New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra

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. For example, if one sets the Higgs couplings of quarks to zero, then no mass parameters appear in the QCD Lagrangian, and the theory is conformal at the classical level. Nevertheless, hadrons have a finite mass. We show that a mass gap and a fundamental color confinement scale arise when one extends the formalism of de Alfaro, Fubini and Furlan (dAFF) 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 [Formula: see text] bound states, a "Light-Front Schrödinger Equation," analogous to the nonrelativistic radial Schrödinger 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 light-front equations with the correct hadron spin dependence arise from the holographic mapping of "soft-wall model" modification of AdS5 space with a specific dilaton profile. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. A fundamental mass parameter κ 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 hadron dynamics — hadronic form factors, the QCD running coupling at small virtuality, the light-front wavefunctions of hadrons, ρ electroproduction, distribution amplitudes, valence structure functions, etc. 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, among the most profound questions in physics.

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Supersymmetric and Conformal Features of Hadron Physics

Universe ◽

10.3390/universe4110120 ◽

2018 ◽

Vol 4 (11) ◽

pp. 120

Author(s):

Stanley Brodsky

Keyword(s):

Equations Of Motion ◽

Conformal Symmetry ◽

Form Factors ◽

Mass Scale ◽

Equal Mass ◽

Superconformal Algebra ◽

Light Front ◽

Bjorken Sum Rule ◽

Nonperturbative Qcd ◽

Hadron Masses

The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion q q ¯ eigenstate has zero mass for m q = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS 5 space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

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Light-front holography and superconformal quantum mechanics: A new approach to hadron structure and color confinement

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194515600812 ◽

2015 ◽

Vol 39 ◽

pp. 1560081 ◽

Cited By ~ 9

Author(s):

Stanley J. Brodsky ◽

Alexandre Deur ◽

Guy F. de Téramond ◽

Hans Günter Dosch

Keyword(s):

Perturbative Qcd ◽

Quark Mass ◽

Bound State ◽

Mass Scale ◽

Light Front ◽

Effective Coupling ◽

Hadron Physics ◽

Color Confinement ◽

Hadron Masses ◽

Holographic Qcd

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 [Formula: see text] emerges. The actual value of the parameter [Formula: see text] 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 Schrödinger 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 [Formula: see text] and orbital angular momentum [Formula: see text]. The same light-front equations for mesons with spin [Formula: see text] also can be derived from the holographic mapping to QCD (3+1) at fixed light-front time from the soft-wall model modification of AdS5 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 – [Formula: see text] 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 momenta of the meson ([Formula: see text]) and baryon ([Formula: see text]) by one unit: [Formula: see text]. We also show how the mass scale [Formula: see text] underlying confinement and the masses of light-quark hadrons determines the scale [Formula: see text] 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. The data for the effective coupling defined from the Bjorken sum rule [Formula: see text] 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 [Formula: see text] is in agreement with the world average [Formula: see text]. We thus can connect [Formula: see text] to hadron masses. The analysis applies to any renormalization scheme.

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Meson/baryon/tetraquark supersymmetry from superconformal algebra and light-front holography

International Journal of Modern Physics A ◽

10.1142/s0217751x16300295 ◽

2016 ◽

Vol 31 (19) ◽

pp. 1630029 ◽

Cited By ~ 18

Author(s):

Stanley J. Brodsky ◽

Guy F. de Téramond ◽

Hans Günter Dosch ◽

Cédric Lorcé

Keyword(s):

Angular Momentum ◽

Perturbative Qcd ◽

Chiral Limit ◽

Form Factors ◽

Structure Functions ◽

Mass Scale ◽

Superconformal Algebra ◽

Light Front ◽

Spin Interaction ◽

Excitation Spectra

Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity — supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons: [Formula: see text] The dynamics of the superpartner hadrons also match; for example, the power-law fall-off of the form factors are the same for the mesonic and baryonic superpartners, in agreement with twist counting rules. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding superconformal quantum mechanics into AdS space. This procedure also generates a spin–spin interaction between the hadronic constituents. A specific breaking of conformal symmetry inside the graded algebra determines a unique quark-confining light-front potential for light hadrons in agreement with the soft-wall AdS/QCD approach and light-front holography. Only one mass parameter [Formula: see text] appears; it sets the confinement mass scale, a universal value for the slope of all Regge trajectories, the nonzero mass of the proton and other hadrons in the chiral limit, as well as the length scale which underlies their structure. The mass for the pion eigenstate vanishes in the chiral limit. When one includes the constituent quark masses using the Feynman–Hellman theorem, the predictions are consistent with the empirical features of the light-quark hadronic spectra. Our analysis can be consistently applied to the excitation spectra of the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] meson families as well as to the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass-squared of the light hadrons can be expressed in a universal and frame-independent decomposition of contributions from the constituent kinetic energy, the confinement potential, and spin–spin contributions. We also predict features of hadron dynamics, including hadronic light-front wave functions, distribution amplitudes, form factors, valence structure functions and vector meson electroproduction phenomenology. The mass scale [Formula: see text] can be connected to the parameter [Formula: see text] in the QCD running coupling by matching the nonperturbative dynamics, as described by the light-front holographic approach to the perturbative QCD regime. The result is an effective coupling defined at all momenta. The matching of the high and low momentum-transfer regimes determines a scale [Formula: see text] proportional to [Formula: see text] which sets the interface between perturbative and nonperturbative hadron dynamics. The use of [Formula: see text] to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the scheme-independent Principle of Maximal Conformality (PMC) procedure for setting renormalization scales, can greatly improve the precision of perturbative QCD predictions.

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