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Register a new userLight-Front Holography and Supersymmetric Conformal Algebra: A Novel Approach to Hadron Spectroscopy, Structure, and Dynamics
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We give an overview of recent progress into the infrared structure of QCD based on the gauge/gravity correspondence and light-front quantization, where the color confining interaction for mesons and baryons is determined by an underlying superconformal algebraic structure. This new approach to hadron physics gives remarkable connections and predictions across the entire mass spectrum of hadrons and also describes the infrared behavior of the strong coupling. More recently, an extensive study of form factors, polarized and unpolarized parton distributions and the sea quark contribution to the nucleon has been carried out by extending the holographic formalism to incorporate the nonperturbative structure of Veneziano amplitudes. Contribution to the report Strong QCD from Hadron Structure Experiments Jefferson Lab Workshop, 5-9 November, 2019
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QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks in the same 4-plet representation with a universal Regge slope. The pion $q bar q$ eigenstate has zero mass for $m_q=0.$ The superconformal relations also can be extended to heavy-light quark mesons and baryons. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key observation is the remarkable dAFF principle 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 $kappa$ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling, and the mass parameter underlying the form of the nonperturbative QCD running coupling: $alpha_s(Q^2) propto exp{-{Q^2/4 kappa^2}}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. The mass scale $kappa$ underlying hadron masses can be connected to the parameter $Lambda_{overline {MS}}$ in the QCD running coupling by matching its predicted nonperturbative form to the perturbative QCD regime. One also obtains predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.
The QCD light-front Hamitonian equation derived from quantization at fixed LF time provides a causal, frame-independent, method for computing hadron spectroscopy and dynamical observables. 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 $kappa^4 zeta^2$ for mesons, where $zeta^2$ is the LF radial variable conjugate to the $q bar q$ invariant mass squared. The same result, including spin terms, is obtained using light-front holography if one modifies the AdS$_5$ action 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 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 $q bar q$ eigenstate has zero mass at $m_q=0.$ The superconformal relations also can be extended to heavy-light quark mesons and baryons. AdS/QCD also predicts the analytic form of the nonperturbative running coupling in agreement with the effective charge measured from measurements of the Bjorken sum rule. The mass scale underlying hadron masses can be connected to the mass parameter in the QCD running coupling. The result is an effective coupling $alpha_s(Q^2)$ defined at all momenta. One also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.
Light-Front Quantization -- Diracs Front Form -- 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 LFWFs. One obtains new insights into the hadronic mass scale, the hadronic spectrum, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons. 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 the momentum and other sum rules for the nuclear parton distribution functions.
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate $z$ with an invariant light-front coordinate $zeta$ which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The mapping of electromagnetic and gravitational form factors in AdS space to their corresponding expressions in light-front theory confirms this correspondence. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates and the behavior of the QCD coupling in the infrared. The distinction between static structure functions such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical structure functions which include the effects of rescattering is emphasized. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined.
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 Schrodinger 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...
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