摘要
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.
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 Department of Energy Department of Energy contract DE-AC02-76SF00515
