5 research outputs found
QCD on the Light-Front -- A Systematic Approach to Hadron Physics
Light-Front Hamiltonian theory provides a rigorous frame-independent
framework for solving nonperturbative QCD. The valence Fock-state wavefunctions
of the light-front QCD Hamiltonian satisfy a single-variable relativistic
equation of motion, analogous to the nonrelativistic radial Schr\"odinger
equation, with an effective confining potential U which systematically
incorporates the effects of higher quark and gluon Fock states. Remarkably, the
potential U has a unique form of a harmonic oscillator potential if one
requires that the chiral QCD action remains conformally invariant. A mass gap
arises when one extends the formalism of de Alfaro, Fubini and Furlan to
light-front Hamiltonian theory. The valence LF meson wavefunctions for zero
quark mass satisfy a single-variable relativistic equation of motion in the
invariant variable , which is conjugate to the
invariant mass squared. The result is a nonperturbative relativistic
light-front quantum mechanical wave equation which incorporates color
confinement and other essential spectroscopic and dynamical features of hadron
physics, including a massless pion for zero quark mass and linear Regge
trajectories with the same slope in the radial quantum number n and orbital
angular momentum L. The corresponding light-front Dirac equation provides a
model of nucleons. The same light-front equations arise from the holographic
mapping of the soft-wall model modification of AdS_5 space with a unique
dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography
thus provides a precise relation between amplitudes in the fifth dimension of
AdS space and light-front wavefunctions. We also discuss the implications of
the underlying conformal template of QCD for renormalization scale-setting, and
the implications of light-front quantization for the value of the cosmological
constant.Comment: Invited talk, presented by SJB at LightCone 2013+, May 20- May 24,
2013, Skiathos, Greece. arXiv admin note: text overlap with arXiv:1309.4856,
arXiv:1308.5251, arXiv:1302.539
Light-Front Holographic QCD and the Confinement Potential
Light-Front Hamiltonian theory, derived from the quantization of the QCD
Lagrangian at fixed light-front time \tau = t+z/c, provides a rigorous
frame-independent framework for solving nonperturbative QCD. The eigenvalues of
the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the
eigensolutions provide the light-front wavefunctions describing hadron
structure. The valence Fock-state wavefunctions of the light-front QCD
Hamiltonian satisfy a single-variable relativistic equation of motion,
analogous to the nonrelativistic radial Schrodinger equation, with an effective
confining potential U which systematically incorporates the effects of higher
quark and gluon Fock states. The potential U has a unique form if one requires
that the action for zero quark mass remains conformally invariant. The
holographic mapping of gravity in AdS space to QCD with a specific soft-wall
dilaton yields the same light-front Schrodinger equation. It also gives a
precise relation between the bound-state amplitudes in the fifth dimension z of
AdS space and the boost-invariant light-front wavefunctions describing the
internal structure of hadrons in physical space-time. The elastic and
transition form factors of the pion and the nucleons are found to be well
described in this framework. The predictions include a zero-mass pion in the
chiral limit, and linear Regge trajectories with the same slope in the radial
quantum number n and orbital angular momentum L. The light-front AdS/QCD
holographic approach thus gives a frame-independent representation of
color-confining dynamics and the excitation spectra of light-quark hadrons in
terms of a single mass parameter. We also discuss the implications of the
underlying conformal template of QCD for renormalization scale-setting and the
implications of light-front quantization for the value of the cosmological
constant.Comment: Presented by SJB at Light-Cone 2012: Relativistic Hadronic and
Particle Physics, 10 to 15 December, 2012 at the University of Delhi, New
Delhi, Indi
Conformal Symmetry, Confinement, and Light-Front Holographic QCD
We show that (a) the conformal properties of Anti-de Sitter (AdS) space, (b)
the properties of a field theory in one dimension under the full conformal
group found by de Alfaro, Fubini and Furlan, and (c) the frame-independent
single-variable light-front Schr\"odinger equation for bound states all lead to
the same result: a relativistic nonperturbative model which successfully
incorporates salient features of hadronic physics, including confinement,
linear Regge trajectories, and results which are conventionally attributed to
spontaneous chiral symmetry breaking.Comment: Presented by SJB at the Third Workshop on the QCD Structure of the
Nucleon (QCD-N'12), Bilbao, Spain, October 22-26, 2012. This work was
supported by the Department of Energy contract DE--AC02--76SF0051