# Supersymmetric and Conformal Features of Hadron Physics

## Abstract

The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion $$q\overline{q}$$ eigenstate has zero mass for m _{q} = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can 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 κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α _{s} (Q ^{2}) ∝ e ^{-Q2/4κ2}, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS _{5} space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

- Authors:

- SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1490464

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Universe

- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 11; Journal ID: ISSN 2218-1997

- Publisher:
- MDPI

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum chromodynamics; color confinement; superconformal algebra; conformal symmetry; light-front holography

### Citation Formats

```
Brodsky, Stanley.
```*Supersymmetric and Conformal Features of Hadron Physics*. United States: N. p., 2018.
Web. doi:10.3390/universe4110120.

```
Brodsky, Stanley.
```*Supersymmetric and Conformal Features of Hadron Physics*. United States. doi:10.3390/universe4110120.

```
Brodsky, Stanley. Thu .
"Supersymmetric and Conformal Features of Hadron Physics". United States. doi:10.3390/universe4110120. https://www.osti.gov/servlets/purl/1490464.
```

```
@article{osti_1490464,
```

title = {Supersymmetric and Conformal Features of Hadron Physics},

author = {Brodsky, Stanley},

abstractNote = {The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion $q\overline{q}$ eigenstate has zero mass for mq = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can 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 κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: αs (Q2) ∝ e-Q2/4κ2, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS 5 space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.},

doi = {10.3390/universe4110120},

journal = {Universe},

issn = {2218-1997},

number = 11,

volume = 4,

place = {United States},

year = {2018},

month = {11}

}