# Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra

## Abstract

A remarkable feature of QCD is that the mass scale $k$ which controls color confinement and light-quark 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 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. The same result, including spin terms, is obtained using light-front 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 light-front 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 light-front 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, frame-independent front-form vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; 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:
- AC02-76SF00515

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Few-Body Systems

- Additional Journal Information:
- Journal Volume: 58; Journal Issue: 3; Journal ID: ISSN 0177-7963

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Brodsky, Stanley J.
```*Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra*. United States: N. p., 2017.
Web. doi:10.1007/s00601-017-1292-4.

```
Brodsky, Stanley J.
```*Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra*. United States. doi:10.1007/s00601-017-1292-4.

```
Brodsky, Stanley J. Wed .
"Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front Holography and Superconformal Algebra". United States.
doi:10.1007/s00601-017-1292-4. https://www.osti.gov/servlets/purl/1367846.
```

```
@article{osti_1367846,
```

title = {Advances in Light-Front QCD: Supersymmetric Properties of Hadron Physics from Light-Front 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 light-quark 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 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. The same result, including spin terms, is obtained using light-front 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 light-front 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 light-front 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, frame-independent front-form vacuum has important consequences for the cosmological constant. In conclusion, I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions.},

doi = {10.1007/s00601-017-1292-4},

journal = {Few-Body 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}

}