Topics on QCD and Spin Physics (fifth lecture) Rodolfo Sassot - PowerPoint PPT Presentation

Topics on QCD and Spin Physics (fifth lecture) Rodolfo Sassot Universidad de Buenos Aires HUGS 2010, JLAB June 2010

the spin of the proton: still an open question... spin is a fundamental property spin is a fundamental tool spin is a permanent focus of interest

the spin “crisis”: EMC 1988 SU(3) flavor x SU(2) spin is badly broken?? naive quarks/partons are not QCD quarks... 90’ s inclusive pDIS QCD pPDFs analysis combined analysis 00’ s pSIDIS global analysis 2005 pp -> h/jets

the spin “crisis”: EMC 1988 SU(3) flavor x SU(2) spin is badly broken?? naive quarks/partons are not QCD quarks... NLO pQCD framework 90’ s inclusive pDIS a polarization, GPDs, 3D, ... 00’ s pSIDIS global analysis 2005 pp -> h/jets

starting from the very beginning: naive quarks: SU(3) flavor x SU(2) spin “static” rest frame QCD improved partons: “fast moving frame” quarks and gluons how much of the naive picture survives? how are they polarized? sea quark and gluons? flavor dependence? ...

Polarized DIS (pDIS): spin of a relativistic particle: s µ T = (0 , 1 , 0 , 0) (0 , 1 , 0 , 0) 1 s µ s 2 = − 1 L = (0 , 0 , 0 , 1) � m ( E 2 − m 2 , 0 , 0 , E ) p µ = ( m, 0 , 0 , 0) � s · p = 0 ( E, 0 , 0 , E 2 − m 2 ) rest frame moving frame m s µ L → p µ E >> m P ( s µ ) = 1 s µ ≡ u ( p ) γ µ γ 5 u ( p ) 2(1 + γ 5 γ µ s µ ) ( γ µ p µ − m ) u ( p ) = 0

Polarized DIS (pDIS): DIS cross section: F 1 ( x, Q 2 ) F 2 ( x, Q 2 ) g 1 ( x, Q 2 ) g 2 ( x, Q 2 ) pDIS cross section: | T | 2 = L µ ν W µ ν L µ ν = 1 lepton pol. vec. s σ � u ( k ′ , λ ′ ) γ µ u ( k, λ ) u ( k, λ ) γ ν u ( k ′ , λ ′ ) 2 S σ nucleon pol. vec. λ ′ = L µ ν unpol + 2 im ǫ µ νρσ q ρ s σ � � � � 1 q ρ S σ − S · q W µ ν = W unpol q ρ S σ g 1 ( x, Q 2 ) + g 2 ( x, Q 2 ) + i ǫ µ νρσ M ν p σ q ρ µ ν M 2 ν g 1 ( x, Q 2 ) + 2 yx 2 M 2 σ ← ⇒ − σ ← g 2 ( x, Q 2 ) ∼ ⇐ Q 2 M � y � σ ← ⇑ − σ ← 2 g 1 ( x, Q 2 ) + g 2 ( x, Q 2 ) ∼ ⇓ � Q 2

double spin asymmetries γ 2 ≡ 4 x 2 M 2 A 1 = ( g 1 − γ 2 g 2 ) /F 1 A 1 = σ 1 / 2 − σ 3 / 2 Q 2 σ 1 / 2 + σ 3 / 2 A 2 = γ ( g 1 + g 2 ) /F 1 g 1 ( x ) = 1 � e 2 q ( ∆ q ( x ) + ∆ q ( x )) ∆ q ( x ) ≡ f q ↑ ( x ) − f q ↓ ( x ) 2 q � W pol L q ↑ µ ν ⊗ f q ↑ ( x ) + L q ↓ � � µ ν = µ ν ⊗ f q ↓ ( x ) q,q � � � � 1 q ρ S σ − S · q W pol q ρ S σ g 1 ( x, Q 2 ) + g 2 ( x, Q 2 ) µ ν = i ǫ µ νρσ M ν p σ q ρ M 2 ν

spin dependent sum rules � 1 � 1 � 4 � 1 ( x ) = 1 9( ∆ u + ∆ u ) + 1 9( ∆ d + ∆ d ) + 1 Γ p dx g p = 9( ∆ s + ∆ s ) dx 1 2 0 0 � 1 � 1 � 4 � 1 ( x ) = 1 9( ∆ d + ∆ d ) + 1 9( ∆ u + ∆ u ) + 1 = 9( ∆ s + ∆ s ) Γ n dx g n dx 1 2 0 0 � 1 n beta decay � � ∆ u + ∆ u − ∆ d − ∆ d = F + D = 1 . 2573 ± 0 . 0028 dx 0 � 1 � � ∆ u + ∆ u + ∆ d + ∆ d − 2( ∆ s + ∆ s ) = 3 F − D = 0 . 579 ± 0 . 025 dx 0 � 1 1 = 1 = 1 Bjorken � � Γ p ∆ u + ∆ u − ∆ d − ∆ d 6( F + D ) 1 − Γ n dx 6 0 � 1 = ± 1 12( F + D ) + 5 36(3 F − D ) + 1 Ellis-Jaffe Γ p,n dx ( ∆ s + ∆ s ) 1 3 0

Spin “crisis” 1 ( < Q 2 > = 10 . 5 GeV 2 ) = 0 . 123 ± 0 . 013 ± 0 . 019 Γ p �� 1 � Γ p 1 | Ellis − Jaffe ≃ 0 . 185 dx ( ∆ s + ∆ s ) = 0 0 � 1 dx ( ∆ s + ∆ s ) ≃ − 0 . 1 ?? 0 � 1 � 1 � � ∆ u + ∆ u + ∆ d + ∆ d + ∆ s + ∆ s dx ∆Σ dx ≡ 0 0 � 1 not ~ 1!! = 3 F − D + 3 dx ( ∆ s + ∆ s ) ≃ 0 . 279 0 � 1 1 quarks − 1 dx ∆ g ?? α s Γ p 1 = Γ p 3 2 π 0

1976 E80 1987 EMC x : [0 . 1 − 0 . 5] Q 2 ≃ 2GeV 2 Γ p 1 = 0 . 123 ± 0 . 013 ± 0 . 019 1983 E130 x : [0 . 2 − 0 . 65] Γ n 1 = − 0 . 08 ± 0 . 04 ± 0 . 04 Q 2 : [3 . 5 − 10] Γ p 1 = 0 . 17 ± 0 . 05 1993 SMC

n g 1 p xg 1 HERMES (Q 2 < 1 GeV 2 ) 0.06 0 HERMES (Q 2 > 1 GeV 2 ) E 143 E 155 (Q 2 -averaged by HERMES) -0.5 0.04 SMC SMC (low x - low Q 2 ) n from p,d: g 1 -1 HERMES (Q 2 < 1 GeV 2 ) COMPASS 0.02 HERMES (Q 2 > 1 GeV 2 ) E155 -1.5 E143 0 SMC d xg 1 n g 1 0 0.02 -0.5 n from 3 He: g 1 0 -1 HERMES JLAB -1.5 ! Q 2 " (GeV 2 ) E142 E154 10 ! Q 2 " (GeV 2 ) 1 -1 10 10 -4 -3 -2 -1 10 10 10 10 x 1 -2 -1 10 10 1 x

pQCD mantra 2 g 1 ( x ) | naive = C 0 q ⊗ ∆ q ( x ) naive 2 g 1 ( x ) | α s = C 1 q ⊗ ∆ q ( x ) + C 1 g ⊗ ∆ g ( x ) LO g 1 ( x ) | LO = C 0 q ⊗ ∆ q LO ( x, Q 2 ) + 2 s = C 2 q ⊗ ∆ q ( x ) + C 2 g 1 ( x ) | α 2 g ⊗ ∆ g ( x ) NLO + ... q ⊗ ∆ q NLO ( x, Q 2 ) + C 1 g ⊗ ∆ g NLO ( x, Q 2 ) g 1 ( x ) | NLO = C 1 NNLO ....

� 1 d ∆ q ( x, Q 2 ) � � x � � x �� dy α s ∆ q ( y, Q 2 ) ∆ P qq + ∆ g ( y, Q 2 ) ∆ P qg = d ln Q 2 2 π y y y x � 1 �� �� d ∆ g ( x, Q 2 ) � x � � x dy α s ∆ q ( y, Q 2 ) ∆ P gq + ∆ g ( y, Q 2 ) ∆ P gg = d ln Q 2 2 π y y y x q � 1 ∆ q 1 + ∆ q 1 � ∆Σ 1 ∆ q 1 ( Q 2 ) ≡ dx ∆ q ( x, Q 2 ) ≡ q 0 � 1 ( ∆ u 1 + ∆ u 1 ) − ( ∆ d 1 + ∆ d 1 ) ∆ q 1 ≡ NS 3 ∆ g 1 ( Q 2 ) ≡ dx ∆ g ( x, Q 2 ) ( ∆ u 1 + ∆ u 1 ) + ( ∆ d 1 + ∆ d 1 ) − 2( ∆ s 1 + ∆ s 1 ) ∆ q 1 ≡ 0 NS 8 � 0 � ∆Σ 1 � � � ∆Σ 1 � 0 d α s + O ( α 2 = s ) β 0 ∆ g 1 ∆ g 1 2 d ln Q 2 2 π 2 d α s 2 π 0 ∆ q NS + O ( α 2 = s ) d ln Q 2 ∆ q NS Q 2 -independent (at LO) ∆ q 1 α s ∆ g 1 ∆Σ 1 NS

Ellis-Jaffe SR NLO � � � ± 1 12( F + D ) + 1 36(3 F − D ) + 1 � 1 − α s Γ p,n 1 ( Q 2 ) = 9 ∆Σ 1 MS ( Q 2 ) + O ( α 2 s ) π � � � ± 1 12( F + D ) + 1 36(3 F − D ) + 1 � 1 − α s − α s Γ p,n 1 ( Q 2 ) = 9 ∆Σ 1 6 π ∆ 1 g off π Ellis-Jaffe SR NNLO � � � � 2 � ± 1 12( F + D ) + 1 � α s 1 − α s Γ p,n 1 ( Q 2 ) = 36(3 F − D ) π − 3 . 5833 π +1 � � 2 � � α s 1 − α s 9 ∆Σ 1 MS ( Q 2 ) O ( α 3 π − 1 . 0959 + s ) π Bjorken SR N 3 LO � 1 � 1 ( Q 2 ) − Γ n 1 ( Q 2 ) Γ p = 6( F + D ) × � � 3 � � 2 � α s � α s 1 − α s + O ( α 4 π − 3 . 5833 − 20 . 2153 s ) π π 0.01 0.06 0.004