Advances in LightFront QCD: Supersymmetric Properties of Hadron Physics from LightFront Holography and Superconformal Algebra
Abstract
A remarkable feature of QCD is that the mass scale $k$ which controls color confinement and lightquark 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. If one applies the same procedure to the lightfront Hamiltonian, it leads uniquely to a confinement potential κ ^{4}ζ ^{2} for mesons, where ζ ^{2} is the LF radial variable conjugate to the $$q\bar{q}$$ invariant mass. The same result, including spin terms, is obtained using lightfront holography$$the duality between the front form and AdS _{5}, the space of isometries of the conformal group$$if one modifies the action of AdS _{5} by the dilaton e ^{$κ^2z^2$} in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting lightfront eigensolutions predict 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 lightfront wavefunctions. The mass scale κκ underlying confinement and hadron masses can be connected to the parameter Λ _{$$\overline{MS}$$} in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α _{s} (Q ^{2}) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q _{0} which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q _{0} to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frameindependent frontform vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is nonuniversal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.
 Authors:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1367846
 Grant/Contract Number:
 AC0276SF00515
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 FewBody Systems
 Additional Journal Information:
 Journal Volume: 58; Journal Issue: 3; Journal ID: ISSN 01777963
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Brodsky, Stanley J. Advances in LightFront QCD: Supersymmetric Properties of Hadron Physics from LightFront Holography and Superconformal Algebra. United States: N. p., 2017.
Web. doi:10.1007/s0060101712924.
Brodsky, Stanley J. Advances in LightFront QCD: Supersymmetric Properties of Hadron Physics from LightFront Holography and Superconformal Algebra. United States. doi:10.1007/s0060101712924.
Brodsky, Stanley J. Wed .
"Advances in LightFront QCD: Supersymmetric Properties of Hadron Physics from LightFront Holography and Superconformal Algebra". United States.
doi:10.1007/s0060101712924. https://www.osti.gov/servlets/purl/1367846.
@article{osti_1367846,
title = {Advances in LightFront QCD: Supersymmetric Properties of Hadron Physics from LightFront Holography and Superconformal Algebra},
author = {Brodsky, Stanley J.},
abstractNote = {A remarkable feature of QCD is that the mass scale $k$ which controls color confinement and lightquark 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. If one applies the same procedure to the lightfront Hamiltonian, it leads uniquely to a confinement potential κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the $q\bar{q}$ invariant mass. The same result, including spin terms, is obtained using lightfront holography$$the duality between the front form and AdS5, the space of isometries of the conformal group$$if one modifies the action of AdS5 by the dilaton e$κ^2z^2$ in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting lightfront eigensolutions predict 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 lightfront wavefunctions. The mass scale κκ underlying confinement and hadron masses can be connected to the parameter Λ$\overline{MS}$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling αs (Q2) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q0 to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frameindependent frontform vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is nonuniversal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.},
doi = {10.1007/s0060101712924},
journal = {FewBody Systems},
number = 3,
volume = 58,
place = {United States},
year = {Wed Apr 19 00:00:00 EDT 2017},
month = {Wed Apr 19 00:00:00 EDT 2017}
}

Here, lightfront holography, together with superconformal algebra, have provided new insights into the physics of color confinement and the spectroscopy and dynamics of hadrons. As shown by de Alfaro, Fubini and Furlan, 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 procedure of de Alfaro et al. to the frameindependent lightfront Hamiltonian, it leads uniquely to a confining qq¯ potential κ ^{4}ζ ^{2}, where ζ ^{2} is the lightfrontmore »

New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from LightFront Holography and Superconformal Algebra
A fundamental problem in hadron physics is to obtain a relativistic colorconfining, first approximation to QCD which can predict both hadron spectroscopy and the frameindependent lightfront (LF) wavefunctions underlying hadron dynamics. The QCD Lagrangian with zero quark mass has no explicit mass scale; the classical theory is conformally invariant. Thus, a fundamental problem is to understand how the mass gap and ratios of masses – such as mρ/mp – can arise in chiral QCD. De Alfaro, Fubini, and Furlan 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 and rescales the time variable. If one applies the same procedure to the lightfront Hamiltonian, it leads uniquely to a confinement potential κ ^{4}ζ ^{2} for mesons, where ζ ^{2} is the LF radial variable conjugate to themore »