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

## Abstract

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.

- Authors:

- SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1433298

- Alternate Identifier(s):
- OSTI ID: 1443762

- Report Number(s):
- SLAC-PUB-17012

Journal ID: ISSN 1687-7357

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Advances in High Energy Physics

- Additional Journal Information:
- Journal Volume: 2018; Journal ID: ISSN 1687-7357

- Publisher:
- Hindawi

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Brodsky, Stanley J.
```*Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra*. United States: N. p., 2018.
Web. doi:10.1155/2018/7236382.

```
Brodsky, Stanley J.
```*Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra*. United States. doi:10.1155/2018/7236382.

```
Brodsky, Stanley J. Mon .
"Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra". United States.
doi:10.1155/2018/7236382.
```

```
@article{osti_1433298,
```

title = {Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra},

author = {Brodsky, Stanley J.},

abstractNote = {The QCD light-front Hamiltonian equation HLFΨ=M2Ψ derived from quantization at fixed LF time τ=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 κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the qq¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and AdS5, if one modifies the AdS5 action by the dilaton eκ2z2 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 qq¯ eigenstate has zero mass at mq=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 αs(Q2)∝e-Q2/4κ2. The mass scale κunderlying hadron masses can be connected to the parameter ΛMS¯ 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. 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.},

doi = {10.1155/2018/7236382},

journal = {Advances in High Energy Physics},

number = ,

volume = 2018,

place = {United States},

year = {Mon Apr 16 00:00:00 EDT 2018},

month = {Mon Apr 16 00:00:00 EDT 2018}

}