Volume 336 -
XIII Quark Confinement and the Hadron Spectrum (Confinement2018) -
A: Vacuum structure and confinement

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

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Pre-published on:
September 12, 2019

Published on:
September 26, 2019

Abstract

The combined approach of light-front holography and superconformal algebra provides insight into the origin of color confinement and the QCD mass scale. Light-front (LF) holography predicts Lorentz-invariant light-front Schr\"odinger bound state equations for QCD, analogous to the quantum mechanical Schrodinger equation for atoms in QED. A key feature is the implementation of the de Alfaro, Fubini and Furlan (dAFF) procedure for breaking conformal invariance which allows a mass parameter to appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $\kappa$ appears which determines hadron masses and universal Regge slopes. It also implies a unique form of the soft-wall dilaton which modifies the action of AdS$_5$. The result is a remarkably simple analytic description of quark confinement, as well as nonperturbative hadronic structure and dynamics. The same mass parameter $\kappa$ controls the Gaussian fall-off of the nonperturbative QCD running coupling: $\alpha_s(Q^2) \propto \exp{\left(-Q^2/4 \kappa^2\right)}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. The mass scale $\kappa$ underlying hadron masses can be connected to the parameter $\Lambda_{\overline {MS}}$ in the QCD running coupling by matching the magnitude and slope of the nonperturbative

coupling to perturbative QCD at large $Q^2$. The result is an effective coupling $\alpha_s(Q^2)$ defined at all momenta and a transition scale $Q_0$ which separates perturbative and nonperturbative dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, when one applies superconformal algebra, one obtains a unified spectroscopy of meson, baryon, and tetraquarks as equal-mass members of the same 4-plet representation. The LF resulting Schrodinger equations match the bound state equation obtained from LF holography. The predicted Regge trajectories have a universal slope in both the principal quantum number $n$ and orbital angular momentum. The meson and baryon Regge trajectories are identical when one compares mesons with baryons with orbital angular momentum $L_M= L_B +1$. The matching of bosonic meson and fermionic baryon masses is a manifestation of a hidden supersymmetry in hadron physics. The pion eigenstate is massless for massless quarks, despite its dynamical structure as a $q \bar q$ bound state. The superconformal relations also can be extended to heavy-light quark mesons and baryons. One also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.

coupling to perturbative QCD at large $Q^2$. The result is an effective coupling $\alpha_s(Q^2)$ defined at all momenta and a transition scale $Q_0$ which separates perturbative and nonperturbative dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, when one applies superconformal algebra, one obtains a unified spectroscopy of meson, baryon, and tetraquarks as equal-mass members of the same 4-plet representation. The LF resulting Schrodinger equations match the bound state equation obtained from LF holography. The predicted Regge trajectories have a universal slope in both the principal quantum number $n$ and orbital angular momentum. The meson and baryon Regge trajectories are identical when one compares mesons with baryons with orbital angular momentum $L_M= L_B +1$. The matching of bosonic meson and fermionic baryon masses is a manifestation of a hidden supersymmetry in hadron physics. The pion eigenstate is massless for massless quarks, despite its dynamical structure as a $q \bar q$ bound state. The superconformal relations also can be extended to heavy-light quark mesons and baryons. One also obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.

DOI: https://doi.org/10.22323/1.336.0040

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