QCD Running Coupling Research Articles

Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra and other Advances in Light-Front QCD

Light-front holography, together with superconformal algebra, have provided new insights into the physics of color confinement and the spectroscopy and dynamics of hadrons. As shown by de Alfaro, Fubini and Furlan, a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the procedure of de Alfaro et al. to the frame-independent light-front Hamiltonian, it leads uniquely to a confining $$q \bar{q}$$ potential $$\kappa ^4 \zeta ^2$$ , where $$\zeta ^2$$ is the light-front radial variable related in momentum space to the $$q \bar{q}$$ invariant mass. The same result, including spin terms, is obtained using light-front holography—the duality between the front form and AdS $$_5$$ , the space of isometries of the conformal group—if one modifies the action of AdS $$_5$$ by the dilaton $$e^{\kappa ^2 z^2}$$ in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions lead to a a unified Regge spectroscopy of meson, baryon, and tetraquarks, including supersymmetric relations between their masses and their wavefunctions. One also predicts hadronic light-front wavefunctions and observables such as structure functions, transverse momentum distributions, and the distribution amplitudes. The mass scale $$\kappa $$ underlying confinement and hadron masses can be connected to the parameter $$\varLambda _{\overline{MS}}$$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling $$\alpha _s(Q^2)$$ defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale $$Q_0$$ which sets the interface between perturbative and nonperturbative hadron dynamics. I also discuss a number of applications of light-front phenomenology.

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

The QCD light-front Hamiltonian equation HLFΨ=M2Ψ derived from quantization at fixed LF time τ=t + z/c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the qq¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and AdS5, if one modifies the AdS5 action by the dilaton eκ2z2 in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion qq¯ eigenstate has zero mass at mq=0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling αs(Q2)∝e-Q2/4κ2. The mass scale κ underlying hadron masses can be connected to the parameter ΛMS¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.

On the relation between pole and running heavy quark masses beyond the four-loop approximation

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.

QCD coupling which respects lattice restrictions at low energies

We consider a phenomenologycal parametrization of the QCD running coupling which arises from the dispersion relation respecting the holomorphic properties of the physical QCD observables in the complex momentum plane. The parameters are fixed by the following requirements: 1) at enough high energies, it reproduces the underlying perturbative coupling, 2) at intermediate energy momenta, it reproduces the experimental semihadronic tau decay ratio, and 3) in the deep IR regime, it satisfies the qualitative properties coming from recent lattice results. Finally, we apply this new coupling to low-energy available experimental data. In particular, to Borel sum rules for τ-decay, extracting the values of the dimension 4 and 6 condensates, to the V-channel Adler function, and to polarized Bjorken Sum Rule.

A method for getting a finite alpha in the IR region from an all-order beta function

The analytical method of the QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov–Shifman–Vainshtein–Zakharov beta function of N=1 supersymmetric gauge theories. In the approach presented here, the running coupling is determined by a transcendental equation with non-elementary integral of the running scale mu . In our approach alpha _text {an}(0), which reads 0.30642, does not rely on any dimensional parameters. This is in accordance with results in the literature on the analytical method of the QCD running coupling constant. The new “analytically improved” running coupling constant is also compatible with the property of asymptotic freedom.

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

A fundamental problem in hadron physics is to obtain a relativistic color-confining, first approximation to QCD which can predict both hadron spectroscopy and the frame-independent light-front (LF) wavefunctions underlying hadron dynamics. The QCD Lagrangian with zero quark mass has no explicit mass scale; the classical theory is conformally invariant. Thus, a fundamental problem is to understand how the mass gap and ratios of masses – such as m ρ/m p – can arise in chiral QCD. De Alfaro, Fubini, and Furlan have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator and rescales the time variable. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the $$ q\overline{q} $$ invariant mass squared. The same result, including spin terms, is obtained using light-front holography – the duality between light-front dynamics and AdS5, the space of isometries of the conformal group if one modifies the action of AdS5 by the dilaton $$ {e}^{\kappa^2}{z}^2 $$ in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κ underlying confinement and hadron masses can be connected to the parameter $$ {\Lambda}_{\overline{MS}} $$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α s (Q 2) defined at all momenta. The matching of the high and low momentum transfer regimes also determines a scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics.

Lattice-motivated holomorphic nearly perturbative QCD

Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual running coupling.

Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra

A remarkable feature of QCD is that the mass scale $$\kappa $$ which controls color confinement and light-quark hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential $$\kappa ^4 \zeta ^2$$ for mesons, where $$\zeta ^2$$ is the LF radial variable conjugate to the $$q \bar{q}$$ invariant mass. The same result, including spin terms, is obtained using light-front holography—the duality between the front form and AdS $$_5$$ , the space of isometries of the conformal group—if one modifies the action of AdS $$_5$$ by the dilaton $$e^{\kappa ^2 z^2}$$ in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale $$\kappa $$ underlying confinement and hadron masses can be connected to the parameter $$\Lambda _{\overline{MS}}$$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling $$\alpha _s(Q^2)$$ defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale $$Q_0$$ which sets the interface between perturbative and nonperturbative hadron dynamics. The use of $$Q_0$$ to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front-form vacuum has important consequences for the cosmological constant. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.

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

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.

Fourier-positivity constraints on QCD dipole models

Fourier-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position (r) space. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical Fourier-positivity constraints on the limit r -> 0 behavior of the dipole amplitudes, we identify the common origin of the violation of Fourier-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior r^{2+epsilon}, epsilon>0, softer, even slightly, than color transparency. Fourier-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant alpha(r).

Properties of quark matter in a new quasiparticle model with QCD running coupling

The running of the QCD coupling in the effective mass causes thermodynamic inconsistency problem in the conventional quasiparticle model. We provide a novel treatment which removes the inconsistency by an effective bag constant. The chemical potential dependence of the renormalization subtraction point is constrained by the Cauchy condition in the chemical potential space. The stability and microscopic properties of strange quark matter are then studied within the completely self-consistent quasiparticle model, and the obtained equation of state of quark matter is applied to the investigation of strange stars. It is found that our improved model can describe well compact stars with mass about two times the solar mass, which indicates that such massive compact stars could be strange stars.

Light-Front Holography, Color Confinement, and Supersymmetric Features of QCD

Light-Front Quantization provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic light-front wavefunctions. One obtains new insights into the hadronic spectrum, light-front wavefunctions, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography -- the duality between the front form and AdS$_5$, the space of isometries of the conformal group. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons of the same parity. The mass scale $\kappa$ underlying confinement and hadron masses can be connected to the parameter $\Lambda_{\overline {MS}}$ in the QCD running coupling by matching the nonperturbative dynamics, as described by the effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The result is an effective coupling defined at all momenta. This matching of the high and low momentum transfer regimes determines a scale $Q_0$ which sets the interface between perturbative and nonperturbative hadron dynamics. The use of $Q_0$ to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality (PMC) for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the front-form vacuum has important consequences for the cosmological constant. I also discuss evidence that the antishadowing of nuclear structure functions is flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.

Magnetized quark matter with a magnetic-field dependent coupling

It was recently derived that the QCD running coupling is a function of the magnetic field strength under the strong magnetic field approximation. Inspired by this progress and based on the self-consistent solutions of gap equations, the properties of two-flavor and three-flavor quark matter are studied in the framework of the Nambu--Jona-Lasinio model with a magnetic-field-dependent running coupling. We find that the dynamical quark masses as functions of the magnetic field strength are not monotonous in the fully chirally broken phase. Furthermore, the stability of magnetized quark matter with the running coupling is enhanced by lowering the free energy per baryon, which is expected to be more stable than that of the conventional constant coupling case. It is concluded that the magnetized strange quark matter described by running coupling can be absolutely stable.

On the interface between perturbative and nonperturbative QCD

The QCD running coupling $\alpha_s(Q^2)$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $\alpha_s(Q^2)$. The high-$Q^2$ dependence of the coupling $\alpha_s(Q^2)$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of $\alpha_s(Q^2)$ then determines the scale $Q_0$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $Q_0$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of $Q_0$ and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the $\bar{MS}$, $g_1$, $MOM$ and $V$ renormalization schemes. Our results show that the discrepancies on the value of $\alpha_s$ at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute $\alpha_s(Q^2)$ over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.

Predictions for the top-quark forward-backward asymmetry at high invariant pair mass using the principle of maximum conformality

The D0 collaboration at FermiLab has recently measured the top-quark pair forward-backward asymmetry in $\bar p p \to t \bar{t} X$ reactions as a function of the $t\bar{t} $ invariant mass $M_{t\bar{t}}$. The D0 result for $A_{\rm FB}(M_{t\bar{t}}>650\, {\rm GeV})$ is smaller than $A_{\rm FB}(M_{t\bar{t}})$ obtained for small values of $M_{t\bar{t}}$, which may indicate an "increasing-decreasing" behavior for $A_{\rm FB}(M_{t\bar{t}}>M_{\rm cut})$. This behavior is not explained using conventional renormalization scale-setting, even by a next-to-next-to-leading order (N$^2$LO) QCD calculation -- one predicts a monotonically increasing behavior. In the conventional scale-setting method, one simply guesses a single renormalization scale $\mu_r$ for the argument of the QCD running coupling and then varies it over an arbitrary range. However, the conventional method has inherent difficulties. ...... In contrast, if one fixes the scale using the Principle of Maximum Conformality (PMC), the resulting pQCD predictions are renormalization-scheme independent since all of the scheme-dependent $\{\beta_i\}$-terms in the QCD perturbative series are resummed into the QCD running couplings at each order. ...... In this paper we show that if one applies the PMC to determine the top versus anti-top quark forward-backward asymmetry by properly using the pQCD predictions up to N$^2$LO level, one obtains the predictions without renormalization scheme or scale ambiguities. ...... In addition, the PMC prediction for $A_{\rm FB}(M_{t\bar{t}}> M_{\rm cut})$ shows an "increasing-decreasing" behavior for increasing values of $M_{\rm cut}$ which is not observed in the NLO and N$^2$LO predictions for $A_{\rm FB}(M_{t\bar{t}}> M_{\rm cut})$ with conventional scale-setting. This behavior could be tested by the future more precise measurements at the LHC.

Cross section for the Drell–Yan process in proton–proton collisions at the Large Hadron Collider (LHC)

The cross sections for the Drell–Yan process at the c.m. collision energy of \(\sqrt s \) = 13 TeV were calculated, and the results of these calculations are presented. The systematic errors associated with the uncertainties in the quark and gluon distributions and with the choice of scale for factorization and for the running QCD coupling constant are considered.

Importance of proper renormalization scale-setting for QCD testing at colliders

A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, giving predictions which are independent of the choice of renormalization scheme. The scales of the QCD couplings and the effective number of quark flavors are set order by order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance and all of the the self-consistency conditions derived from the renormalization group......In this brief report, we summarize the results of our recent PMC applications for a number of collider processes, emphasizing their generality and applicability....... These results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing the sensitivity of the colliders to possible new physics beyond the Standard Model.

Off-shell supersymmetry

Supersymmetry does not dictate the way we should quantize the fields in the supermultiplets, and so we have the freedom to quantize the Standard Model (SM) particles and their superpartners differently. We propose a generalized quantization scheme under which a particle can only appear off-shell, while its contributions to quantum corrections are exactly the same as those in the usual quantum field theory. We apply this quantization scheme solely to the sparticles in the R-parity preserving Minimal Supersymmetric Standard Model (MSSM). Thus, sparticles can only appear off-shell. They could be light but would completely escape the direct detection at any experiments such as the LHC. However, our theory still retains the same desirable features of the usual MSSM at the quantum level. For instance, the gauge hierarchy problem is solved and the three MSSM gauge couplings are unified in the usual way. Although direct detection of sparticles is impossible, their existence can be revealed by precise measurements of some observables (such as the running QCD coupling) that may receive quantum corrections from them and have sizable deviations from the SM predictions. Also, the experimental constraints from the indirect sparticle search are still applicable.

Uncertainties of Drell-Yan production cross section in pp collisions at the LHC

The results of calculations of uncertainties of the Drell-Yan production cross section at the energy √s = 13 TeV are presented. Systematic errors related to uncertainties in the quark and gluon distribution functions, the choice of the QCD factorization scale, and the QCD running coupling constant are considered.

Light-front holographic QCD and color confinement

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.