Proton Compton Scattering In Unified Proton- + Theory ZHANG Yun - PowerPoint PPT Presentation

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 Vertex Structure Summary 1 Background and Motivation The Model 2 Proton Compton Scattering 3 Vertex Structure 4 Summary 5

Outline Background and Motivation The Model Proton Compton Scattering Vertex Structure Summary + ) freedom must be taken into ∆ + (1232MeV, J P = 3 2 account in proton Compton scattering

Outline Background and Motivation The Model Proton Compton Scattering Vertex Structure Summary + ) freedom must be taken into ∆ + (1232MeV, J P = 3 2 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 + ) freedom must be taken into ∆ + (1232MeV, J P = 3 2 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 + ) freedom must be taken into ∆ + (1232MeV, J P = 3 2 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 + ) freedom must be taken into ∆ + (1232MeV, J P = 3 2 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 + ) freedom must be taken into ∆ + (1232MeV, J P = 3 2 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 Vertex Structure Summary Generalized Rarita-Schwinger Theory The Lagrangian Konstantin G. Savvidy, arXiv:1005.3455: L = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2

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 = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2 L invariant under point transformation: ψ µ → ψ µ + λγ µ γ ν ψ ν ξ ′ = ξ ( 1 − 4 λ ) − 2 λ

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 = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2 L invariant under point transformation: ψ µ → ψ µ + λγ µ γ ν ψ ν ξ ′ = ξ ( 1 − 4 λ ) − 2 λ ξ = 2 z − 1 = ⇒ p µ ψ µ ( p ) = 0.

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 = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2 L invariant under point transformation: ψ µ → ψ µ + λγ µ γ ν ψ ν ξ ′ = ξ ( 1 − 4 λ ) − 2 λ ξ = 2 z − 1 = ⇒ p µ ψ µ ( p ) = 0. mass spectrum: m m 3 / 2 = m , m 1 / 2 = 6 z − 2 .

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 = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2 L invariant under point Original Rarita-Schwinger Theory: transformation: z = ( 1 + 3 ξ ) 2 + 3 ( 1 + ξ ) 2 . ψ µ → ψ µ + λγ µ γ ν ψ ν 4 ξ ′ = ξ ( 1 − 4 λ ) − 2 λ ξ = 2 z − 1 = ⇒ p µ ψ µ ( p ) = 0. mass spectrum: m m 3 / 2 = m , m 1 / 2 = 6 z − 2 .

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 = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2 L invariant under point Original Rarita-Schwinger Theory: transformation: z = ( 1 + 3 ξ ) 2 + 3 ( 1 + ξ ) 2 . ψ µ → ψ µ + λγ µ γ ν ψ ν 4 no spin 1/2 on shell ξ ′ = ξ ( 1 − 4 λ ) − 2 λ component. ξ = 2 z − 1 = ⇒ p µ ψ µ ( p ) = 0. mass spectrum: m m 3 / 2 = m , m 1 / 2 = 6 z − 2 .

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 = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν , ζ = 3 ξ 2 + 2 ξ + 1 2 L invariant under point Original Rarita-Schwinger Theory: transformation: z = ( 1 + 3 ξ ) 2 + 3 ( 1 + ξ ) 2 . ψ µ → ψ µ + λγ µ γ ν ψ ν 4 no spin 1/2 on shell ξ ′ = ξ ( 1 − 4 λ ) − 2 λ component. ξ = 2 z − 1 = ⇒ superluminal propagation p µ ψ µ ( p ) = 0. mass spectrum: m m 3 / 2 = m , m 1 / 2 = 6 z − 2 .

Outline Background and Motivation The Model Proton Compton Scattering Vertex Structure Summary L = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν

Outline Background and Motivation The Model Proton Compton Scattering Vertex Structure Summary L = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν Spin 1/2 component wave function: u 2 ( 0 , + 1 2 ) = 1 1 1 i i 1 1 3 , 0 ) T 3 z − 1 ( 0 , 0 , 0 , 0 , 0 , 3 , 0 , − 3 , 0 , 3 , 0 , − 3 , 3 , 0 , − √ √ √ √ √ √ 2 2 2 2 2 2 u 2 ( 0 , − 1 2 ) = 1 1 1 i i 1 1 3 ) T 3 z − 1 ( 0 , 0 , 0 , 0 , 3 , 0 , − 3 , 0 , − 3 , 0 , 0 , − 3 , 0 , 3 , 0 , √ √ √ √ √ √ 2 2 2 2 2 2 u µ 2 α ( k , σ ) = L µναβ ( k , M ) u ν 2 β ( 0 , σ ) L µναβ = LV µν ⊗ LS αβ LV , LS : boost matrix for vector and dirac spinor fields respectively.

Outline Background and Motivation The Model Proton Compton Scattering Vertex Structure Summary L = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν  k 1 k 2 k 3  E M M M M M − 1 ) k 2 k 1 1 + ( E ( E M − 1 ) k 1 k 2 ( E M − 1 ) k 1 k 3   1  M | � | � | �  k | 2 k | 2 k | 2   LV = M − 1 ) k 2  k 2 M − 1 ) k 2 k 1 M − 1 ) k 2 k 3  ( E 1 + ( E ( E 2   | � | � | � M k | 2 k | 2 k | 2   k 2   k 3 M − 1 ) k 3 k 1 M − 1 ) k 3 k 2 ( E ( E ( E M − 1 ) 3 M | � | � | � k | 2 k | 2 k | 2 � � E + M − � k · � σ 0 1 √ LS = E + M + � 2 M ( E + M ) 0 k · � σ

Outline Background and Motivation The Model Proton Compton Scattering Vertex Structure Summary L = ¯ ψ µ [ D µν − m Θ µν ] ψ ν , D µν = γ ρ p ρ δ µν + ξ ( γ µ p ν + γ ν p µ ) + ζγ µ γ ρ p ρ γ ν , Θ µν = δ µν − z γ ν γ ν Electrodynamic Interaction p µ → p µ − A µ ⇒ L I = A µ J µ = e ¯ ψ ν Γ µνρ ψ ρ A µ , p µ J µ = 0 Γ µνρ = γ µ δ νρ + ξ ( γ ν δ µρ + γ ρ η νµ ) + ζγ ν γ µ γ ρ