+ production in (anti)proton-proton Data collection Kinematics - PowerPoint PPT Presentation

Wang Ying Motivation π + π − production in (anti)proton-proton Data collection Kinematics collisions in the kinematical domain relevant Crossing symmetry for PANDA Conclusion Wang Ying Univ Paris-Sud, CNRS/IN2P3, Institut de Physique Nucléaire, Orsay, France 8 décembre 2014

Motivation Wang Ying Motivation Data collection pp → e + e − allows to measure ◮ The reaction ¯ Kinematics Crossing symmetry electromagnetic proton form factors. Conclusion ◮ Important simulation work is under way. pp → π + π − is the main background : ◮ The reaction ¯ ◮ has a large cross section, ◮ contains information on the quark content of the proton ◮ allow to test different QCD models pp → π + π − at It is necessary to fully understand the process ¯ PANDA energies.

Situation of data Wang Ying Motivation pp → π + π − experimental data ¯ Data collection ◮ Total cross section. Kinematics Crossing symmetry ◮ Data from : Conclusion ◦ NPB 411 :3(1994) NPB 172 :302(1980) NPB 517 :3(1998) NPB 51 :29(1973) PRD 4 :2658(1971) ⋆ PLB 25 :486(1967) NPB 284 :643(1987) solid line Generator dash line A Dbeyssi, PhD, Orsay (2013)

Differential cross section : Low energy range Wang Ying (0.79-2.43GeV/c NPB 96 :09(1975) & 2.5-3.0GeV/c) Motivation Data collection Kinematics Crossing symmetry Conclusion ◮ Complete data sets ◮ Oscillatory behavior ◮ Fit by Legendre polynomes

Differential cross section : higher energy range Wang Ying Motivation 3 10 Data collection Data from : Kinematics P Lab = 1.7GeV/c, 2 10 Crossing symmetry NPB 96 :109(1975) Conclusion 10 P Lab = 5GeV/c, b] µ NPB 60 :173(1973) [ θ /dcos 1 P Lab = 6.21GeV/c, σ NPB 116 :51(1976) d -1 10 Generator P Lab = 3GeV/c Generator P Lab = 10GeV/c -2 10 -3 10 -0.5 0 0.5 θ cos ◮ Incomplete angular distributions ◮ Mostly forward/backward data ◮ Some measurements at cos θ = 0

pp → π + π − in Modelization of the reaction ¯ Wang Ying Panda Root Motivation Data collection Kinematics Generators : Crossing symmetry ◮ Dual Parton Model(generic annihilation background in Conclusion pp annihilation) ¯ ◮ Phase Space Model(flat distribution in cos θ ) ◮ EvtGen (generate benchmark reactions by user) : twoPionGen ( M. Zambrana et al. ) ◮ Legendre polynomials (low energy region : 0 . 79 ≤ p ¯ p < 2.43 GeV) ; ◮ Interpolation (intermediate energy region : 2.43 GeV ≤ p ¯ p < 5 GeV) ◮ Regge theory (high energy region : 5 GeV ≤ p ¯ p < 12 GeV)

p + p → π − + π + My study of the reaction ¯ Wang Ying ◮ Kinematics : Motivation Data collection p ( p 1 ) + p ( p 2 ) → π − ( k 1 ) + π + ( k 2 ) ¯ Kinematics Crossing In CM System symmetry In Lab System Conclusion π - (k ) 1 π - (k ) 1 p (p ) p (p ) θ p (p ) p (p ) θ 1 2 2 1 π + π (k ) + (k ) 2 2 particle Momentum Lab CMS ¯ p p 1 ( E ℓ ,� p ℓ ) ( E 1 ,� p 1 ) p p 2 ( M p , 0 ) ( E 2 ,� p 2 ) ( ǫ 1 ,� 1 , � π − k ℓ ( ε ′ k 1 1 ) k 1 ) ( ǫ 2 ,� 2 , � π + k ℓ ( ε ′ k 2 2 ) k 2 ) Table 1. Notation of four-momenta in different reference frames.

Wang Ying ◮ The (s-, t- , u-) Mandelstam variables : Motivation s = ( p 1 + p 2 ) 2 = ( k 1 + k 2 ) 2 Data collection t = ( p 1 − k 1 ) 2 = ( k 2 − p 2 ) 2 Kinematics Crossing u = ( p 1 − k 2 ) 2 = ( k 1 − p 2 ) 2 symmetry Conclusion ◮ Finally, we get the relation between t and s, and cos θ In CM system : M 2 p + m 2 π − 2 E 2 t = 1 ( 1 − β p β π cos θ ) � 1 − 4 M 2 p = β p s � 1 − 4 m 2 π β π = s 4 E 2 s = 1

Dependence of t on cos θ Wang Ying Motivation In PANDA, p Lab > 1.5 GeV, s > 5.08 GeV 2 Data collection Kinematics ◮ The range of cos θ : -1 < cos θ < 1 Crossing symmetry ◮ Different values of s : s = 5, 10, 20, 30 GeV 2 Conclusion ] 0 2 t [GeV -10 -20 -30 -1 -0.5 0 0.5 1 θ cos

Dependence of t on s Wang Ying Motivation ◮ The range of s : 5 - 30 GeV 2 Data collection ◮ Different values of cos θ : cos θ = -1, -0.5, 0, 0.5, 1 Kinematics Crossing symmetry Conclusion ] 2 0 t [GeV -10 -20 -30 5 10 15 20 25 30 2 s [GeV ]

Relation between CM system and Lab system Wang Ying Motivation ◮ The Mandelstam variables s , t , u and the scalars (i.e., Data collection the masses of particles) are kinematical invariants, Kinematics ◮ So the relations between two systems of cos θ : Crossing symmetry Conclusion ǫ ± is the energy of π − in lab system(E) : � MW 2 ± ℓ cos 2 θ ℓ ℓ cos 2 θ ℓ p 2 � W 2 ( M 2 p − m 2 π ) + m 2 π p 2 � ǫ ± 1 = ( W 2 − p 2 ℓ cos 2 θ ℓ ) W = E ℓ + M p π cos 2 θ Lab ) cos θ CMS = E 2 1 − E ℓ ǫ ± ( 1 − β ℓ p β ℓ E 2 1 β p β π

Relation between CM system and Lab system Wang Ying Motivation Data collection plots of ǫ ± 1 and cos θ Kinematics Crossing symmetry 3 1 Conclusion [GeV] CMS θ cos 2.5 1 ∈ 0.5 2 1.5 0 1 -0.5 0.5 0 -1 0 50 100 150 -1 -0.5 0 0.5 1 θ θ [deg] cos Lab 1

Crossing symmetry : from annihilation ( σ a ) to Wang Ying elastic scattering ( σ s ) Motivation Data collection p ( p 1 ) + p ( p 2 ) → π − ( k 1 ) + π + ( k 2 ) ¯ Kinematics Crossing Crossed reactions : elastic π ± p → π ± p scattering : symmetry Conclusion 1 . π − ( − k 2 ) + p ( p 2 ) → π − ( k 1 ) + p ( − p 1 ) , p 1 → − k 2 2 . π + ( − k 1 ) + p ( p 2 ) → p ( − p 1 ) + π + ( k 2 ) , p 1 → − k 1 1. s s = ( − k 2 + p 2 ) 2 → t a t s = ( − k 2 − k 1 ) 2 → s a u s = ( − k 2 + p 1 ) 2 → u a 2. s s = ( − k 1 + p 2 ) 2 → u a t s = ( − k 1 + p 1 ) 2 → t a u s = ( − k 1 − k 2 ) 2 → s a

Crossing symmetry Wang Ying s a = 4 E 2 = 4 ( M 2 + | � p a | 2 ) Motivation Data collection s s = m 2 + M 2 + 2 E ′ 2 ǫ ′ 2 + 2 | k s | 2 Kinematics Crossing |M ( a ) | 2 | � symmetry σ a = 1 k a | Conclusion 64 π 2 s 4 | � p a | |M ( s ) | 2 | � σ s = 1 k s | 64 π 2 s 2 | � p s | From equality of s a = s s , get k s k s | 2 = 1 m 4 − 2 m 2 ( M 2 + s ) + ( M 2 − s ) 2 � | � � 4 s Then the cross sections are related by : | � k s | 2 σ a = 1 | p a | 2 σ s = f σ s 2

Crossing symmetry Wang Ying Motivation Data collection | � k s | 2 σ a = 1 | p a | 2 σ s = f σ s Kinematics b] 1 2 Crossing µ symmetry /dt [ Conclusion σ when t is small, d -1 10 σ s ≃ const · s − 2 σ s ( s ) = σ s ( s 1 ) · s − 2 -2 10 s − 2 1 σ a ( s ) = f σ s ( s 1 ) · s − 2 0 0.5 1 1.5 2 2.5 3 s − 2 1 2 t [GeV] p + p → π − + π + (red empty circles) at 6.2 GeV/c, Data for ¯ π − + p → π − + p (black solid circles) at 6.73 GeV/c. f = 0 . 589

conclusion and perspective Wang Ying Motivation Data collection Kinematics Crossing ◮ Finalize the collection of data, on annihilation and symmetry Conclusion scattering ◮ Calculate simple t- u- s- channel diagrams and compare with data ◮ Refine the models (Regge exchange, off-shell..) ◮ Understand the change of regime from Legendre polynomes to Regge-type angular distributions