Center-of-Mass Energy Removal in Relativistic Three-Quark Models of the Proton

A variant of a squared three-body Dirac equation is used to determine center-of-mass energy effects in independent particle motion approximations for three quarks in the nucleon. A scalar linear flux tube potential is used to confine the quarks. The relativistic nearly massless three-quark system, in the rest frame where the total momentum is zero, has a squared energy that is 3/5 the value compared to when the quarks are assumed to move independently. This is smaller than the 2/3 energy ratio determined using the non-relativistic harmonic oscillator model. This analytic model has one parameter, the flux tube constant. Choosing the flux tube constant to reproduce the proton rest energy, results in the analytic wave function well reproducing the proton axial charge and rms charge radius. The proton magnetic moment predicted is 2.235, lower than experiment.     

Structure of the gauge fields inside baryon

We present the results of lattice calculations of the distributions of the gauge fields inside a baryon constructed from three heavy quarks. It turns out that the chromoelectric flux tube has a Y shape. At nonzero temperature, we observe the breaking of the confining string below the deconfining temperature and the disappearance of the string above the critical temperature.     

Monopole Excitation of the Nucleon in a Relativistic Three-Quark Model

The densities and form factors of the proton andthe Roper monopole excitedstate resonance are calculatedusing a relativistic three-quark model. Small currentquark masses are used with the three-body Dirac equation solved in hypercentralapproximation. A QCD-based three-body potential,proportional to a minimum string length between thethree quarks, is used for confinement. The calculatedelectric form factor for the proton reproduces closelya dipole fit to the data. The proton density is morecompact than is the Roper resonance density. The centraldensity of the proton is about five times that for the Roper resonance. The hyperradial nodein the Roper resonance composite three-quark wavefunction shows up as a node in the transition densitybetween the proton and the Roper resonance. This node also causes the calculated transition formfactor to be larger than either the proton or Roperresonance form factors, all evaluated at the same valueof momentum transfer. The Roper resonance form factor is smaller than the proton form factor, asexpected, indicative of the Roper resonance being a morediffuse system than the proton.     

Rest Frame Properties of the Proton

The proton is modeled as three quarks of smallcurrent quark mass. The threebody Dirac equation issolved with spin-independent central diagonal linearconfining potentials with an attractive Coulombic term in a relativistic threequark model.Hyperspherical coordinates are used, and the bound stateis found analytically. After integrating over thehyperangles, the Hamiltonian is an 8 by 8 matrix ofcoupled first-order differential equations in onevariable, the hyperradius. These are analytically solvedin hypercentral approximation. For the(1/2⁺)³ ground-state configurationin the nonrelativistic large-quark-mass limit, there are no nodes in the wave function.However, in the extreme relativistic limit of smallcurrent quark masses of a few MeV, the expectation valueof the number of nodes is about 1.30 when the potential parameters are chosen to reproducethe proton rms charge radius. The quarks are assumed topossess a Pauli anomalous magnetic moment, like that ofthe electron and muon of (/2)(e/m). Assuming all three quarks have equal mass, one can fitthe rest energy, magnetic moment, rms charge radius, andaxial charge of the proton with this relativisticthree-body Dirac equation model. The solution found shows the necessity of including all componentsof the composite three-quark wave function, as the uppercomponent contributes only 0.585 to the norm.     

Pion fluctuation around the hedgehog solution in the chiral bag plus skyrmion hybrid model

The Roper excitation is studied in the chiral bag plus skyrmion hybrid model. The lagrangian is expanded around the classical solution in the hedgehog vibrational mode. In the adiabatic approximation we find a self consistent solution for the fluctuating system of quarks and pions up to the first order of the fluctuations. Only half of the excitation energy was found in the phase shift analysis. It is also discussed that the system is stable for all bag radii against the hedgehog vibration.     

Spin-Dependent Forces and Current Quark Masses

The J = (3/2) , J = 1/2 Nucleon mass difference shows the quark energies can be spin dependent. It is natural to expect that the quark wave functions also depend on spin. A spin-dependent quark force is fitted to the proton and neutron magnetic moments, axial charge, and spin content using a (1/2⁺)³ configuration for the quarks and assuming only zero mass u and d quarks are in the nucleon. In the octet, such spin-dependent forces lead to different wave functions for quarks with spin parallel or antiparallel to the nucleon spin. The eigen-energy of this potential is 0.15 GeV higher for quark spin parallel than for the quark spin antiparallel to the proton spin. This potential predicts a single quark energy of 0.37 GeV for mass-less quarks in the Delta. Assuming the quark forces are flavor independent, this potential predicts magnetic moments of a bound strange quark to be very close to those determined empirically from the octet magnetic moments.     

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.     

Flux confinement for a class of effective Lagrangians

Confinement properties recently proved in the leading logarithm model are shown to be generally truc for a wide class of effective Lagrangians. These include nonexistence of isolated quarks, confining static potential between \(q\bar q\) pair and flux confinement within a characteristic acting as a free boundary. A new variational principle is formulated.     

On operating deflection shapes of the violin body including in-plane motions

Earlier investigations have assumed only "out-of-plane" vibrations of the plates of the violin. The violin body can, however, be described as a thin-walled, double-arched shell structure and as such it may very well elongate in one direction as it contracts in another. Therefore, at least two orthogonal vibration components have to be included to describe the vibrations. The operating deflection shapes (ODSs) of a good, professionally made and carefully selected violin were therefore measured in several directions by TV holography to determine both "in-plane" and out-of-plane vibration components of the ODSs. The observations were limited to the frequency range 400-600 Hz, as this interval includes two most-prominent resonance peaks of bridge mobility and sound radiation as well as a third poorly radiating resonance. These three peaks clearly showed orthogonal vibration components in the ODSs. The vibration behavior of the violin body, sectioned in the bridge plane, was interpreted as the vibrations of an "elliptical tube" with nodal diameters. The number of nodal diameters increases from two to three in the selected frequency range. The TV holography measurements were supported by electrodynamical point measurements of bridge mobility, of air volume resonances, and by reciprocity, of radiation properties. Furthermore, a fourth mode, the air mode, A1, is involved indirectly in the sound radiation via influence on the body vibrations.     

Correlation of the Flux Tube Constant with the Nucleon Electric Polarizability

A three-quark shell model of the nucleon is used to calculate analytically thepolarizability using a scalar linear flux tube potential with no one-gluon exchangepotential included. A value of 12.02 × 10^–4 f ³ is obtained for the proton, ingood agreement with experiment, with the flux tube constant adjusted to reproducethe proton average rest energy. The magnetic polarizability of the proton isthen calculated as 1.51 × 10^–4 f ³, which is in agreement with the experimentalvalue. The neutron/proton electric polarizability ratio is calculated as 2/3, andthe neutron electric polarizability is predicted to be 8.01 × 10^–4 f ³.     

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.     

Calculation of gluon contribution to the proton spin by using the non-perturbative quantization à la Heisenberg

The contribution of crossed gluon fields in flux tubes connecting quarks to the proton spin is calculated. The calculations are performed following non-perturbative Heisenberg’s quantization technique. In our approach a proton is considered as consisting of three quarks connected by three flux tubes. The flux tubes contain colour longitudinal electric and transversal electric and magnetic fields. The transversal fields causes the appearance of the angular momentum density. The dimensionless relation between the angular momentum and the mass of the gluon fields is obtained. The contribution to proton spin from rotating quarks and flux tubes connecting quarks is estimated. Simple numerical relation between the proton mass, the speed of light and the proton radius, which is of the same order as the Planck constant, is discussed.     

Proton dissociation into three jets

We explore the possibility to observe hard exclusive three-jet production in early LHC runs, corresponding to diffractive dissociation of the incident proton into three jets with large but compensating transverse momenta. This process is sensitive to the proton unintegrated gluon distribution at small x   and to the distribution of the three valence quarks in the proton at small transverse distances. The corresponding cross section is calculated using an approach based on kt$k_t$ factorization. According to our estimates, observation of hard diffractive three-jet production at LHC is feasible for jet transverse momenta q_⊥∼5 GeV$q_{\perp }\sim 5\text{GeV}$.     

Proton sea quark flavour asymmetry and Roper resonance

We study the proton and the Roper resonance together with the meson cloud model, by constructing a Hamiltonian matrix and solving the eigenvalue equation. The proton sea quark flavour asymmetry and some properties of the Roper resonance are thus reproduced in one scheme.     

Magnetic Symmetry,Regge Trajectories,and the Linear Confinement in Dual QCD

Using the magnetic symmetry structure of non-Abelian gauge theories, we analyze the flux tube formulation and its implications on the hadronic Regge trajectories and the confinement of color isocharges in magnetically condensed (with as well as without the electric excitations) QCD vacuum. Starting with the fiber bundle structure of QCD, the dual potentials are used to construct the QCD Lagrangian which has been shown to develop a unique flux tube configuration in its dynamically broken phase. The vector mass mode of the condensed vacuum has been shown to play a leading role in flux tube energy and other confinement parameters. Using the flux tube energy and the angular momentum, the Regge trajectories for hadrons have been obtained and the linear confining properties of dual QCD have been established. The dyonic flux tube structure of the condensed QCD vacuum has been obtained by inducing the electric excitation of QCD monopoles and the confining nature along with the linearity of Regge trajectories in dyonically condensed QCD vacuum are shown to remain intact. Implications of the modification in Regge slope parameter, on improving the confining properties of dual QCD vacuum are also discussed. PACS: 12.38.Aw; 11.30.-j; 14.80.Hv; 12.39.Mk An erratum to this article is available at .     

Low-Lying Baryons in Hybrid Quark Model

We study the strong decay processes of the Roper resonance, N*(1440) in the picture of hybrid baryon in which the Roper resonance N*(1440) is interpreted as a state of three quarks and one transverse-electric gluon, q ³ G. A nonrelativistic quark–gluon model is employed, where the dynamics of antiquark–quark–gluon is described in the effective \({^{3}S_{1}}\) vertex in which a quark–antiquark pair is created (destroyed) from (into) a gluon. The wave function of the Roper resonance is properly constructed to take into account the gluon freedom in the nonrelativistic regime. The evaluated strong decay width ratios of N*(1440) are in good agreement with the experimental data.     

Off-shell behaviour of theN-N interaction in a six-quark resonating group model of the deuteron

Two different 6-quark resonating group models of the deuteron are investigated to study the off-shell property of theN-N interaction. In the first model the quarks interact by a central one-gluon-exchange potential plus confinement potential. The meson-exchange contribution to then-p potential is simulated by a central GaussianN-N potential. In the second model the quarks interact by one-gluon-and one-pion-exchange potentials (central and noncentral) plus confinement potential. A small additional -exchange potential between neutron and proton binds the deuteron at the correct energy.Several off-shell variants of the two resonating group models are compared with each other by analyzing their elastic electron scattering cross sections. It is found that the standard renormalized version of the resonating group model yields potentials and wave functions that may be considered physical within the limitations of the model. Unitary off-shell transformations, which modify potentials and wave functions in any sizeable way, lead to a disagreement between the charge distribution predicted by the model via analysis of electron scattering and the charge distribution following from the microscopic quark distribution.Both of the 6-quark models support a soft repulsive core of the tripletn-p potential with a core height of around 900 MeV.     

Calculation of the Parameters of the Dimeric Association of Water Molecules and Determination of Their Temperature Dependence

The conditions are determined, and the parameters for the onset of the mode of dimeric molecular association in the water system are estimated. The characteristics of dimeric associates of molecules are determined. The region of anomalous thermal compression water is increased from T ≤ 4°C to T ≤ 66.4°C by introducing the temperature equivalent T₀ of the energy of proton transition from molecule to molecule into the parameter of resonant interaction of atoms of different molecules. The time of transfer of excitation energy correlates with the periods of the valence and deformation vibrations of the molecules. Therefore, a molecule that performs valence vibrations “has time” to store an excitation energy sufficient to provide a parallel orientation of the spins of the nuclei of the hydrogen atoms in the molecules. Molecules that perform deformation vibrations have zero spins because of the smallness of the frequencies of such vibrations.