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

摘要

The QCD light-front Hamitonian equation derived from quantization at fixed LFtime provides a causal, frame-independent, method for computing hadronspectroscopy and dynamical observables. de Alfaro, Fubini, and Furlan (dAFF)have made an important observation that a mass scale can appear in theequations of motion without affecting the conformal invariance of the action ifone adds a term to the Hamiltonian proportional to the dilatation operator orthe special conformal operator. If one applies the dAFF procedure to the QCDlight-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, isobtained using light-front holography if one modifies the AdS$_5$ action by thedilaton $e^{\kappa^2 z^2}$ in the fifth dimension $z$. When one generalizesthis procedure using superconformal algebra, the resulting light-fronteigensolutions provide a unified Regge spectroscopy of meson, baryon, andtetraquarks, including remarkable supersymmetric relations between the massesof 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 beextended to heavy-light quark mesons and baryons. AdS/QCD also predicts theanalytic form of the nonperturbative running coupling in agreement with theeffective charge measured from measurements of the Bjorken sum rule. The massscale underlying hadron masses can be connected to the mass parameter in theQCD running coupling. The result is an effective coupling $\alpha_s(Q^2)$defined at all momenta. One also obtains empirically viable predictions forspacelike and timelike hadronic form factors, structure functions, distributionamplitudes, and transverse momentum distributions.