1. American Physical Society1
QCD Quark Confinement
Presented To
American Physical Society
DPF JSF2006
31 October 2006 By
Carl T. Case
Case R&D Consulting

2. Outline Framework for a Baryon Confinement Theory2
Outline
Framework for a Baryon Confinement Theory
Long Standing QCD Confinement Questions
Dirac Equation for Baryon Quarks (Composite of Q &G)
Solution of Dirac Equation for Composite Baryon Quark
Flavors & Generations
Baryon Mass Spectrum Calculations
Quark Generations

3. Framework and Approach for Theory3
Framework and Approach for Theory
Massless Quarks Described by Dirac Equation
Massless Gluons Described by QCD Maxwell Equations
Seeking Eigenstates: Energy; Momenta; Angular Momenta; Parity
Using Hartree Self-Consistent-Field (SCF) Methodology
Converts Multi-Particle Problem to Multiple Single Particle Problems
Second Quantization
Enables Treating Quark & Gluon Operators on Common Basis
Gluon Fields Expressed as Complete Orthogonal Multipole Expansions
Lowest Order Multipoles Use for QCD Fields in Confinement Range
QCD Maxwell Eq. Commutator Terms contribute at Higher Orders

4. Long Standing Questions4
Long Standing Questions
Mechanism for Chiral Symmetry Breaking in QCD?
Confinement Mechanism For Quarks?
Confinement Mechanism For Gluons?
Why Do Quark Flavors Occur?
How Do Massless Quarks & Gluons Acquire Mass?
Is QCD a Calculable Theory in Confinement Range?
Are there Only Three Generations? … If so Why?

5. Quark-Gluon Velocity Synchronization Triggers 5
Quark-Gluon Velocity Synchronization Triggers
Chiral Symmetry Breaking (CSB)
Consider Quarks & Gluons Moving with Same Velocity
Countervailing Magnetic Force Cancels Electric Force
Only a Color Magnetic Field Remains

6. Color Magnetic Bottle Confines Quarks6
Color Magnetic Bottle Confines Quarks
If Quarks and Gluons have same velocity, then CSB is triggered
Magnetic Bottle Pushes Quark into Force-Free Orbital Plane

7. CSB Simplifies the Dirac Equation7
CSB Simplifies the Dirac Equation
Before CSB
After CSB

8. Quantized Magnetic Flux Mechanism Confines Gluons8
Quantized Magnetic Flux Mechanism Confines Gluons
Quark’s Phase Angle is Given By Line Integral of Vector Potential or Surface Integral of Magnetic Field
Gluons Trapped by Circulating Quarks
Results in Quantized Bundles of Color Magnetic Flux
Implies

9. Dirac Equation- Angular Momentum9
Dirac Equation- Angular Momentum
From Chart 7
Using Angular part of the operator
Dirac Equation can be written as

10. Composite Angular Momentum10
Dirac Equation-
Composite Angular Momentum
Addition of Angular Momentum Quark & Gluon Operators Indicates that Total Orbital Ang. Mom. Is a Good Quantum Number
where

11. Mass Acquisition by Quarks & Gluons11
Mass Acquisition by Quarks & Gluons
The Equatorial Plane is a Force-Free Region for Quarks
However, Well-Defined Angular Momentum for Quarks and Gluons
Implies Polar Angle, , is not Well-Defined; Location Uncertain
Tus, Magnetic Force Applies Inertial Drag Against Quarks & Gluons
Results in Kinetic Energy lost to Inertial Drag that shows up as Mass
Mass is Necessary for Quark-Gluon Composite to Conserve Energy

12. Dirac Equation - The Mass Term12
Dirac Equation - The Mass Term
Dirac Equation in terms of Quark-Gluon Composite Ang. Mom.
where
Mass term can be added in Gauge Invariant manner

13. Flavor States & Amount of Mass Gain are Connected13
Flavor States & Amount of Mass Gain are Connected
CSB depends on Countervailing Magnetic Force cancelling Electric Force
Requires that the Countervailing Force is Constant
Quantized Flux Equations Produce a series of Topological Degenerate Ground States that Correspond 1-to-1 to the Quark Flavor States
Winding Number, n, serves as Quantum Number Gluon
If Quark Mass is known, then Quark speed can be calculated.

14. Flavor State Data for Baryon Quarks14
Flavor State Data for Baryon Quarks

15. Is QCD a Calculable Theory in Confinement Range?15
Is QCD a Calculable Theory in Confinement Range?
Key Issue
Calculation Strong Running Coupling Constant
Quantized Color Flux Equations Enable Calculation
Summary of Calculation is on Next Chart

16. Calculation of Strong Running Coupling Constant16
Calculation of Strong Running Coupling Constant

17. Is QCD a Calculable Theory17
Is QCD a Calculable Theory
in Confinement Range?
Composite Q-G Dirac Equation provides Approximate Solutions

18. Approximate Energy Eigenstates18
Approximate Energy Eigenstates
for Baryon Quarks
Baryon Mass is

19. Baryon Mass Spectra Calculations Results19
Baryon Mass Spectra Calculations Results
- Spin Only-

20. Baryon Mass Spectra Calculations Results
- Orbital States- 20
Baryon
State
Flavor
Number f 1 2 3
Orbital
Angular
Momenta l J
pair
2 J k
Calc.
Mass
(Mev)
Variance
N (1440)
N (1520)
N (1675)
N (1680)
N (2190)
N (2220) D
(1950)
(2420) L
(1405)
(1520)
(1820)
(1830) S
(1670)
(1775)
(1915)
(2030) X
(1690) W
(2250)
P11
D13
D15
F15
G17
H19
F37
H3,11
S01
D03
F05
D05
F17
S33 2
2 2
1,0 3
3,4 4 1
3,1
1442
1530
1681
1665
2156
2241
1965
2411
1410
1524
1848
1840
1666
1769
1915
2060
1682
1828
2254
0.2%
0.7%
0.3% -
0.9%
1.6%
0.8%
0.4%
1.5%
0.6% -
0.2% -
0.4%
0.0%
1.5% -
0.5%
0.4%
0.1%

21. Empirical Scaling Law for Quark Speed C related to Coulomb Charge21
Empirical Scaling Law for Quark Speed C related to Coulomb Charge

22. Are There more Than 3 Generations?22
Higher Flavor States?
Are There more Than 3 Generations?
Scaling Law Suggests possible 4th Gen. Quark (b’) w/ Mass > 100 GeV
Scaling Law also suggests all other quarks have energies are > TeV which is well above the Quark-Gluon Plasma Critical Energy

23. Summary Dynamical Relationship Identified that Triggers CSB23
Summary
Dynamical Relationship Identified that Triggers CSB
Baryon Quarks Are Shown to be Composite of Massless Quarks and Gluons
Baryon Quarks Occupy a series of Degenerate Ground States Corresponding to the Six Quark Flavors
Each Flavor has Unique Quantum Number, Mass, and Speed
Baryon Mass Spectra Calculations are in Good Agreement with Experimental Data
Empirical Power Law for Speed of Quark Flavors indicates a Possible 4th Generation Quark (b’) with Mass of GeV
Other Projected Quark Masses are above Quark-Gluon Plasma Limit

24. 24
Backup Charts

25. Spin Percentage of Angular Momentum25
Total Angular Momentum Distribution for Baryon
is given by
Total = 3*(2n+1+0.5) = 3*(2n+1.5)
n=1 (u, d) Total = Spin %= 14.3%
n=2 (s, c) Total = Spin %= 9.1%
n=3 (b, t) Total = Spin %= %

26. Theoretical Framework26
Theoretical Framework
Lowest Order Multipole Color Fields

27. 27
Abstract
Dirac equation is solved for 3 massless quarks under influence of generated color fields. If quarks and gluons have identical velocities, then chiral symmetry is broken. Color electric field is totally cancelled; quarks are trapped in color magnetic bottle; gluons are trapped by circulating quarks in quantized color magnetic flux bundles. Second quantization and Hartree approach are used to solve Dirac equation. Each quark along with its bundle of gluons behaves as a composite particle with mass gained from symmetry breaking. Solution exhibits a series of degenerate ground states that give rise to quark flavor states. Spinor wave function solutions from Dirac equation are used to calculate baryon mass spectrum.