spin physics (experimental)
TRANSCRIPT
SPIN, Strangeness and QGP.Raimondo Bertini *.
*Universita’ and INFN-Torino
Spin Physics (Experimental)Spin Physics (Experimental)
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OUTLOOK
• What is SPIN• Polarised sources• Polarised beams• Polarised targets• Polarimeters• Measurement of spin observables• Future projects
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Why Spin ?
• Stern- Gerlach experiment (1921)• G.E. Uhlenbeck and S.A.Goudsmith (1925)
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Electron Spin
• The electron is not point like.– In addition to its orbital angular momentum about the nucleus,
an electron rotates like a top.– This new intrinsic electron motion was called SPIN.
– Magnetic moment problems– Ex: Yang-Hamilton Modern Atomic and Nuclear Physics
McGraw-Hill
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Magnetic Moment
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Magnetic moment of the electron
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Stern-. Gerlach ExperimentZ Physik 9 (1922) 249
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TkzDdB
TkzDdBgm
TkzDdBz
mvdzdB
mvtF
dxdz
Tkvm
zB
zBjj
zz
zz
z
333
tantantan
23
21
2
2111
2
∂∂
±⇒∂∂
−=∂∂
=
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∂=⎟
⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛=
=
−−−
μμμ
μθ
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Stern-Gerlach ExperimentZ. Physik 9 (1922) 249
Deflection
cm
TeVKeVk
KTmDmdmTz
kTdD
z
z
B
Bz
B
z
zB
12.1
105788.0;10617.8
400;2;1;10
3
2
45
2
±=
×=×=
====∂∂
∂∂
=
−− μ
μ
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Results
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Transitions
( )
1,0
0
12
1122
1111
2222
1212
±=Δ=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−=−+=′
+=′
+=′
>−=
=−=⋅−=
mandggasB
BBgmgmhh
BgmEE
BgmEE
EEEEh
BgmBBU
B
B
B
B
B
Bz
μ
μμνν
μ
μ
ν
μμμrr
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Nucleon Spin
( ) ( )
( )TeV
cme
SLcm
e
TeVcm
e
SLSLcm
e
pN
spspp
p
eB
Bselee
e
gg
gg
8
,,
4
,,
10152.32
58.5;2
105788.02
22
−
−
×==
=+=
×==
+−=+−=
h
rrh
h
rrrrh
r
r
r
r
μ
μ
μ
μμ
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Spin Rotation
( ) ( )[ ]
( )( )resonancesrinsicPkG
resonancesonimperfectikG
G
GGsmes
dtsd
z
sp
longtr BB
int
1
11
νγγ
γ
γγ
ν
+==
+=
+++×=Ω×=rrrrr
r
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Tools to preserve spin during the acceleration
• Siberian snakes• RFQ• See RHIC
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Installed and commissioned during run 4To be commissionedInstalled/commissioned in run 5
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Other Polarised beams
+
±±
+⇒Λ
=
+⇒
π
νμπ μ
p
J21
210
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Polarimeters
• Measure polarisation via an interaction spin dependent• Ex. Pp elastic scattering• Measure angular distributions of weak decays• Ex. Λ p + π- B.R. = 0.64 α = 0.64
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Λ Polarisation
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Cross-section depends on spin
• Scattering of neutrons by ortho and parahydrogen• Schwinger and Teller Phys. Rev. 52 (1937) 286• Para-H² (J=0 S=0)• Ortho-H² (J=1 S=1)• Transition para ortho ΔE = 0.023 eV
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Proton-Proton elastic scattering 1P.R.L. 85 (2000) 1819
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Analyzing power
Ex. Proton-proton elastic scattering
( ) ( )
( ) ( )ωϕθσ
ωϕθσ
ωϕθσ
ωϕθσ
dd
dd
dd
dd
PAb
N ↓+↑
↓−↑
=,,
,,1
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Proton-Proton elastic scattering 2
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Antiproton-proton total cross-sections
pp
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Antiproton-proton differential cross-sections 1
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Antiproton-proton differential cross-sections 2
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Antiproton-proton analyzing powers
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Polarised targets spin 1/2
• Gaseous polarised targets• Frozen spin polarised targets• T=0.5 K; B=2.5 T P(el)=-.9975 ; P(nucl)=0.0051
21
±==−= ±−+ mspinsoffractionnnnP
⎟⎠⎞⎜
⎝⎛=⎟
⎠⎞⎜
⎝⎛−=
+
−
s
B
s
mkT
BmgkT
Enn μexpexp
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Dynamic Polarisation
( )( ) spinsnucleldipr
rIrSISr
ggH
energiesZeemannuclearandelectronIZandSZsimplifiedHHHHH
neSI
RFSIIZSZ
...int.323
2
⎥⎦
⎤⎢⎣
⎡ ⋅⋅−⋅=
+++=
rrrrrrh
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=
=
=
f1
h1T
g1L g1T =
f1T =
h1 =
h1T =h1L =
S = kx +k TTquarkp
Pp P
f1, g1 studied for decades: h1 essentially unknown
)kx,(fkd)x(f T1T2
1 ∫=
Twist-2 PDFs
κT-dependent Parton Distributions
Distributionfunctions
Chiralityeven odd
Twist-2
ULT
f1g1
, h1,
h1⊥
h1L⊥
h1T⊥f 1T
⊥ g1T
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Transversity and Λ Polarisation
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Semi-inclusive deep inelastic scattering
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Kinematics of Λ production
( ) ( )
EPkPqy
EEmmkkEEqQ
MQxEE
MPq
ll
ν
ϑν
ν
=⋅⋅
=
′≈−−′⋅−′=−=
=′−=⋅
=
′
rr
rr
rr
rr
2sin42
2;
22222
2
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Definition of Λ polarisation axis
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The COMPASS setup
Target First Spectrometer: LASGeometrical Acceptance: θ>30 mradGap: 172 × 229 cm2
Integral field: 1 TmAnalyzed momentum: p<60 GeV/c
Second Spectrometer: SASGeometrical Acceptance: θ<30 mradGap: 200× 100 cm2
Integral field: 4.4 TmAnalyzed momentum: p>10 GeV/c
Rich1ECal1
HCal2
HCal1
ECal2
MWPC
μWall1
μWall2
μΩSDCSciFi
SDCGEMStraw
SciFiGEMMWPC
50 m
SM2
SM1
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Selection of Λ events
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Data Analysis 1
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Data Analysis 2
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Available statistics
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COMPASS Trigger
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Study of systematic effects
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Transverse Structure FunctionsFor q non collinear with hadron (→ k = xP + k⊥)
f(x) → f(x,k⊥)• f1(x,k2
⊥)g1(x,k2
⊥)h1(x,k2
⊥)
integrating on k2⊥→ f(x), Δf(x), ΔTf(x)
• g1T(x,k2⊥)
h1L(x,k2⊥)
h1T(x,k2⊥)
integrating on k2⊥→ 0
relaxing time reversal invariance
f1T⊥(x,k2
⊥) for unpolarized quark in transversally polarized hadron(Sivers function)
h1⊥(x,k2
⊥) for transversally polarized quark in unpolarized hadron
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Transverse Structure Functions (Drell-Yan)
Xμμ)pp(p −+− →πKinematics
q2PMx
1
2
1 •=
xxx 21F −=q2P
Mx2
2
2 •=
sMxxτ
2
21 ==
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Uncorrelated quark helicities access chirally-odd functions
TRANSVERSITY
Drell-Yan Asymmetries — Polarised beam and target
⇒
Ideal because:
• h1 not to be unfolded with fragmentation functions
• chirally odd functionsnot suppressed (like in DIS)
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Transverse Structure Functions (Drell-Yan)
⎟⎠⎞
⎜⎝⎛ +++
+= θcos2φsin
2νθcosφμsinθλcos1
3λ1
4π3
dΩdσ
σ1 222
Di-Lepton Rest Frame
E615 @ Fermilab
π-N → μ+μ-X @ 252 GeV/c
-0.6 < cosϑ < 0.64 < M < 8.5 GeV/c2
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Transverse Structure Functions (Drell-Yan)
Initial state interactions – non zero )κ(xh 2,1 ⊥
⊥
⎟⎠⎞
⎜⎝⎛ +++
+= θcos2φsin
2νθcosφμsinθλcos1
3λ1
4π3
dΩdσ
σ1 222
NLO pQCD: λ ∼ 1, μ ∼ 0, υ ∼ 0Experimental data [1]: υ ∼ 30 %
[1] J.S.Conway et al., Phys. Rev. D39(1989)92.
υ involves transverse spin effects at leading twist [2]:cos2φ contribution to angular distribution provide:
[2] D. Boer et al., Phys. Rev. D60(1999)014012, D.Boer, S.Brodsky and D.S.Hwang Phys.Rev.D67(2003)054003.
)κ,(xh )κ(xh 211
22,1 ⊥
⊥⊥
⊥ ′×
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Transverse Structure Functions (Drell-Yan)
Drell-Yan asymmetries - Polarized target, Unpolarized beam
⎟⎠⎞
⎜⎝⎛ +−+++∝ L)φθsin(φsinSρθcos2φsin
2νθcos1
dΩdσ
σ1
1S2
1T22
[ ]∑
∑ ⊥⊥ +
+
−=
a 2a
11a
12a
a 2a11
a122
a11
a11
2a
22S
1TT )(x)f(xfe)(x)h(xhx)(x)f(xfxe
QM
θcos1)φθsin(φ2sin2
SA 1
λ ∼ 1, μ ∼ 0
Unpolarised beam and polirized targetis a powerful tool to investigate кT
dependence of QDFD. Boer et al., Phys. Rev. D60(1999)014012, D. Boer et al Phys.Rev.D67,054003,2003
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Transverse Structure Functions (Drell-Yan)
30 GeV/c
15 GeV/c
40 GeV/c
τ = const: hyperbolaexF = const: diagonal
PANDA (GSI)
ASSIA (GSI)COMPASS (CERN)
Phase space
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Transverse Structure Functions (Drell-Yan)
Upgraded COMPASS spectrometer
• New polirazed target (wide acceptance)• GEM, MICROMEGA detetors small angle• MWPC, STRAW detectors large angle• vertex resolution• LARGE AREA HODOSCOPEs → Trigger• Iarocci like tubes or large area drift chambers → μId• New Powerful E-calorimery
μm 70σ ≤
mm 1.5σ ≤
cm 1 mm 2σ ÷=
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Transverse Structure Functions (Drell-Yan)
Drell-Yan Counting rate:Realistic approach, the intensity of the beam
Target: 15 g/cm2
Luminosity: L =
Cross section value = 0.3 nb/nucl
Acceptance A = 0.5
Expected rate: R = events/s
1232823 1021010615173 −−•≅ו×× scm
)9M(4GeV GeV≤≤ −+μμ
03.0103102 3432 ≅וו − A
3NH
1810 −−sπ
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Scaling:
Full x1,x2 range .
needed
[1] Anassontzis et al., Phys. Rew. D38 (1988) 1377
Drell-Yan Di-Lepton Production Xμμpp −+→
[ ]∑ ++
=a 2
aa2
a1
a2a
212
2
F2
2
)(x(x1)ff)(x)f(xfexx
1s9Mπ4α
dxdMσd
[ ]0,1τ∈⇒
s1
dxτdσd
F
2
∝
Gev/c 40p BEAM ≥r
[ ]1Xμμpp nb 0.3σ ≈−+→
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Open charm from production and subsequent weak decay
• low branching ratio: B.R. = 0.9%• huge self-analysing asymmetry:
++ → πΛΛ c
[1] Smith Vogt Z. Phys. C75 (1997)271
Open Charm ΔG
XΛc+
Λ , p cc
rr longitudinally polarised
0.98 α −=? GeV 40 @
cpp Λ→σ
days ev/100 36000 /s10 5 ev. #
μb 1 Assume
3-
[1]
•
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Strong Spin Flip Interaction