Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from LightFront Holography and Superconformal Algebra
The QCD lightfront Hamiltonian equation ${H}_{\mathrm{L}\mathrm{F}}\left(\mathrm{\Psi}\right)={M}^{2}\left(\mathrm{\Psi}\right)$ derived from quantization at fixed LF time $\tau =t+z/c$ provides a causal, frameindependent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. 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 lightfront Hamiltonian, it leads to a colorconfining potential ${\kappa}^{4}{\zeta}^{2}$ for mesons, where ${\zeta}^{2}$ is the LF radial variable conjugate to the $q\overline{q}$ invariant mass squared. The same result, including spin terms, is obtained using lightfront holography, the duality between lightfront dynamics and ${\mathrm{A}\mathrm{d}\mathrm{S}}_{5}$, if one modifies the ${\mathrm{A}\mathrm{d}\mathrm{S}}_{5}$ action by the dilaton ${e}^{{\kappa}^{2}{z}^{2}}$ in the fifth dimension $z$. When one generalizes this procedure using superconformal algebra, the resulting lightfront 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 $q\overline{q}$ eigenstate has zero mass at ${m}_{q}=0.$ The superconformal relations also can be extended to heavylight quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by lightfront quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling ${\alpha}_{s}\left({Q}^{2}\right)\propto {e}^{{Q}^{2}/4{\kappa}^{2}}$. The mass scale $\kappa $underlying hadron masses can be connected to the parameter ${\mathrm{\Lambda}}_{\overline{\mathrm{M}\mathrm{S}}}$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling ${\alpha}_{s}\left({Q}^{2}\right)$ defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.
 Authors:

^{[1]}
 SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)
 Publication Date:
 Report Number(s):
 SLACPUB17012
Journal ID: ISSN 16877357
 Grant/Contract Number:
 AC0276SF00515
 Type:
 Published Article
 Journal Name:
 Advances in High Energy Physics
 Additional Journal Information:
 Journal Volume: 2018; Journal ID: ISSN 16877357
 Publisher:
 Hindawi
 Research Org:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1433298
 Alternate Identifier(s):
 OSTI ID: 1443762