[Show abstract][Hide abstract] ABSTRACT: A primary question in hadron physics is how the mass scale for hadrons
consisting of light quarks, such as the proton, emerges from the QCD Lagrangian
even in the limit of zero quark mass. If one requires the effective action
which underlies the QCD Lagrangian to remain conformally invariant and extends
the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian
theory, then a unique, color-confining potential with a mass parameter $\kappa$
emerges. The actual value of the parameter $\kappa$ is not set by the model -
only ratios of hadron masses and other hadronic mass scales are predicted. The
result is a nonperturbative, relativistic light-front quantum mechanical wave
equation, the Light-Front Schr\"odinger 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 identical slope in the radial quantum number $n$ and
orbital angular momentum $L$. The same light-front equations for mesons with
spin $J$ also can be derived from the holographic mapping to QCD (3+1) at fixed
light-front time from the soft-wall model modification of AdS$_5$ space with a
specific dilaton profile. Light-front holography thus provides a precise
relation between the bound-state amplitudes in the fifth dimension of AdS space
and the boost-invariant light-front wavefunctions describing the internal
structure of hadrons in physical space-time. One can also extend the analysis
to baryons using superconformal algebra - $2 \times 2$ supersymmetric
representations of the conformal group. The resulting fermionic LF bound-state
equations predict striking similarities between the meson and baryon spectra.
In fact, the holographic QCD light-front Hamiltonians for the states on the
meson and baryon trajectories are identical if one shifts the internal
angular...
[Show abstract][Hide abstract] ABSTRACT: QCD is well understood at short distances where perturbative calculations are
feasible. Establishing an explicit analytic connection between the
short-distance regime and the large-distance physics of quark confinement has
been a long-sought goal. A major challenge is to relate the scale $\Lambda_{s}$
underlying the evolution of the QCD coupling in the perturbative regime to the
masses of hadrons. We show here how new theoretical insights into the behavior
of QCD at large distances leads to such a relation. The resulting prediction
for $\Lambda_{s}$ in the $\overline{MS}$ scheme agrees well with experimental
measurements. Conversely, the relation can be used to predict the masses of
hadrons composed of light quarks with the measured value of $\Lambda_{s}$ as
the sole parameter. We also use "light-front holography" to determine the
analytic form of $\alpha_s(Q^2)$ at small $Q^2$.
[Show abstract][Hide abstract] ABSTRACT: Relativistic light-front bound-state equations for mesons and baryons can be
constructed in the chiral limit from the supercharges of a superconformal
algebra which connect baryon and meson spectra. Quark masses break the
conformal invariance, but the basic underlying supersymmetric mechanism, which
transforms meson and baryon wave functions into each other, still holds and
gives remarkable connections across the entire spectrum of light and
heavy-light hadrons. We also briefly examine the consequences of extending the
superconformal relations to double-heavy mesons and baryons.
[Show abstract][Hide abstract] ABSTRACT: The valence Fock-state wavefunctions of the light-front (LF) QCD Hamiltonian satisfy a relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to LF Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic LF 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. Only one mass parameter κ appears. The corresponding LF Dirac equation provides a dynamical and spectroscopic model of nucleons. The same LF equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed LF time. LF holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of Anti-de Sitter (AdS) space and the boost-invariant LFWFs describing the internal structure of hadrons in physical space-time. We also show how the mass scale \({\kappa= m_\rho/\sqrt{2}}\) underlying confinement and the masses of light-quark hadrons determines the scale \({\Lambda_{\overline{MS}}^{(N_F=3)}}\) controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the LF and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The data for the effective coupling defined from the Bjorken sum rule \({\alpha_{g_1}(Q^2)}\) are remarkably consistent with the Gaussian form predicted by LF holographic QCD. The result is an effective coupling defined at all momenta. The predicted value \({\Lambda^{(N_F=3)}_{\overline{MS}} = 0.423 m_\rho = 0.328 \pm 0.034}\) GeV is in agreement with the world average \({0.339 \pm 0.010}\) GeV. We thus can connect \({\Lambda_{\overline{MS}}^{(N_F=3)}}\) to hadron masses. The analysis applies to any renormalization scheme.
Few-Body Systems 03/2015; DOI:10.1007/s00601-015-0964-1 · 0.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We construct an effective QCD light-front Hamiltonian for both mesons and
baryons in the chiral limit based on the generalized supercharges of a
superconformal graded algebra. The superconformal construction is shown to be
equivalent to a semi-classical approximation to light-front QCD and its
embedding in AdS space. The specific breaking of conformal invariance inside
the graded algebra uniquely determines the effective confinement potential. The
generalized supercharges connect the baryon and meson spectra to each other in
a remarkable manner. In particular, the $\pi/b_1$ Regge trajectory is
identified as the superpartner of the nucleon trajectory. However, the
lowest-lying state on this trajectory, the $\pi$-meson is massless in the
chiral limit and has no supersymmetric partner.
Physical Review D 01/2015; 91(8). DOI:10.1103/PhysRevD.91.085016 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We describe the observed light-baryon spectrum by extending superconformal
quantum mechanics to the light front and its embedding in AdS space. This
procedure uniquely determines the confinement potential for arbitrary
half-integer spin. To this end, we show that fermionic wave equations in AdS
space are dual to light-front supersymmetric quantum mechanical bound-state
equations in physical space-time. The specific breaking of conformal invariance
inside the algebra explains hadronic properties common to light mesons and
baryons, such as the observed mass pattern in the radial and orbital
excitations. The holographic embedding in AdS also explains distinctive and
systematic features, such as the spin-J degeneracy observed in the light baryon
spectrum.
Physical Review D 11/2014; 91(4). DOI:10.1103/PhysRevD.91.045040 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The valence Fock-state wavefunctions of the light-front QCD Hamiltonian
satisfy a relativistic equation of motion with an effective confining potential
$U$ which systematically incorporates the effects of higher quark and gluon
Fock states. If one requires that the effective action which underlies the QCD
Lagrangian remains conformally invariant and extends the formalism of de
Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential $U$
has a unique form of a harmonic oscillator potential, and a mass gap arises.
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 $L$. Only one mass
parameter $\kappa$ appears. Light-front holography thus provides a precise
relation between the bound-state amplitudes in the fifth dimension of AdS space
and the boost-invariant light-front wavefunctions describing the internal
structure of hadrons in physical space-time. We also show how the mass scale
$\kappa$ underlying confinement and hadron masses determines the scale
$\Lambda_{\overline{MS}} $ controlling the evolution of the perturbative QCD
coupling. The relation between scales is obtained by matching the
nonperturbative dynamics, as described by an effective conformal theory mapped
to the light-front and its embedding in AdS space, to the perturbative QCD
regime computed to four-loop order. The result is an effective coupling defined
at all momenta. The predicted value $\Lambda_{\overline{MS}} = 0.328 \pm 0.034$
GeV is in agreement with the world average $0.339 \pm 0.010$ GeV. The analysis
applies to any renormalization scheme.
[Show abstract][Hide abstract] ABSTRACT: We show how the physical mass scale $\kappa$ underlying confinement and
hadron masses determines the scale $\Lambda_s$ in the QCD running coupling. The
relation between scales is obtained by matching the nonperturbative dynamics,
as described by an effective conformal theory mapped to the light-front and its
embedding in AdS space, to the perturbative QCD regime computed to four-loop
order. The result is an effective coupling defined at all momenta. The
predicted value $\Lambda_{\overline{MS}} = 0.328 \pm 0.034$ GeV is in agreement
with the world average $0.339 \pm 0.010$ GeV. Our analysis applies to any
renormalization scheme.
[Show abstract][Hide abstract] ABSTRACT: In this Report we explore the remarkable connections between light-front
dynamics, its holographic mapping to gravity in a higher-dimensional anti-de
Sitter (AdS) space, and conformal quantum mechanics. This approach provides new
insights into the origin of a fundamental mass scale and the physics underlying
confinement dynamics in QCD in the limit of massless quarks. The result is a
relativistic light-front wave equation for arbitrary spin with an effective
confinement potential derived from a conformal action and its embedding in AdS
space. This equation allows for the computation of essential features of hadron
spectra in terms of a single scale. The light-front holographic methods
described here gives a precise interpretation of holographic variables and
quantities in AdS space in terms of light-front variables and quantum numbers.
This leads to a relation between the AdS wave functions and the boost-invariant
light-front wavefunctions describing the internal structure of hadronic
bound-states in physical space-time. The pion is massless and the excitation
spectra of relativistic light-quark meson and baryon bound states lie on linear
Regge trajectories with identical slopes in the radial and orbital quantum
numbers. In the light-front holographic approach described here currents are
expressed as an infinite sum of poles, and form factors as a product of poles.
At large $q^2$ the form factor incorporates the correct power-law fall-off for
hard scattering independent of the specific dynamics and is dictated by the
twist. At low $q^2$ the form factor leads to vector dominance. The approach is
also extended to include small quark masses. We briefly review in this Report
other holographic approaches to QCD, in particular top-down and bottom-up
models based on chiral symmetry breaking. We also include a discussion of open
problems and future applications.
[Show abstract][Hide abstract] ABSTRACT: We describe a procedure to extend the light-front holographic approach to
hadronic physics to include light-quark masses. The proposed framework allows
us to extend the formalism of de Alfaro, Fubini and Furlan to the
frame-independent light-front Hamiltonian theory in the approximation where the
dynamics in the invariant transverse variable is unchanged to first order in
the quark masses. The confinement potential follows from an effective theory
which encodes the fundamental conformality of the classical QCD Lagrangian and
leads to a semiclassical relativistic light-front wave equation for arbitrary
spin. In particular, the K meson spectrum is successfully described without
modifying the emerging confinement scale. The Wilson loop criteria for
confinement is maintained, since for light quark masses a harmonic potential
and linear Regge trajectories in the light-front form of dynamics corresponds
to a linear potential in the usual instant-form.
[Show abstract][Hide abstract] ABSTRACT: We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for arbitrary spin. In particular, the K meson spectrum is successfully described without modifying the emerging confinement scale. The Wilson loop criteria for confinement is maintained, since for light quark masses a harmonic potential and linear Regge trajectories in the light-front form of dynamics corresponds to a linear potential in the usual instant-form.
[Show abstract][Hide abstract] ABSTRACT: One of the most fundamental problems in Quantum Chromodynamics is to
understand the origin of the mass scale which controls the range of color
confinement and the hadronic spectrum. We show that a mass gap and a
fundamental color confinement scale arise when one extends the formalism of de
Alfaro, Fubini and Furlan to frame-independent light-front Hamiltonian theory.
Remarkably, the resulting light-front potential has a unique form of a harmonic
oscillator in the light-front invariant impact variable if one requires that
the action remains conformally invariant. The result is a single-variable
relativistic equation of motion for $q \bar q$ bound states, a "Light-Front
Shr\"odinger Equation", analogous to the nonrelativistic radial Schr\"odinger
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 and orbital angular momentum. The same equations with
the correct hadron spin dependence arise from the holographic mapping of
modified AdS$_5$ space with a specific dilaton profile. A fundamental mass
parameter $\kappa$ appears, determining the hadron masses and the length scale
which underlies hadron structure. Quark masses can be introduced to account for
the spectrum of strange hadrons. This Light-Front Holographic approach predicts
not only hadron spectroscopy successfully, but also hadronic form factors, the
QCD running coupling at small virtuality, and the light-front wavefunctions of
hadrons. Thus the combination of light-front dynamics, its holographic mapping
to gravity in a higher-dimensional space and the dAFF procedure provides new
insight into the physics underlying color confinement, chiral invariance, and
the QCD mass scale.
International Journal of Modern Physics A 04/2014; 29(21). DOI:10.1142/S0217751X14440138 · 1.70 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We observe that the effective potentials obtained from lattice gauge theory,
derived from string models of hadrons, and determined from models using
front-form dynamics and light-front holography agree with each other at leading
approximation, not only in their shape - which depends on the form of dynamics
- but also in their numerical strength.
Physical Review D 03/2014; 90(7). DOI:10.1103/PhysRevD.90.074017 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We briefly review the remarkable connections between light-front QCD, gravity
in AdS space, and conformal quantum mechanics. We discuss, in particular, the
group theoretical and geometrical aspects of the underlying one-dimensional
quantum field theory. The resulting effective theory leads to a
phenomenologically successful confining interaction potential in the
relativistic light-front wave equation which incorporates relevant
non-perturbative dynamical aspects of hadron physics.
[Show abstract][Hide abstract] ABSTRACT: To a first semiclassical approximation one can reduce the multi-parton
light-front problem in QCD to an effective one-dimensional quantum field
theory, which encodes the fundamental conformal symmetry of the classical QCD
Lagrangian. This procedure leads to a relativistic light-front wave equation
for arbitrary spin which incorporates essential spectroscopic and
non-perturbative dynamical features of hadron physics. The mass scale for
confinement and higher dimensional holographic mapping to AdS space are also
emergent properties of this framework.
The European Physical Journal Conferences 01/2014; 73. DOI:10.1051/epjconf/20147301014
[Show abstract][Hide abstract] ABSTRACT: 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 $\zeta^2=b^2_\perp x(1-x)$, 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.
Few-Body Systems 10/2013; 55(5). DOI:10.1007/s00601-013-0740-z · 0.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Anti-de Sitter space in five dimensions provides an exact geometrical
representation of the conformal group. Remarkably, gravity in AdS$_5$ space is
holographically dual to frame-independent light-front Hamiltonian theory,
derived from the quantization of the QCD Lagrangian at fixed light-front time
$\tau = x^0+x^3$. Light-front holography also leads to a precise relation
between the bound-state amplitudes in the fifth dimension $z$ of AdS space and
the variable $\zeta$, where $\zeta^2 = b^2_\perp x(1-x)$ is the argument of the
boost-invariant light-front wavefunctions describing the internal structure of
hadrons in physical space-time. The holographic mapping of AdS space with a
specific "soft-wall" dilaton yields a confining potential $U(\zeta^2)$ for the
light-front Schr\"odinger equation for hadrons with arbitrary spin $J$.
Remarkably, $U(\zeta^2)$ has a unique form of a harmonic oscillator potential
if one requires that the chiral QCD action remains conformally invariant. One
thus obtains an effective light-front effective theory for general spin which
respects the conformal symmetry of the four-dimensional classical QCD
Lagrangian. The predictions of the LF equations of motion include a zero-mass
pion in the chiral $m_q\to 0$ limit, and linear Regge trajectories $M^2(n,L)
\propto n+L$ with the same slope in the radial quantum number $n$ and the
orbital angular momentum $L$. The light-front AdS/QCD holographic approach
gives a frame-independent representation of color-confining dynamics, Regge
spectroscopy, as well as the excitation spectra of relativistic light-quark
meson and baryon bound states in QCD in terms of a single mass parameter. We
also briefly 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
Nuclear Physics B - Proceedings Supplements 08/2013; s 251–252. DOI:10.1016/j.nuclphysbps.2014.04.001 · 0.88 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We review some outstanding puzzles and experimental anomalies in hadron
physics that appear to challenge conventional wisdom and, in some cases, the
foundations of QCD. We also discuss possible solutions and propose new tests
and experiments that could illuminate the underlying physics and novel
phenomenological features of QCD. In some cases, new perspectives for QCD
physics have emerged.
Annual Review of Nuclear and Particle Science 02/2013; 62(1). DOI:10.1146/annurev-nucl-102711-094949 · 11.26 Impact Factor