# New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra

## Abstract

A fundamental problem in hadron physics is to obtain a relativistic color-confining, first approximation to QCD which can predict both hadron spectroscopy and the frame-independent light-front (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 light-front 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 squared. The same result, including spin terms, is obtained using light-front holography – the duality between light-front dynamics and AdS _{5}, the space of isometries of the conformal group if one modifies the action of AdS _{5} by the dilaton e ^{$κ^2$} ^{z$^2$} in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict 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 light-front wavefunctions. The mass scale κ 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. Lastly, the matching of the high and low momentum transfer regimes also determines a scale Q _{0} which sets the interface between perturbative and nonperturbative hadron dynamics.

- 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

- OSTI Identifier:
- 1389548

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Russian Physics Journal

- Additional Journal Information:
- Journal Volume: 60; Journal Issue: 3; Journal ID: ISSN 1064-8887

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; hadron structure and dynamics; color confinement; wave functions; spectroscopy; formfactors; structure functions

### Citation Formats

```
Brodsky, S. J. New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra. United States: N. p., 2017.
Web. doi:10.1007/s11182-017-1089-4.
```

```
Brodsky, S. J. New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra. United States. doi:10.1007/s11182-017-1089-4.
```

```
Brodsky, S. J. Tue .
"New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra". United States. doi:10.1007/s11182-017-1089-4. https://www.osti.gov/servlets/purl/1389548.
```

```
@article{osti_1389548,
```

title = {New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra},

author = {Brodsky, S. J.},

abstractNote = {A fundamental problem in hadron physics is to obtain a relativistic color-confining, first approximation to QCD which can predict both hadron spectroscopy and the frame-independent light-front (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 light-front 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 squared. The same result, including spin terms, is obtained using light-front holography – the duality between light-front dynamics and AdS5, the space of isometries of the conformal group if one modifies the action of AdS5 by the dilaton e$κ^2$z$^2$ in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict 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 light-front wavefunctions. The mass scale κ 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. Lastly, the matching of the high and low momentum transfer regimes also determines a scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics.},

doi = {10.1007/s11182-017-1089-4},

journal = {Russian Physics Journal},

number = 3,

volume = 60,

place = {United States},

year = {2017},

month = {7}

}

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