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Topics on QCD and Spin Physics (fifth lecture) Rodolfo Sassot - - PowerPoint PPT Presentation
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
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the spin “crisis”: SU(3)flavor x SU(2)spin is badly broken?? naive quarks/partons are not QCD quarks...
90’ s inclusive pDIS QCD pPDFs analysis 00’ s pSIDIS combined analysis 2005 pp -> h/jets global analysis
EMC 1988
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the spin “crisis”: SU(3)flavor x SU(2)spin is badly broken?? naive quarks/partons are not QCD quarks...
90’ s inclusive pDIS 00’ s pSIDIS 2005 pp -> h/jets global analysis NLO pQCD framework a polarization, GPDs, 3D, ...
EMC 1988
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starting from the very beginning:
naive quarks: SU(3)flavor x SU(2)spin QCD improved partons:
“static” rest frame “fast moving frame” quarks and gluons how much of the naive picture survives? how are they polarized? sea quark and gluons? flavor dependence? ...
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Polarized DIS (pDIS):
spin of a relativistic particle:
pµ = (m, 0, 0, 0)
rest frame
s2 = −1 s · p = 0
(E, 0, 0,
- E2 − m2)
moving frame
1 m(
- E2 − m2, 0, 0, E)
sµ
T = (0, 1, 0, 0)
(0, 1, 0, 0) sµ
L = (0, 0, 0, 1)
E >> m
m sµ
L → pµ
sµ ≡ u(p)γµγ5u(p)
P(sµ) = 1 2(1 + γ5γµsµ) (γµpµ − m)u(p) = 0
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Polarized DIS (pDIS):
DIS cross section: pDIS cross section:
|T|2 = LµνWµν
Lµν = 1 2
- λ′
u(k′, λ′)γµu(k, λ)u(k, λ)γνu(k′, λ′)
= Lµν
unpol + 2imǫµνρσqρsσ
σ←
⇒ − σ← ⇐
∼ g1(x, Q2) + 2yx2M 2 Q2 g2(x, Q2) σ←
⇑ − σ← ⇓
∼ M
- Q2
y 2g1(x, Q2) + g2(x, Q2)
- sσ
Sσ
lepton pol. vec. nucleon pol. vec.
g1(x, Q2) g2(x, Q2)
F1(x, Q2) F2(x, Q2)
Wµν = W unpol
µν
+ iǫµνρσ 1 M 2ν
- qρSσg1(x, Q2) +
- qρSσ − S · q
Mν pσqρ
- g2(x, Q2)
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double spin asymmetries
A1 = σ1/2 − σ3/2 σ1/2 + σ3/2 A1 = (g1 − γ2g2)/F1 A2 = γ(g1 + g2)/F1
γ2 ≡ 4x2M 2 Q2
W pol
µν = iǫµνρσ
1 M 2ν
- qρSσg1(x, Q2) +
- qρSσ − S · q
Mν pσqρ
- g2(x, Q2)
- W pol
µν =
- q,q
- Lq↑
µν ⊗ fq↑(x) + Lq↓ µν ⊗ fq↓(x)
- ∆q(x) ≡ fq↑(x) − fq↓(x)
g1(x) = 1 2
- q
e2
q(∆q(x) + ∆q(x))
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spin dependent sum rules
Γp
1
= 1 dx gp
1(x) = 1
2 1 dx 4 9(∆u + ∆u) + 1 9(∆d + ∆d) + 1 9(∆s + ∆s)
- 1
dx
- ∆u + ∆u − ∆d − ∆d
- =
F + D = 1.2573 ± 0.0028 1 dx
- ∆u + ∆u + ∆d + ∆d − 2(∆s + ∆s)
- =
3F − D = 0.579 ± 0.025
Γn
1
= 1 dx gn
1 (x) = 1
2 1 dx 4 9(∆d + ∆d) + 1 9(∆u + ∆u) + 1 9(∆s + ∆s)
- n beta decay
Γp
1 − Γn 1 = 1
6 1 dx
- ∆u + ∆u − ∆d − ∆d
- = 1
6(F + D)
Bjorken
Γp,n
1
= ± 1 12(F + D) + 5 36(3F − D) + 1 3 1 dx (∆s + ∆s)
Ellis-Jaffe
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Spin “crisis”
Γp
1(< Q2 >= 10.5 GeV2) = 0.123 ± 0.013 ± 0.019
Γp
1 |Ellis−Jaffe≃ 0.185
1 dx (∆s + ∆s) = 0
- 1
dx(∆s + ∆s) ≃ −0.1??
1 dx ∆Σ ≡ 1 dx
- ∆u + ∆u + ∆d + ∆d + ∆s + ∆s
- =
3F − D + 3 1 dx(∆s + ∆s) ≃ 0.279
not ~1!!
Γp
1 = Γp 1 quarks − 1
3 αs 2π 1 dx∆g ??
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1976 E80
x : [0.1 − 0.5] Q2 ≃ 2GeV2
1983 E130
x : [0.2 − 0.65] Q2 : [3.5 − 10]
1987 EMC
Γp
1 = 0.17 ± 0.05
Γp
1 = 0.123 ± 0.013 ± 0.019
Γn
1 = −0.08 ± 0.04 ± 0.04
1993 SMC
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0.02 0.04 0.06 0.02
HERMES (Q2 < 1 GeV2) HERMES (Q2 > 1 GeV2) E 143 E 155 (Q2-averaged by HERMES) SMC SMC (low x - low Q2) COMPASS xg1
p
xg1
d
x !Q2"(GeV2)
10
- 1
1 10 10
- 4
10
- 3
10
- 2
10
- 1
- 1.5
- 1
- 0.5
- 1.5
- 1
- 0.5
g1
n from p,d:
HERMES (Q2< 1 GeV2) HERMES (Q2> 1 GeV2) E155 E143 SMC
g1
n
E154 E142 JLAB HERMES
g1
n from 3He:
g1
n
x !Q2" (GeV2)
1 10 10
- 2
10
- 1
1
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pQCD mantra
2
naive LO NLO
2
+ ...
NNLO ....
+
2
g1(x) |naive= C0
q ⊗ ∆q(x)
g1(x) |αs= C1
q ⊗ ∆q(x) + C1 g ⊗ ∆g(x)
g1(x) |LO= C0
q ⊗ ∆qLO(x, Q2)
g1(x) |α2
s= C2
q ⊗ ∆q(x) + C2 g ⊗ ∆g(x)
g1(x) |NLO= C1
q ⊗ ∆qNLO(x, Q2) + C1 g ⊗ ∆gNLO(x, Q2)
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d∆q(x, Q2) d ln Q2 = αs 2π 1
x
dy y
- ∆q(y, Q2) ∆Pqq
x y
- + ∆g(y, Q2) ∆Pqg
x y
- d∆g(x, Q2)
d ln Q2 = αs 2π 1
x
dy y
- q
∆q(y, Q2) ∆Pgq x y
- + ∆g(y, Q2) ∆Pgg
x y
- ∆q1(Q2) ≡
1 dx ∆q(x, Q2) ∆g1(Q2) ≡ 1 dx ∆g(x, Q2) d d ln Q2
- ∆Σ1
∆g1
- =
αs 2π 2
β0 2
∆Σ1 ∆g1
- + O(α2
s)
d d ln Q2 ∆qNS = αs 2π 0 ∆qNS + O(α2
s)
∆Σ1 ∆q1
NS
αs ∆g1 Q2-independent (at LO)
∆Σ1 ≡
- q
∆q1 + ∆q1 ∆q1
NS3
≡ (∆u1 + ∆u1) − (∆d1 + ∆d
1)
∆q1
NS8
≡ (∆u1 + ∆u1) + (∆d1 + ∆d
1) − 2(∆s1 + ∆s1)
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Γp,n
1 (Q2) =
- 1 − αs
π ± 1 12(F + D) + 1 36(3F − D) + 1 9∆Σ1
MS(Q2)
- + O(α2
s)
Γp,n
1 (Q2) =
- 1 − αs
π ± 1 12(F + D) + 1 36(3F − D) + 1 9∆Σ1
- ff
- − αs
6π ∆1g Γp,n
1 (Q2) =
- ± 1
12(F + D) + 1 36(3F − D) 1 − αs π − 3.5833 αs π 2 +1 9∆Σ1
MS(Q2)
- 1 − αs
π − 1.0959 αs π 2 + O(α3
s)
Γp
1(Q2) − Γn 1(Q2)
= 1 6(F + D)
- ×
- 1 − αs
π − 3.5833 αs π 2 − 20.2153 αs π 3 + O(α4
s)