Qinghua Xu, ( LBNL) EIC workshop, July 19, 206

1

Qinghua Xu, (LBNL)

EIC workshop, July 19, 206

• Introduction

• Spin transfer of (anti)Lambda in pp collisions

• (anti)Lambda polarization in lp collisions

• Summary

Spin transfer of Lambda in polarized ep collider

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• With its “self-analyzing” decay ->p+ (Br~64%), the Lambda polarization

can be measured from the angular distribution of decay proton:

decay parameter 0.642(PDG)

)ˆ( 1d

dNppP ⋅+∝

Ω

rα Unit vector along proton mom

entum in rest frame.

polarization vector

• polarization palys an important role in spin physics:

1. Well-known transverse polarization in unpolarized pp, pA (G. Bunce et al 1976).

2. Study pol. fragmentation function and spin content of hyperon.

3. A tool to study spin structure of nucleon .

Why do we study Lambda?

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• Transverse polarization with pol. beam: fixed Target pp: E704 (PRL’97), DISTO(PRL’99)… lepton-nucleon : COMPASS

pp collider : RHIC

Experiment overview on Lambda polarization

• Longitudinal polarization:

e+e-: ALEPH(PLB’96), OPAL(EPJC’98); Polarized lepton-nucleon DIS:

E665(EPJC’00), HERMES(PRD’01),

NOMAD(NPB’01), COMPASS Polarized pp collider: RHIC

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• Study polarized fragmentation function with polarization in pp :

Lambda polarization in pp collisions

QM

DIS

equal contr.

(D.de Florian, M.Stratmann, W.Vogelsang, PRL’98)XppXpp

XppXppLL PD

−+++

−+++

→→

→→ +

−≡=

σσ

σσ

),(ˆ

),(),( 2)(

222

μη

σμμησ

cHc

T

cdab

bbaabcd

acbaT

zDddp

dxfxfdzdxdx

ddpd

ΔΔ

Δ=Δ →

∑∫

XppXppd −+++ →→

−≡Δ σσσ

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Q. Xu, E. Sichtermann, Z. Liang, PRD’06

Anti-Lambda polarization at high pT are sensitive to strange quark polarization, more so than the spin transfer models in fragmentation.

Anti_Lambda polarization in pp collisionsQuickTime™ and a

TIFF (LZW) decompressorare needed to see this picture.

Q. Xu, E. Sichtermann, Z. Liang, PRD 73, 077503(2006)

discard keep

GeV 8

GeV 200

>=

Tps

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Inclusive (anti)Lambda with STAR

AGS Heclical Partial Snake

4 spin

orientations:++,+-,-+,--

Stable polarization direction - transverseLongitudinal polarization at STAR/Phenix

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• primary vertex

p

V0_vertex

V0_DCA

rr

The cross-section of inclusive has been measured with STAR, and reasonably described by NLO calculation.

TPC

−

)|(| 1<η

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.PANIC05: M.Heinz for the STAR collaboration

Inclusive (anti)Lambda with STAR

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Extracting pol. from the asymmetry

• Momentum distribution of decay proton:

• Assuming 2 sample with opposite pol., consider a small bin in : [1,2]:

221 α coscos

)()()()( +

⋅≈−+−−

= PPNPNPNPN

As

)cos(cos 12

2

α +≈ sA

P

,2/0 totNN = A(cos): detector acceptance

(acceptance is cancelled!)

• Symmetry relations )()( 00 ηη −

+ −= PP

• Extraction of Lambda polarization:

−+

−++ −

−⋅><⋅

≈=NN

NN

PPD

beamLL θα cos

1

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+=∫

2

1

cos)cos1)((cos)( 0

θ

θ

θθαθ dPANPN

)ˆ )((cos *ppPANdN ⋅+=

rαθ 10

cosΛP

N+(-): number of with beam positively (negativly) polarized

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• D_LL with data of 0.8 pb-1 in 2003 and 2004:

• No. of events:

~30 K for Lambda

~27 K for anti-lambda

• Kinematics : |<xF>|~0.008

<pT>~1.5GeV

Stat. error ~0.05

• With data of 2005 (~3 pb-1) and 2006 (~8 pb-1), a stat. error of 0.03 with pT>4GeV can be reached. --- ~100 pb-1 data needed to get stat. error of ~0.01 at pT>8 GeV!

PANIC05: Q.Xu for the STAR

(anti)Lambda polarization with STAR

• This is essentially the only way in which RHIC can access strangeness, since the charm-associated W production will be luminosity hungry.

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Transverse polarization of hyperons in pp and q(x)

)(

)(

)()(

)()(

HXpp

XHppT

XHppXHpp

XHppXHppH

T d

d

dd

ddP →

→

→→

→→ ⊥⊥

↓↑↑↑

↓↑↑↑ Δ≡

+−

=σσ

σσσσ

rr

ησμμμ

ησ

d

dzDxfxfdzdxdxdp

d

d dcbaTH

cTbbaabcd

aba

p

T

XHppT

T

)(222

)( ˆ),(),(),(

min

⊥⊥⊥⊥ →→ ΔΔ=

Δ∑∫∫

rrrr

• PH in transversely polarized pp collisions:

transversity distribution :

f(x) = f (x) - f(x)



pQCD

• Information on ΔTD(z) or q(x) can be accessed

via transverse Lambda polarization in pp collisions.

--- ΔTD(z) is one of the few quantities can decouple q(x) as

well as the Collins frag. function, Drell-Yan process…

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Transverse polarization of hyperon in pp

J.Collins et al, NPB420 (1995)565

Transverse polarization direction of the parton may be changed in the hard subprocess!

Spin transfer factor in hard scattering can be obtained with pQCD.

Magnitude of transverse polarization:



η0 1-1

Q. Xu, Z. Liang, PRD 70, (2004)

qin

qout

(J.Soffer)

(B.Q.Ma et al)

)(xq

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Longitudinal polarization in letpon-nucleon reactions

222

)2()(

yy

yyyD

+−−

=

∑∑

Δ=

fff

fff

l QzDQxqe

QzDQxqe

yDPP),(),(

),(),(

)(222

222

• PN=0, Pl0:

∑∑

ΔΔ=

fff

fff

l QzDQxqe

QzDQxqe

PP),(),(

),(),(

222

222

)()()(

)()()(

xqPyDPxq

xqPxqyDPP

fNlf

fNflf Δ+

Δ+=

current fragmentation region

−e−e

N

Hr

• Polarization of scattered quark:

clean measurement of pol. fragmentation function

polarized p.d.f

Depolarization factor Lar ge y needed to have big D(y)!

• PN 0, Pl=0:

(Pl, PN : pol. of lepton and nucleon)

),(),( 22 μμ zDzDD Hc

Hc

−+

++ −=Δ

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Current fragmentation & target remnant effects

• HERMES: Ee= 27 GeV (CME=3.6 GeV)

• NOMAD: Enu= 44 GeV (CME=4.5 GeV)

• COMPASS: Emu= 160 GeV (CME=8.7GeV)

• E665: Emu= 500 GeV (CME=15GeV), limited by statistics

Containing at least one valence quark from the target

Containing the struck quark

H.Dong et al, PRD 72, 033006(2005)

• EIC collider: much better with sqrt(s)=22 ~100 GeV

Ee= 27 GeV

Low CME : there is some contribution from target remnant fragmentation at xF>0 other than from current quark .(xF=pl /plmax in hadronic frame)



Target remnant contri.

J. Ellis et al, EPJC 25, 603(2002)

HERMESNOMAD

COMPASS

LEPTO

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• NOMAD With remnant contribution

Without remnant contribution

Z. Liang, C.Liu, PRD 66(2002)

Example of target remnant effects

N

Hr

μ μThe scattered quark is polarized with pol.=-1 with nutrino CC reaction

Data of pol. at NOMAD:

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• The measured quantity at HERMES and COMPASS:

,)(

)(yDP

PyS

l

=∑∑

Δ=

fff

fff

l QzDQxqe

QzDQxqe

yDPP),(),(

),(),(

)(222

222

S(y) is determined by ΔDf(z)/ Df(z) and their relative contributions of each flavor!

Data with PN=0, Pl0:

M.G.Sapozhnikov et al, hep-ex/0503009

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hep-ex/0607004



Data with PN=0, Pl0:

HERMES, hep-ex/0607004



relative contributions of each flavor

• u quark dominate production• Measured small spin transfer

ΔDu(z) is small (within stat. error)!

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ΔDf/ Df ~ ΔQf () : average polarization of qf in

• The spin transfer in fragmentation is expected to be related to the spin content of Lambda.

G.Gustafson, J.Hakkinen, 1993

C.Boros, Z.Liang,1998

D.Ashery, H.J. Lipkin,1999

B.Q.Ma, J.J.Yang, I. Schmidt, 2000

• For those Lambdas directly produced and contains the struck quark, assuming its helicity is preserved during the fragmentation process:

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Spin content of Lambda

SU(6) : SU(6) wave function of (Quark Model)

DIS : obtained from DIS data for proton and SU(3) flavor symmetry :

)2()()()( 361

363

364

1

0 11 SDUDUSDUdxxg pp Δ−Δ+Δ+Δ−Δ+Δ+Δ+Δ==Γ ∫

))]()([( ∫ Δ+Δ=Δ1

0

dxxqxqQ

Σ DF + DF −3

Neutron, hyperon beta decay data

DIS data

])([ ,↑↑ = sud 00

(M.Burkardt, R.Jaffe, 1993)

A feeling of possible difference among ΔDu, ΔDd ,ΔDs!

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SPIN2005 M.G.Sapozhnikov et al, hep-ex/0602002

Pb= -0.76

• What does it mean if they are different or same?

Different polarization for Lambda and anti_Lambda?

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Relative contribution of different flavors

Anti_LambdaLambda

Ee=10 GeV

Ep=250 GeV PYTHIA

• Anti_Lambda is dominated by s_bar frag. at large xF !

--- good measurement of ΔDs_bar(z)/Ds_bar(z) • Anti_Lambda pol. will be larger than at large xF if ΔDu(d) is small !

• Different , anti_Lambda pol. at xF<0.4 will indicates sizable ΔDu !---effects from decay contribution and target remnant not included.

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• There is no contamination from gluon at leading order!

Longitudinal Lambda pol. with PN 0, Pl=0:

∑∑

ΔΔ=

fff

fff

l QzDQxqe

QzDQxqe

PP),(),(

),(),(

222

222

• polarization related with helicity distribution of quark in nucleon:

• Information of Δs_bar(x) can be accessed with anti_Lambda polarization with PN=0, Pl0 !

N

ΔDs_bar(z)/ Ds_bar(z) can be extracted from anti_Lambda polarization at large xF with PN=0, Pl0 !



Anti_Lambda

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Transverse Lambda polarization in ep collier

222

)1(2)(

yy

yyDT +−

−=

),(

),()(

2

2

Qxq

QxqyDP Tq

=

∑∑

=

fff

fff

N QzDQxqe

QzDQxqe

PP),(),(

),(),(

222

222 δδ

• Information on q(x) or ΔTD(z) can be accessed

via transverse polarization of Lambda in ep and pp!

• Polarization of scattered quark:



Pq is independent of lepton polarization, and small y is required !

transversity



(Artru, Mekhfi 1991)

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• Spin transfer of Lambda and anti-Lambda in polarized pp collisions being measured with STAR at RHIC

• (Anti)Lambda polarization with high precision at ep collider give new insights into spin transfer in fragmentation

process, especially access of ΔDs-bar(z) at large xF from anti_Lambda pol.

Information Δs_bar(x) can be accessed with anti_Lambda polarization in case Pl=0, PN0!

Transverse polarization can give an access to transversity distribution of nucleon!

Summary

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Backup slides

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Spin content of Lambda

SU(6) : SU(6) wave function of (Quark Model)

DIS : obtained from DIS data for proton and SU(3) flavor symmetry :

)2()()()( 361

363

364

1

0 11 SDUDUSDUdxxg pp Δ−Δ+Δ+Δ−Δ+Δ+Δ+Δ==Γ ∫

))]()([( ∫ Δ+Δ=Δ1

0

dxxqxqQ

Σ DF + DF −3

Neutron, hyperon beta decay data

DIS data

])([ ,↑↑ = sud 00

(M.Burkardt, R.Jaffe, 1993)

Agree with available data on small ΔDu !

SU6

DIS

(C.Boros, Z.Liang, 1998)

Documents

Qinghua Xu, ( LBNL) EIC workshop, July 19, 206