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3 Madrid, April 27, 2009 Aram Kotzinian Intrinsic Strangeness Model (ISM) for Λ polarization P u (ud) 0 s s - Λ μ μ′μ′ R qq
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Madrid, April 27, 2009 Aram Kotzinian 1
Longitudinal target polarization dependence of Λ polarization and polarized strangeness PDF
Λ polarizationUnpolarized target
Strangeness distribution in nucleon
Polarized targetPolarized strangeness in polarized nucleon
Conclusions
Aram KotzinianCEA-Saclay, IRFU/Service de Physique Nucléaire, 91191 Gif-sur-Yvette, France
On leave in absence from YerPhI, Armenia and JINR, Russia
DIS 2009, 26-30 April 2009, Madrid
Madrid, April 27, 2009 Aram Kotzinian 2
Simple model: LO, independent fragmentationfor current fragmentation region
0TP
2
,0 2
( ) ( )( )
( ) ( )B
q qq
P Bq q
q
e q x D zP P D y P
e q x D z
2
(6) Model for spin transfer in fragmentation:
only ( )
( ) ( )1 ( ) ( )9 : ( , )
( ) ( ) ( )
0,
s s
s
q
s
x sB q q
D z D z
s x D zPS F x zD y P e q
SU
D z
x D z
Fraction of events with hard scattering off s-bar
(s-bar purity)
Madrid, April 27, 2009 Aram Kotzinian 3
Intrinsic Strangeness Model (ISM) for Λ polarization
P
u
(ud)0
ss-
Λ
μ
μ′
Rqq<Rq: spin transfer from intrinsic
strangeness and polarized diquark via heavier hyperons
P
u
(ud)0
Λ
μ
μ′
Rq<Rqq: spin transfer only
from final quark
J.Ellis,M.Karliner,D.Kharzeev,M.G.Sapozhnikov, 1995J.Ellis, D.Kharzeev, A.K., 1996
J. Ellis, A. K. & D. Naumov, 2002
TFR
CFR
Madrid, April 27, 2009 Aram Kotzinian 4
Spin transfer in SIDIS
Spin transferfrom qq side
Spin transferfrom q side
Madrid, April 27, 2009 Aram Kotzinian 5
NOMAD data
Madrid, April 27, 2009 Aram Kotzinian 6
Λ polarization
P
u
ss-μ
μ′
Rqq<Rq: spin transfer only
from intrinsic strangeness
Λ P
u
(ud)0
Λ
μ
μ′
Rq<Rqq: spin transfer only
from final quark
J.Ellis, A.K., D.Naumov and M.Sapozhnikov
EPJ.C52:283-294,2007
Madrid, April 27, 2009 Aram Kotzinian 7
NOMAD tuning usedBest description with SU(6)
model for spin transfer. polarization = s(x) filter
Unpolarized target
LEPTO MCs-bar purity
SU(6), CTEQ5L
Madrid, April 27, 2009 Aram Kotzinian 8
Quark type fraction in anti-Lambda production
( ) 0.15 0.2for x 0.1
sF x
LEPTO MC with CTEQ5L
and COMPASS cuts
In contrast to K production asymmetry,
here mainly s-bar contributes to
and P P
ud s
s
s
s
s
su
u
u
u
u
d
d
dd
d
Madrid, April 27, 2009 Aram Kotzinian 9
PDFs
2 22.5 (GeV/c)Q
Madrid, April 27, 2009 Aram Kotzinian 10
Hyperon production x-section and polarizationfor polarized beam and target
,
,
1
1
B
B
T
T
P B T
B B T TP
T
P
P
B
P P
P S P SPP P
Target polarization sign is written explicitlyBeam polarization contains sign
From general considerations for double and triple longitudinal polarization observables:
Triple-spin effect
Madrid, April 27, 2009 Aram Kotzinian 11
Polarization Asymmetry ( )P
A x
, ,
, ,
1:2:
B B
B
T
T B
T
T
P PP P
P PP P
P P P
P P P
( )( ) :( )P
P xA xP x
Polarization asymmetry
Madrid, April 27, 2009 Aram Kotzinian 12
Factorized LO QCD parton model2
,2
( )( ) ( ) ( )( )
( )1 ( ) ( ) ( )( )
B T
q B T qq
P P
q B T qq
q xe D y P fP q x D zq x
Pq xe D y P fP q x D z
q x
0.2 Deuteron0.14 Proton
effT T
forP fP
for
( )( ) 0.5 0.85, 0.5( )
( )( ) 0.85 0.8 0.2 0.5 0.068( )B T
q xD yq x
q xD y P fPq x
We can neglect
pol.dep. part in denom.
ISM expression is more complicated, but results are almost unchanged
Madrid, April 27, 2009 Aram Kotzinian 13
2 2
( ) ( )( ) ( ) ( )( ) 2
1 1( ) ( ) ( ) ( )( )9 9( ) , 2( )( ) ( ) ( ) ( )
( )1, for COMP
( )( )
2
ASS Deuteron target
( )(
( )
)
2
s s
B Tq q q q
B BP
T
q q
T
T
P
B
D y P D y Ps x P x A xs x fP fPP
s x D z s x D zs xP D y P P fPs xe q x D z e q x D z
D
P xA
y P
x COMPASSP x
x
fP
( )( )s x
s x
in LO QCD parton SU(6) model ( )P
A x
Madrid, April 27, 2009 Aram Kotzinian 14
ISM calculations using LEPTO
,
2
( )
2
( )
2
( , ,...) ( , ,...)( , ,...)
( , ,...)
( )( , ,...) ( ) ( ) ( )( )
( )( , ,...) ( ) ( ) ( )( )
( , ,...)
B T
q qq
q qq
q F qq FP P F
F
q F q B T q qq R R
qq F q B T q sqq R R
F q
N x x N x xP x x
N x x
q xN x x e D y P fP q x D z Sq x
q xN x x e D y P fP q x D z cq x
N x x e
( )1 ( ) ( ) ( )( )B T q
q
q xD y P fP q x D zq x
Separately calculate numerator and denominator by reweighting each generated event
Nomad settings and sq sqc cSymbolic notations: Lund Model is realization of Fracture Functions.
Spin transfer via heavy hyperons is taken into account.
Madrid, April 27, 2009 Aram Kotzinian 15
Two inputs for Pq=Δq/q
DSSV+MRST022008
GRSV+GRV2000sP
Madrid, April 27, 2009 Aram Kotzinian 16
COMPASS cuts
Q2 > 1 (GeV/c)2; 0.2 < y <0.9Primary vertex: -100 < z < 100 or -30 < z < 30 (cm)
Decay vertex: 35 < zdec < 140 (cm)
Vertexes colinearity cut: θcol = 0.01
Decay particles momentum: p > 1 GeV/c
Feynman variable: 0.05 < xF < 0.5
Λ rest frame decay angle cut: cos(θ*) < 0.6
Madrid, April 27, 2009 Aram Kotzinian 17
Dependence on pol. PDFs
To verify sign change of Δsmeasure in two bins of x: x < 0.03 and 0.03 <x
Madrid, April 27, 2009 Aram Kotzinian 18
COMPASS preliminary
TP
TP
Sing change of ΔP corresponds to DSSV PDFs
Madrid, April 27, 2009 Aram Kotzinian 19
Conclusions(Anti)Lambda polarization measurements in SIDIS of polarized leptons off unpolarized and polarized targets can shed light unpolarized and polarized s-bar distributions in nucleon
(Anti)Lambda polarization on unpolarized target strongly depends on strangeness PDFPolarization asymmetry strongly depends on strangeness polarization shape
(Anti)Lambda polarization in SIDIS is well suited filter for nucleon strangeness study