spin physics (experimental)

SPIN, Strangeness and QGP.Raimondo Bertini *.

*Universita’ and INFN-Torino

Spin Physics (Experimental)Spin Physics (Experimental)

9-15/10/2005 Raimondo Bertini

OUTLOOK

• What is SPIN• Polarised sources• Polarised beams• Polarised targets• Polarimeters• Measurement of spin observables• Future projects


Why Spin ?

• Stern- Gerlach experiment (1921)• G.E. Uhlenbeck and S.A.Goudsmith (1925)


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


Magnetic Moment


Magnetic moment of the electron


Stern-. Gerlach ExperimentZ Physik 9 (1922) 249


TkzDdB

TkzDdBgm

TkzDdBz

mvdzdB

mvtF

dxdz

Tkvm

zB

zBjj

zz

zz

z

333

tantantan

23

21

2

2111

2

∂∂

±⇒∂∂

−=∂∂

=

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∂=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

=

−−−

μμμ

μθ


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


Results


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


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


Spin Rotation

( ) ( )[ ]

( )( )resonancesrinsicPkG

resonancesonimperfectikG

G

GGsmes

dtsd

z

sp

longtr BB

int

1

11

νγγ

γ

γγ

ν

+==

+=

+++×=Ω×=rrrrr

r


Tools to preserve spin during the acceleration

• Siberian snakes• RFQ• See RHIC


Installed and commissioned during run 4To be commissionedInstalled/commissioned in run 5


Other Polarised beams

+

±±

+⇒Λ

=

+⇒

π

νμπ μ

p

J21

210


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


Λ Polarisation


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


Proton-Proton elastic scattering 1P.R.L. 85 (2000) 1819


Analyzing power

Ex. Proton-proton elastic scattering

( ) ( )

( ) ( )ωϕθσ

ωϕθσ

ωϕθσ

ωϕθσ

dd

dd

dd

dd

PAb

N ↓+↑

↓−↑

=,,

,,1


Proton-Proton elastic scattering 2


Antiproton-proton total cross-sections

pp


Antiproton-proton differential cross-sections 1


Antiproton-proton differential cross-sections 2


Antiproton-proton analyzing powers


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


Dynamic Polarisation

( )( ) spinsnucleldipr

rIrSISr

ggH

energiesZeemannuclearandelectronIZandSZsimplifiedHHHHH

neSI

RFSIIZSZ

...int.323

2

⎥⎦

⎤⎢⎣

⎡ ⋅⋅−⋅=

+++=

rrrrrrh


=

=

=

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


Transversity and Λ Polarisation


Semi-inclusive deep inelastic scattering


Kinematics of Λ production

( ) ( )

EPkPqy

EEmmkkEEqQ

MQxEE

MPq

ll

ν

ϑν

ν

=⋅⋅

=

′≈−−′⋅−′=−=

=′−=⋅

=

′

rr

rr

rr

rr

2sin42

2;

22222

2


Definition of Λ polarisation axis


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


Selection of Λ events


Data Analysis 1


Data Analysis 2


Available statistics


COMPASS Trigger


Study of systematic effects


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


Transverse Structure Functions (Drell-Yan)

Xμμ)pp(p −+− →πKinematics

q2PMx

1

2

1 •=

xxx 21F −=q2P

Mx2

2

2 •=

sMxxτ

2

21 ==


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)



⎟⎠⎞

⎜⎝⎛ +++

+= 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



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 ⊥

⊥⊥

⊥ ′×



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



30 GeV/c

15 GeV/c

40 GeV/c

τ = const: hyperbolaexF = const: diagonal

PANDA (GSI)

ASSIA (GSI)COMPASS (CERN)

Phase space



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 ÷=



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 −−•≅×•×× scm

)9M(4GeV GeV≤≤ −+μμ

03.0103102 3432 ≅×•×• − A

3NH

1810 −−sπ


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 ≈−+→


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]

•


Strong Spin Flip Interaction

spin physics (experimental)

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