In this paper, we solve the eigen solutions to the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The energy spectrum is quite di...In this paper, we solve the eigen solutions to the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The energy spectrum is quite different from that with Coulomb potential. The mass spectrum of some bary-ons is similar to this one. The angular momentum-mass relation is quite similar to the Regge trajectories. The parabolic potential has a structure of asymptotic freedom near the center and confinement at a large distance. So, the results imply that, the local parabolic potential may be more suitable for describing the nuclear potential. The procedure of solving can also be used for some other cases of Dirac equation with complicated potential.展开更多
： In this work the mass spectra for some of the baryon resonances of the particle data group with three and four star status are obtained, and a unified description of the ground states and excitation spectra of bary...： In this work the mass spectra for some of the baryon resonances of the particle data group with three and four star status are obtained, and a unified description of the ground states and excitation spectra of baryons are provided in the framework of a non-relativistic potential model. For this goal we have analytically solved the radial SchrSdinger equation for three identical interacting particles with the anharmonic potential by using the Ansatz method and then we have calculated the baryon resonances spectrum by using the G/irsey Radicati mass formula （GR） and with generalized Giirsey Radicati mass formula （GGR）. The results of our model show that the calculated masses of baryon resonances by using the generalized Giirsey Radicati mass formula are found to be in good agreement with the tabulations of the Particle Data Group. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiples up to 3 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon.展开更多
The combination of Anti-de Sitter space （AdS） methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states.Starting...The combination of Anti-de Sitter space （AdS） methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states.Starting from the bound-state Hamiltonian equation of motion in QCD,we derive relativistic lightfront wave equations in terms of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time.These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti–de Sitter （AdS） space.Its eigenvalues give the hadronic spectrum,and its eigenmodes represent the probability distributions of the hadronic constituents at a given scale.Applications to the light meson and baryon spectra are presented.The predicted meson spectrum has a string-theory Regge form M^ 2 = 4κ ^2 （n＋L＋S/2）;i.e.,the square of the eigenmass is linear in both L and n,where n counts the number of nodes of the wavefunction in the radial variable ζ.The space-like pion and nucleon form factors are also well reproduced.One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time τ.The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD lightfront Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.展开更多
Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional phys...Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.展开更多
文摘In this paper, we solve the eigen solutions to the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The energy spectrum is quite different from that with Coulomb potential. The mass spectrum of some bary-ons is similar to this one. The angular momentum-mass relation is quite similar to the Regge trajectories. The parabolic potential has a structure of asymptotic freedom near the center and confinement at a large distance. So, the results imply that, the local parabolic potential may be more suitable for describing the nuclear potential. The procedure of solving can also be used for some other cases of Dirac equation with complicated potential.
文摘： In this work the mass spectra for some of the baryon resonances of the particle data group with three and four star status are obtained, and a unified description of the ground states and excitation spectra of baryons are provided in the framework of a non-relativistic potential model. For this goal we have analytically solved the radial SchrSdinger equation for three identical interacting particles with the anharmonic potential by using the Ansatz method and then we have calculated the baryon resonances spectrum by using the G/irsey Radicati mass formula （GR） and with generalized Giirsey Radicati mass formula （GGR）. The results of our model show that the calculated masses of baryon resonances by using the generalized Giirsey Radicati mass formula are found to be in good agreement with the tabulations of the Particle Data Group. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiples up to 3 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon.
基金Supported by Department of Energy Department of Energy contract DE-AC02-76SF00515
文摘The combination of Anti-de Sitter space （AdS） methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states.Starting from the bound-state Hamiltonian equation of motion in QCD,we derive relativistic lightfront wave equations in terms of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time.These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti–de Sitter （AdS） space.Its eigenvalues give the hadronic spectrum,and its eigenmodes represent the probability distributions of the hadronic constituents at a given scale.Applications to the light meson and baryon spectra are presented.The predicted meson spectrum has a string-theory Regge form M^ 2 = 4κ ^2 （n＋L＋S/2）;i.e.,the square of the eigenmass is linear in both L and n,where n counts the number of nodes of the wavefunction in the radial variable ζ.The space-like pion and nucleon form factors are also well reproduced.One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time τ.The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD lightfront Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
基金Supported by the Department of Energy Contract DE-AC02-76SF00515,SLAC-PUB-14525
文摘Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.
