Holographic Pomeron and Schwinger Mechanism G ok ce Ba sar Stony - PowerPoint PPT Presentation

Holographic Pomeron and Schwinger Mechanism G¨ ok¸ ce Ba¸ sar Stony Brook University April 30, 2012 GB, D. Kharzeev, H.U. Yee & I. Zahed arXiv:1202.0831, Phys.Rev. D 85 (2012) 105005 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Outline ◮ Motivation and basics ◮ Calculation of the scattering amplitude ◮ Schwinger string production ◮ Conclusions G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Motivation p 1 2 2 s=(p +p ) -t=-(p -p ) 1 2 1 3 p 2 ◮ Understand near forward, high energy ( s >> − t ) hadronic scattering amplitudes G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Motivation p 1 2 2 s=(p +p ) -t=-(p -p ) 1 2 1 3 p 2 ◮ Understand near forward, high energy ( s >> − t ) hadronic scattering amplitudes ◮ Small momentum transfer → non-pertrubative G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Motivation p 1 2 2 s=(p +p ) -t=-(p -p ) 1 2 1 3 p 2 ◮ Understand near forward, high energy ( s >> − t ) hadronic scattering amplitudes ◮ Small momentum transfer → non-pertrubative ◮ Large impact parameter → confinement G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Motivation p 1 2 2 s=(p +p ) -t=-(p -p ) 1 2 1 3 p 2 ◮ Understand near forward, high energy ( s >> − t ) hadronic scattering amplitudes ◮ Small momentum transfer → non-pertrubative ◮ Large impact parameter → confinement ◮ Total cross section: σ tot ( s ) = s − 1 I m [ T ( s, t = 0)] G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Regge theory Analyticity and crossing symmetry of the S matrix T ( s, t ) ≈ β ( t ) s α ( t ) ± ( − s ) α ( t ) sin( πα ( t )) Singularities of T in the complex angular momentum plane � Exchange of families of states in t-channel (“Reggeons”) � Regge trajectory: α ( t ) G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Regge theory Analyticity and crossing symmetry of the S matrix T ( s, t ) ≈ β ( t ) s α ( t ) ± ( − s ) α ( t ) sin( πα ( t )) Singularities of T in the complex angular momentum plane � Exchange of families of states in t-channel (“Reggeons”) � Regge trajectory: α ( t ) = α (0) + α ′ t (Apel et al. 79) G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

P Pomeron σ tot ∝ s α (0) − 1 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

P Pomeron σ tot ∝ s α (0) − 1 80 70 60 50 40 ( Donnaschie et al.) 30 10 100 1000 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Pomeron σ tot ∝ s α (0) − 1 Pomeron: Regge trajectory with α P (0) ≈ 1 80 70 60 50 40 ( Donnaschie et al.) 30 10 100 1000 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Pomeron σ tot ∝ s α (0) − 1 Pomeron: Regge trajectory with α P (0) ≈ 1 80 70 ? 60 50 40 ( Donnaschie et al.) 30 10 100 1000 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Pomeron σ tot ∝ s α (0) − 1 Pomeron: Regge trajectory with α P (0) ≈ 1 ◮ (Donnachie, Landshoff), fit to experiment, α (0) ≈ 1 . 08 ◮ (Low-Nussinov), two gluon exchange, α (0) = 1 ◮ (BFKL), gluon ladder, (cylinder topology at large N c ), α (0) ≈ 1 . 3 ◮ ... 80 70 ? 60 50 40 ( Donnaschie et al.) 30 10 100 1000 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Idea Calculate dipole-dipole amplitude through gauge/string duality G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Idea Calculate dipole-dipole amplitude through gauge/string duality ◮ (Janik, Peschanski): classical string worldsheet by variation ◮ (Brower, Polchinski, Strassler, Tan) : diffusion of string in curved space G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Idea Calculate dipole-dipole amplitude through gauge/string duality ◮ (Janik, Peschanski): classical string worldsheet by variation ◮ (Brower, Polchinski, Strassler, Tan) : diffusion of string in curved space Dipole ∼ Wilson loop G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines W ( C ) = 1 � � � �� A µ ( x ) dx µ Tr P c exp ig N c C G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines W ( C ) = 1 � � � �� A µ ( x ) dx µ Tr P c exp ig N c C Static Wilson loop: T L < W > ≈ e − V ( L ) T V ( L ) : potential between 2 static charges ◮ Abelian gauge field: V ( L ) ∝ 1 /L ⇒ “Perimeter law” ◮ Confining potential: V ( L ) = σ T L ⇒ “Area law” G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) ◮ Eikonal ( e + e − ): < W > = ( b 2 µ 2 ) − i g 2 4 π G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) ◮ Eikonal ( e + e − ): < W > = ( b 2 µ 2 ) − i g 2 � q · � � d 2 q e i� b 4 π = exp ig 2 � (2 π ) 2 q 2 + µ 2 G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) ◮ Eikonal ( e + e − ): < W > = ( b 2 µ 2 ) − i g 2 � q · � � d 2 q e i� b 4 π = exp ig 2 � (2 π ) 2 q 2 + µ 2 ◮ Dipole-dipole scattering G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) ◮ Eikonal ( e + e − ): < W > = ( b 2 µ 2 ) − i g 2 � q · � � d 2 q e i� b 4 π = exp ig 2 � (2 π ) 2 q 2 + µ 2 ◮ Dipole-dipole scattering high energy hadron ∼ gluon cloud G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) ◮ Eikonal ( e + e − ): < W > = ( b 2 µ 2 ) − i g 2 � q · � � d 2 q e i� b 4 π = exp ig 2 � (2 π ) 2 q 2 + µ 2 ◮ Dipole-dipole scattering high energy hadron ∼ gluon cloud gluon ∼ color dipole at large N c G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines High energy scattering: ◮ Recoil of scatterers is negligible → follow fixed trajectories ◮ Gives rise to non-perturbative techniques 1 d 2 b e iq ⊥ · b � W − 1 � � − 2 is T ( θ, q ) ≈ (Nachtmann, ’91) ◮ Eikonal ( e + e − ): < W > = ( b 2 µ 2 ) − i g 2 � q · � � d 2 q e i� b 4 π = exp ig 2 � (2 π ) 2 q 2 + µ 2 ◮ Dipole-dipole scattering high energy hadron ∼ gluon cloud ∼ bunch of dipoles gluon ∼ color dipole at large N c G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Dipole-dipole kinematics D 1 ( p 1 ) + D 2 ( p 2 ) → D 1 ( k 1 ) + D 2 ( k 2 ) 0 T x p /m = (cos(θ/2) , −sin(θ/2), 0 ) 1 W ( θ/2 , b/2 ) W (- θ/2 , - b/2 ) T a p /m = (cos(θ/2) , sin(θ/2), 0 ) θ/2 2 T -θ/2 q= (0,0, q ) T b= (0,0, b ) -i χ θ χ ≈ log ( s/2m ) >>1 2 T x b/2 -b/2 (Meggiolaro, Giordano, Janik, Peschanski, Nowak, Shuryak, Zahed...) L x a (Nachtmann, ‘91) 1 � d 2 b e iq ⊥ · b � ( W ( θ/ 2 , b/ 2) W ( − θ/ 2 , − b/ 2) − 1 ) � − 2 is T ( θ, q ) ≈ G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines in holography < WW > = Z string [ ∂ B = C ] (Maldacena, ’98) Deconfined Geometry C W( C ) UV boundary z G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism

Wilson lines in holography < WW > = Z string [ ∂ B = C ] ≈ e − S cl (Maldacena, ’98) Deconfined Geometry C W( C ) UV boundary z G¨ ok¸ ce Ba¸ sar Holographic Pomeron and Schwinger Mechanism