Supersymmetric Meson-Baryon Properties of QCD from Light-Front Holography and Superconformal Algebra

Abstract

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 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. 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.