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

Journal Article · 31 December 2017 · Advances in High Energy Physics

DOI: https://doi.org/10.1155/2018/7236382 · OSTI ID:1433298

Brodsky, Stanley J.  ^[1]

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1. SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, USA

The QCD light-front 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, frame-independent 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 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 $q\overline{q}$ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front 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 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 $q\overline{q}$ eigenstate has zero mass at $m_q=0.$ The superconformal relations also can be extended to heavy-light 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 light-front 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.

• Research Organization: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: AC02-76SF00515
• OSTI ID: 1433298
• Report Number(s): SLAC-PUB--17012; SLAC-PUB-17012; PII: 7236382; 7236382
• Journal Information: Advances in High Energy Physics, Journal Name: Advances in High Energy Physics Vol. 2018; ISSN 1687-7357
• Publisher: HindawiCopyright Statement
• Country of Publication: Egypt
• Language: English