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تسجيل مستخدم جديدNovel Perspectives from Light-Front QCD, Superconformal Algebra, and Light-Front Holography
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Stanley J. Brodsky
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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.
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A remarkable feature of QCD is that the mass scale which controls color confinement and 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 equatio
ns 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. Applying the same procedure to the light-front Hamiltonian leads to a unique confinement potential $kappa^4 zeta^2$ for mesons, where $zeta$ is the LF radial variable conjugate to the invariant mass. The same result, including spin terms, is obtained using light-front holography, the duality between the front form and AdS$_5,$ if one modifies the action by the dilaton $e^{kappa^2 z^2}$ in the fifth dimension $z$. Generalizing this procedure using superconformal algebra, leads to 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 underlying confinement and hadron masses can be connected to the mass parameter in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling defined at all momenta and the determination of a momentum scale which sets the interface between perturbative and nonperturbative hadron dynamics. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.
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 under
lying 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.
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 thei
r baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding superconformal quantum mechanics into AdS space. The breaking of conformal symmetry determines a unique quark-confining light-front potential for light hadrons including spin-spin interactions in agreement with the soft-wall AdS/QCD approach and light-front holography. The mass-squared of the light hadrons can be expressed as a frame-independent decomposition of contributions from the constituent kinetic energy, the confinement potential, and spin-spin contributions. The mass of the pion eigenstate vanishes in the chiral limit. Only one mass parameter 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 mass parameter of the pQCD running coupling. The result is an effective coupling 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. as well as the factorization scale for structure functions and distribution amplitudes. This procedure, in combination with the scheme-independent PMC procedure for setting renormalization scales, can greatly improve the precision of QCD predictions.
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 dim
ension 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.
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 o
bservation 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.
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