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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
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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)
QuickTime™ and aTIFF (LZW) decompressor
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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:
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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)
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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
QuickTime™ and aTIFF (Uncompressed) decompressor
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Data with PN=0, Pl0:
HERMES, hep-ex/0607004
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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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QuickTime™ and aTIFF (Uncompressed) decompressor
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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 !
QuickTime™ and aTIFF (Uncompressed) decompressor
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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:
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Pq is independent of lepton polarization, and small y is required !
transversity
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
(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)