Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
2011 Cross Strait Meeting on Particle Physics and Cosmology
Proton Compton Scattering In Unified
Proton-∆+ Theory
ZHANG Yun
(Collaboration With Konstantin G. Savvidy)
Physics Department, Nanjing University
April 1, 2011
Outline
Background and Motivation
The Model
Proton Compton Scattering
1
Background and Motivation
2
The Model
3
Proton Compton Scattering
4
Vertex Structure
5
Summary
Vertex Structure
Summary
Outline
Background and Motivation
The Model
+
Proton Compton Scattering
Vertex Structure
∆+ (1232MeV, J P = 32 ) freedom must be taken into
account in proton Compton scattering
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
+
∆+ (1232MeV, J P = 32 ) freedom must be taken into
account in proton Compton scattering
Previously p is treated as spin 1/2 Dirac spinor and ∆+ in a
different theory
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
+
∆+ (1232MeV, J P = 32 ) freedom must be taken into
account in proton Compton scattering
Previously p is treated as spin 1/2 Dirac spinor and ∆+ in a
different theory
Our innovation:
We treat p and ∆+ in a unified spin 3/2 field theory
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
+
∆+ (1232MeV, J P = 32 ) freedom must be taken into
account in proton Compton scattering
Previously p is treated as spin 1/2 Dirac spinor and ∆+ in a
different theory
Our innovation:
We treat p and ∆+ in a unified spin 3/2 field theory
How Motivated
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
+
∆+ (1232MeV, J P = 32 ) freedom must be taken into
account in proton Compton scattering
Previously p is treated as spin 1/2 Dirac spinor and ∆+ in a
different theory
Our innovation:
We treat p and ∆+ in a unified spin 3/2 field theory
How Motivated
Proton and ∆+ are both comprised of the same quarks.
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
+
∆+ (1232MeV, J P = 32 ) freedom must be taken into
account in proton Compton scattering
Previously p is treated as spin 1/2 Dirac spinor and ∆+ in a
different theory
Our innovation:
We treat p and ∆+ in a unified spin 3/2 field theory
How Motivated
Proton and ∆+ are both comprised of the same quarks.
Three spin 1/2 particles results in 8 spin states, that for a spin
3/2 particle and two spin 1/2 particles.
Outline
Background and Motivation
The Model
Proton Compton Scattering
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
Vertex Structure
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
L invariant under point
transformation:
ψ µ → ψ µ + λγ µ γν ψ ν
ξ 0 = ξ(1 − 4λ) − 2λ
Vertex Structure
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
L invariant under point
transformation:
ψ µ → ψ µ + λγ µ γν ψ ν
ξ 0 = ξ(1 − 4λ) − 2λ
ξ = 2z − 1 =⇒
pµ ψ µ (p) = 0.
Vertex Structure
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
L invariant under point
transformation:
ψ µ → ψ µ + λγ µ γν ψ ν
ξ 0 = ξ(1 − 4λ) − 2λ
ξ = 2z − 1 =⇒
pµ ψ µ (p) = 0.
mass spectrum:
m3/2 = m,m1/2 =
m
6z−2 .
Vertex Structure
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
L invariant under point
transformation:
ψ µ → ψ µ + λγ µ γν ψ ν
ξ 0 = ξ(1 − 4λ) − 2λ
ξ = 2z − 1 =⇒
pµ ψ µ (p) = 0.
mass spectrum:
m3/2 = m,m1/2 =
m
6z−2 .
Original Rarita-Schwinger Theory:
z=
(1+3ξ)2 +3(1+ξ)2
.
4
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
L invariant under point
transformation:
ψ µ → ψ µ + λγ µ γν ψ ν
ξ 0 = ξ(1 − 4λ) − 2λ
ξ = 2z − 1 =⇒
pµ ψ µ (p) = 0.
mass spectrum:
m3/2 = m,m1/2 =
m
6z−2 .
Original Rarita-Schwinger Theory:
z=
(1+3ξ)2 +3(1+ξ)2
.
4
no spin 1/2 on shell
component.
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Generalized Rarita-Schwinger Theory
The Lagrangian
Konstantin G. Savvidy, arXiv:1005.3455:
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
2
Θµ ν = δ µ ν − zγ ν γν ,ζ = 3ξ +2ξ+1
2
L invariant under point
transformation:
ψ µ → ψ µ + λγ µ γν ψ ν
ξ 0 = ξ(1 − 4λ) − 2λ
ξ = 2z − 1 =⇒
pµ ψ µ (p) = 0.
mass spectrum:
m3/2 = m,m1/2 =
Original Rarita-Schwinger Theory:
z=
(1+3ξ)2 +3(1+ξ)2
.
4
no spin 1/2 on shell
component.
superluminal propagation
m
6z−2 .
Outline
Background and Motivation
The Model
Proton Compton Scattering
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
Θµ ν = δ µ ν − zγ ν γν
Vertex Structure
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
Θµ ν = δ µ ν − zγ ν γν
Spin 1/2 component wave function:
u2 (0, + 21 ) =
1
1
1
i
i
1
1
T
√
√
√
√
√
√
3z−1 (0, 0, 0, 0, 0, 2 3 , 0, − 2 3 , 0, 2 3 , 0, − 2 3 , 2 3 , 0, − 2 3 , 0)
u2 (0, − 12 ) =
1
1
1
i
i
1
1 T
√
√
√
√
√
√
3z−1 (0, 0, 0, 0, 2 3 , 0, − 2 3 , 0, − 2 3 , 0, 2 3 , 0, 0, − 2 3 , 0, 2 3 )
u2µ α (k , σ) = Lµ ναβ (k , M)u2ν β (0, σ)
Lµ ν αβ = LV µ ν ⊗ LSαβ
LV , LS: boost matrix for vector and dirac spinor fields respectively.
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
Θµ ν = δ µ ν − zγ ν γν




LV = 



LS = √
E
M
k1
M
k1
M
k2
E
1 + (M
− 1) ~12
k2
M
E
(M
k3
M
E
(M
1
2M(E+M)
−
−
|k |
k2 k1
1) ~ 2
|k |
k3 k1
1) ~ 2
|k |
E
(M
− 1) k~1 k22
|k |
1+
E
(M
E
(M
−

k3
M
k2
M
k2
− 1) ~22
|k |
k3 k2
1) ~ 2
|k |

E
(M
− 1) k~1 k23 
|k | 

k2 k3 
E
( M − 1) ~ 2 
|k |

k2
E
( M − 1) ~32
E + M − ~k · ~σ
0
0
E + M + ~k · ~σ
|k |
!
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
Θµ ν = δ µ ν − zγ ν γν
Electrodynamic Interaction
pµ → pµ − Aµ ⇒ LI = Aµ J µ = eψ̄ν Γµν ρ ψ ρ Aµ , pµ J µ = 0
Γµν ρ = γ µ δ ν ρ + ξ(γ ν δ µ ρ + γρ η νµ ) + ζγ ν γ µ γρ
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,
D µ ν = γ ρ pρ δ µ ν + ξ(γ µ pν + γν pµ ) + ζγ µ γ ρ pρ γν ,
Θµ ν = δ µ ν − zγ ν γν
Electrodynamic Interaction
pµ → pµ − Aµ ⇒ LI = Aµ J µ = eψ̄ν Γµν ρ ψ ρ Aµ , pµ J µ = 0
Γµν ρ = γ µ δ ν ρ + ξ(γ ν δ µ ρ + γρ η νµ ) + ζγ ν γ µ γρ
Comparison
V. Pascalutsa and O. Scholten, Nucl. Phys. A591, 658 (1995)
α
νµ + h.c.
1
L1I = iG
2m ψ̄ Θαµ (zf )γν γ5 T3 NF
−G
L2I = (2m)22 ψ̄ α Θαµ (zf )γ5 T3 ∂µ NF νµ + h.c.
L3I =
−G3 α
ψ̄ Θαµ (zf )γ5 T3 N∂ν F νµ
(2m)2
+ h.c.
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
In L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,we identify spin 3/2 component as
∆+ and spin 1/2 component as proton.
Proton Compton Scattering Feynman Diagrams
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
In L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,we identify spin 3/2 component as
∆+ and spin 1/2 component as proton.
Feynman Rules
Out line: u2 (k1 ), ū2 (k4 )
Vertex: Γµν ρ = γ µ δ ν ρ + ξ(γ ν δ µ ρ + γρ η νµ ) + ζγ ν γ µ γρ
Propogator: [D µ ν − mΘµ ν ]−1
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
In L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,we identify spin 3/2 component as
∆+ and spin 1/2 component as proton.
Feynman Rules
Out line: u2 (k1 ), ū2 (k4 )
Vertex: Γµν ρ = γ µ δ ν ρ + ξ(γ ν δ µ ρ + γρ η νµ ) + ζγ ν γ µ γρ
Propogator: [D µ ν − mΘµ ν ]−1
Two poles in propogator:
p2 = m2 : ∆+ pole
p2 = M 2 : proton pole(M =
m
6z−2 )
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
In L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,we identify spin 3/2 component as
∆+ and spin 1/2 component as proton.
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
In L = ψ̄µ [D µ ν − mΘµ ν ]ψ ν ,we identify spin 3/2 component as
∆+ and spin 1/2 component as proton.
Amplitude and Differential Cross Section
Mσ1 ,σ4 ,λ2 ,λ3 =
ie2 (ū2η (k4 , σ4 )Γµη ρ S ρ γ (k1 − k3 )Γνγ κ u2 κ (k1 , σ1 )
+ū2η (k4 , σ4 )Γνη ρ S ρ γ (k1 + k2 )Γµγ κ u2 κ (k1 , σ1 ))
dσ
=
dΩ
µ (k2 , λ2 )∗ν (k3 , λ3 )
1 ω0 2 X
( )
|M|2
64π 2 ω
σ1 ,σ4 ,λ2 ,λ3
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Low energy expansion agrees with F.E.Low,PR96,1428(1954):
dσ = α2 (1+cos2 θ) − α2 (1−cos θ)(1+cos2 θ) ω + O(ω 2 )
2M 2
M3
dΩ
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Low energy expansion agrees with F.E.Low,PR96,1428(1954):
dσ = α2 (1+cos2 θ) − α2 (1−cos θ)(1+cos2 θ) ω + O(ω 2 )
2M 2
M3
dΩ
Difference at O(ω 2 ) from Dirac theory affects the extraction of
polarizability parameters(ᾱ,β̄) from experiment(δ ᾱ,δ β̄ = O(1))
dσ = ( dσ ) − αω2 ( ᾱ+β̄ (1 + cos θ)2 + ᾱ−β̄ (1 − cos θ)2 )
M
2
2
dΩ
dΩ Born
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Low energy expansion agrees with F.E.Low,PR96,1428(1954):
dσ = α2 (1+cos2 θ) − α2 (1−cos θ)(1+cos2 θ) ω + O(ω 2 )
2M 2
M3
dΩ
Difference at O(ω 2 ) from Dirac theory affects the extraction of
polarizability parameters(ᾱ,β̄) from experiment(δ ᾱ,δ β̄ = O(1))
dσ = ( dσ ) − αω2 ( ᾱ+β̄ (1 + cos θ)2 + ᾱ−β̄ (1 − cos θ)2 )
M
2
2
dΩ
dΩ Born
8. ´ 10-11
6. ´ 10-11
θ=0
4. ´ 10-11
Blue: current theory
2. ´ 10-11
Red: Dirac theory
50
100
150
200
250
Ω
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Low energy expansion agrees with F.E.Low,PR96,1428(1954):
dσ = α2 (1+cos2 θ) − α2 (1−cos θ)(1+cos2 θ) ω + O(ω 2 )
2M 2
M3
dΩ
Difference at O(ω 2 ) from Dirac theory affects the extraction of
polarizability parameters(ᾱ,β̄) from experiment(δ ᾱ,δ β̄ = O(1))
dσ = ( dσ ) − αω2 ( ᾱ+β̄ (1 + cos θ)2 + ᾱ−β̄ (1 − cos θ)2 )
M
2
2
dΩ
dΩ Born
3.5 ´ 10-11
3. ´ 10-11
2.5 ´ 10-11
θ=
2. ´ 10-11
π
2
Blue: current theory
1.5 ´ 10-11
1. ´ 10-11
Red: Dirac theory
5. ´ 10-12
50
100
150
200
250
Ω
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Low energy expansion agrees with F.E.Low,PR96,1428(1954):
dσ = α2 (1+cos2 θ) − α2 (1−cos θ)(1+cos2 θ) ω + O(ω 2 )
2M 2
M3
dΩ
Difference at O(ω 2 ) from Dirac theory affects the extraction of
polarizability parameters(ᾱ,β̄) from experiment(δ ᾱ,δ β̄ = O(1))
dσ = ( dσ ) − αω2 ( ᾱ+β̄ (1 + cos θ)2 + ᾱ−β̄ (1 − cos θ)2 )
M
2
2
dΩ
dΩ Born
6. ´ 10-11
5. ´ 10-11
4. ´ 10-11
θ=π
3. ´ 10-11
Blue: current theory
2. ´ 10-11
Red: Dirac theory
1. ´ 10-11
50
100
150
200
250
Ω
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Low energy expansion agrees with F.E.Low,PR96,1428(1954):
dσ = α2 (1+cos2 θ) − α2 (1−cos θ)(1+cos2 θ) ω + O(ω 2 )
2M 2
M3
dΩ
Difference at O(ω 2 ) from Dirac theory affects the extraction of
polarizability parameters(ᾱ,β̄) from experiment(δ ᾱ,δ β̄ = O(1))
dσ = ( dσ ) − αω2 ( ᾱ+β̄ (1 + cos θ)2 + ᾱ−β̄ (1 − cos θ)2 )
M
2
2
dΩ
dΩ Born
6. ´ 10-11
5. ´ 10-11
We are not ready to fit
experimental data yet,
since proton is not a
fundamental particle.
4. ´ 10-11
-11
3. ´ 10
2. ´ 10-11
1. ´ 10-11
50
100
150
200
250
Ω
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Vertex Structure
Reminiscence
Dirac spinor electrodynamic interaction:
0 )µ
iσ µν qν
2
2
ū(p0 )[ (p+p
2m F1 (q ) + 2m F2 (q )]u(p)Aµ
F1 , F2 : form factors.
q = p0 − p
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Reminiscence
Dirac spinor electrodynamic interaction:
0 )µ
iσ µν qν
2
2
ū(p0 )[ (p+p
2m F1 (q ) + 2m F2 (q )]u(p)Aµ
F1 , F2 : form factors.
Vertex Structure
q = p0 − p
Our Task
Find (all) possible Γµν ρ (p, p0 ) in ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p)Aµ
Gauge Invariance: qµ ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p) = 0
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Our Task
Find (all) possible Γµν ρ (p, p0 ) in ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p)Aµ
Gauge Invariance: qµ ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p) = 0
Structures We Have Found
Γµν ρ (p, p0 ) =
Scalar Type
η ν ρ (p + p0 )µ
γ ν γρ (p + p0 )µ
× η ν ρ γ 5 (p + p0 )µ
× γ ν γρ γ 5 (p + p0 )µ
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Our Task
Find (all) possible Γµν ρ (p, p0 ) in ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p)Aµ
Gauge Invariance: qµ ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p) = 0
Structures We Have Found
Γµν ρ (p, p0 ) =
Vector Type
ην ργ µ
γ ν γ µ γρ
γ ν η µ ρ + γρ η µν
× γ ν η µ ρ − γρ η µν
× γ 5 (· · · )
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Our Task
Find (all) possible Γµν ρ (p, p0 ) in ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p)Aµ
Gauge Invariance: qµ ψ̄ν (p0 )Γµν ρ (p, p0 )ψ ρ (p) = 0
Structures We Have Found
Γµν ρ (p, p0 ) =
Tensor Type
τ µλν ρ qλ
σ µλ η ν ρ qλ
σ µλ σ ν ρ qλ
τ µλν κ σ κ ρ qλ
τ µλκ ρ σ ν κ qλ
× γ 5 (· · · )
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Structures We Have Found
Scalar Type:
Vector Type:
η ν ρ (p + p0 )µ
ην ργ µ
ν
0
µ
γ γρ (p + p )
γ ν γ µ γρ
γ ν η µ ρ + γρ η µν
Vertex Structure
Summary
Tensor Type:
τ µλν ρ qλ
σ µλ η ν ρ qλ
σ µλ σ ν ρ qλ
τ µλν κ σ κ ρ qλ
τ µλκ ρ σ ν κ qλ
Our Claim
The scalar, vector and tensor type vertexes we have found
comprise the most general set of vertexes that are at most first
order in q, and dominate the low energy Compton scattering
amplitude.
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Proton Compton scattering amplitude and cross section
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Proton Compton scattering amplitude and cross section
* Low energy limit;
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Proton Compton scattering amplitude and cross section
* Low energy limit;
* comparison with Dirac theory calculation
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Proton Compton scattering amplitude and cross section
* Low energy limit;
* comparison with Dirac theory calculation
Constructing general electrodynamic interaction vertexes
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Proton Compton scattering amplitude and cross section
* Low energy limit;
* comparison with Dirac theory calculation
Constructing general electrodynamic interaction vertexes
* Scalar, vector and tensor type vertexes;
Summary
Outline
Background and Motivation
The Model
Proton Compton Scattering
Vertex Structure
Summary
Summary
Motivation for unifying proton and ∆+ in a generalized
Rarita-Schwinger theory, and the model
* Lagrangian;
* spin 1/2 solution;
* electrodynamic interaction
Proton Compton scattering amplitude and cross section
* Low energy limit;
* comparison with Dirac theory calculation
Constructing general electrodynamic interaction vertexes
* Scalar, vector and tensor type vertexes;
* claiming that other vertexes are higher order in q
Summary
Outline
Background and Motivation
The Model
Thank you all!
Proton Compton Scattering
Vertex Structure
Summary