spin(8) gauge field theory, I derive the following particle masses (quark masses are constituent masses) and force constants: up quark mass=312.7542 MeV; down quark mass=312.7542 MeV; proton mass=938.2626 MeV; neutrino masses (all types)=0; muon mass=104.76 MeV; strange quark mass=523 MeV; charmed quark mass=1989 MeV; tauon mass=1877 MeV; bottom quark mass=5631 MeV; top quark mass=129.5 GeV;W ⁺ mass=80.87 GeV;W ^– mass=80.87 GeV;W ₀ mass=99.04 GeV; fine structure constant= 1/137.036082; weak constant times the proton mass squared M _p ² =0.97×10^–5; color constant=0.6286. From the pion mass in addition, I derive the Planck mass (1–1.6)×10¹⁹ GeV, so that the gravitational constant times the proton mass squared GM _p ² (3.6–8.8)×10^–39.     

Single heavy flavour baryons using Coulomb plus a power law interquark potential

Properties of single heavy flavor baryons in a non-relativistic potential model with colour Coulomb plus a power law confinement potential have been studied using a simple variational method. The ground-state masses of single heavy baryons and the mass difference between the J ^P = ⁺ and J ^P = ⁺ states are computed using a spin-dependent two-body potential. Using the spin-flavour structure of the constituting quarks and by defining an effective confined mass of the constituent quarks within the baryons, the magnetic moments are computed. The masses and magnetic moments of the single heavy baryons are found to be in accordance with the existing experimental values and with other theoretical predictions. It is found that an additional attractive interaction of the order of -200 MeV is required for the antisymmetric states of (Q c, b) . It is also found that the spin-hyperfine interaction parameters play a decisive role in hadron spectroscopy.     

Spin Structure of Baryons in Orbiting Valence Quark Model

The quark model with orbital motion of the valence quarks is constructed to reproduce the spin structure of baryons. The relations between the spin-averaged sum rules and baryon magnetic moments found in the previous works do not remain, unless the small orbital magnetic moments are neglected. In particular, when the orbital motion of the valence quarks leads to the small contribution of quark orbit-spin to baryon magnetic moments, the sum rules for polarized nucleon are in agreement with the recent experiment.     

Magnetic moments and the proton structure function

The EMC collaboration have reported a measurement of the proton structure function which has been interpreted to mean that the spin of the proton is not predominantly that of the quarks (=u+d+s=0.13±0.19). We show that the magnetic moments of the baryons are independent of this measurement and are given (within 10–20%) for a range of including the valence model value =1. The magnetic moments of the quarks can only be fixed if the quantity is determined very accurately.     

Physics results from HERMES

The Hermes experiment at the Desy laboratory in Hamburg, Germany, studies the spin structure of the nucleon. Its unique feature is the combination of a polarized internal gas target with the longitudinally polarized 27.5 GeV electron/positron beam of the Hera accelerator. Recent Hermes measurements include the proton spin structure function g ₁ ^p , the flavor decomposition of the polarized quark distributions in the nucleon, the DIS contribution to the generalized GDH sum rule, the first observation of a spin asymmetry in exclusive vector meson production and the first observation of a single-spin azimuthal asymmetry in semi-inclusive pion production. Additionally, the possibility of using various unpolarized gases as target material broadens the spectrum of physics measurements with Hermes.     

Proton dipole form factor quark model

The dipole-shaped electromagnetic form factors of the proton may imply an exponential radial dependence of the wave function describing the charged constituents of the proton. The hypercentral potential required by the three-body Dirac equation to produce such an exponential radial wave function for three bound quarks is found to have a linear confining potential plus an attractive Coulombic central diagonal part. The configuration assumed for the quark constituents is the (1/2⁺)³ positive parity configuration, coupled to the spin of the proton. Assuming equal-mass Dirac quarks with no anomalous magnetic moments, we find the largest magnetic moment for this wave function to be 2.763 nuclear magnetons, close to, but less than the experimental value of 2.793. The hypercentral potential is mostly the sum of three quark-quark potentials, but a small three-body potential is required.     

Geometrical basis for the Standard Model

The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary planeC ², the quaternion spaceQ, and the real spaceR ⁴—as well as the real spaceR ³ uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge groupSU(2) _L ×U(1) _Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The (u, d) and (c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/c ², theb quark at 80 GeV/c ², and thet quark at 2600 GeV/c ².     

Transverse spin structure of hadrons from lattice QCD

This paper presents recent lattice QCD calculations of transverse spin densities of quarks in hadrons.² Based on our simulation results for the tensor generalized form factors, we find substantial correlations between spin and coordinate degrees of freedom in the nucleon and the pion. They lead to strongly distorted transverse spin densities of quarks in the nucleon and a surprisingly non-trivial transverse spin structure of the pion. Following recent arguments by Burkardt [M. Burkardt, Phys. Rev. D 72 (2005) 094020], our results imply that the Boer-Mulders function , describing correlations of the transverse spin and intrinsic transverse momentum of quarks, is large and negative for up-quarks in the proton and the π⁺. This supports the recent hypothesis that all Boer-Mulders functions are alike [arXiv:0705.1573], and also provides additional motivation for future studies of azimuthal asymmetries in πp Drell-Yan production at, e.g., COMPASS.     

Sea Level Muon Spectrum Derived from the All Particle Primary Spectrum of GRIGOROV et al.

The all particle primary spectrum of GRIGOROV et al. surveyed by HILLAS has been fitted by a power law fit of the form I_{all particle}(>E) = 1.3 E^?1.65 (cm² s sr)^?1 where E is the energy in GeV/nucleus. Using our recently determined conversion factor for protonnuclei flux ratio of equal energies the primary proton spectrum has been calculated and the result agrees with the Goddard Space Flight Centre primary proton spectrum data satisfactorily. The primary nucleon spectrum has also been calculated and follows the form N_nucleons(E) dE = 2.664 E^?2.75 dE (cm² s sr GeV/nucleon)^?1. Using this primary nucleon spectrum as the source of hadrons and accelerator data for various inclusive reactions viz. used for the estimation of hadronic energy moments in the frame work of FEYNMAN- Scaling, the differential meson spectra have been estimated. The meson atmospheric diffusion equation after Bugaev et al. has been considered for the derivation of sea level muon spectrum. The magnetic spectrograph data of Allkofer et al., Ayre et al., Green et al., and MUTRON group are in accord with the calculated muon spectrum.     

Static observables of relativistic three-fermion systems with instantaneous interactions

We show that static properties like the charge radius and the magnetic moment of relativistic three-fermion bound states with instantaneous interactions can be formulated as expectation values with respect to intrinsically defined wave functions. The resulting operators can be given a natural physical interpretation in accordance with relativistic covariance. We also indicate how the formalism may be generalized to arbitrary moments. The method is applied to the computation of static baryon properties with numerical results for the nucleon charge radii and the baryon octet magnetic moments. In addition, we make predictions for the magnetic moments of some selected nucleon resonances and discuss the decomposition of the nucleon magnetic moments in contributions of spin and angular momentum, as well as the evolution of these contributions with decreasing quark mass.     

Imaging the Transverse (Spin) Structure of Hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark–gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for u and d quarks, as well as the signs of quark–gluon correlations embodied in the polarized structure function g ₂ can be understood in terms of the proton and neutron anomalous magnetic moments.     

Non-linear quark theory of a spin 2 field (gravitational mesons). I

An equation for a spin 2 meson octet (an octet of gravitational mesons) interacting with mesons of spin 0^– and 1^– is derived in the context of a non-linear quark model by the confluence method. We determine the magnetic moments and the decay constants for the octet of gravitational mesons into mesons of spin 0^– and 1^–.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 94–100, March, 1973.     

S-wave baryons in an equally mixed scalar-vector square root potential model of independent quarks

A relativistic model of independent quarks based on Dirac equation with an equally mixed scalar-vector square root confining potential is used to compute the quark core contributions to the static properties like magnetic moments, charge radii and axial vector coupling constant ratios of the baryon octet. The results obtained with appropriate corrections due to centre-of-mass motion agree fairly well with experimental values. The model is also extended to the study of magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors and the overall predictions so obtained compare well with other model predictions.     

Relativistic quarks bound with a one-body tensor potential

A dipole fit to electromagnetic form factors is used to determine a quark density in the nucleon. A radial tensor potential is used to bind the quarks into states of goodJ, J _z, and parity. The tensor potential radial component is taken to satisfy the equationT = T ₀, whereT ₀ is a parameter of the model. This linear divergence equation can be simultaneously solved with the Dirac equation for the bound quark wave functions. A self-consistent solution is possible where the mass density used as the source for the binding potential is the same as that determined from the solution for the quark wave functions.