Light-Front Holography and Superconformal Quantum Mechanics: A New Approach to Hadron Structure and Color Confinement

Understand

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 Schr\"odinger 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 $L$.