JLab, May 27, 2005 Aram Kotzinian 1
Polarized Semi-Inclusive DIS in Current and Target Fragmentation
Introduction The flavor separation of the quark helicity distributionsThe spin and azimuthal asymmetries in the current and target fragmentation regions Polarization of Λs produced in SIDIS of polarized leptons on unpolarized targetConclusions
Aram Kotzinian
Torino University & INFNOn leave in absence from YerPhI, Armenia and JINR, Russia
JLab, May 27, 2005 Aram Kotzinian 2
Lepton-Nucleon EM Interactions
Study of Confinement in QCDStructure of nucleon & hadronization dynamics
Elastic – Form-factors
Exclusive – GPDs
DIS – DFs
SIDIS:CFR: DFs & Fragmentation Functions
TFR: Fracture Functions
More general: Hadronization Functions
Spin phenomena play crucial role in all channels
JLab, May 27, 2005 Aram Kotzinian 3
DIS
2 2 2( , ) (1 (1 ) ) ( )
, , , , ,
x Q y e q x
q u u d d s s
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Nucleon Spin from polarized DIS
Gluon Spin
Nucleonspin zLG
2
1
2
1Quark Spin
Orbital Angular Momentum
2 2 2( , ) (1 (1 ) ) ( )
( ) ( ) ( )
x Q y e q x
q x q x q x
Spin Sum Rule
COMPASS 2005
LSS 2005
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SIDIS in LO QCD: CFR
( , , ) ( , ; )lN lhX lq lq hq q N q q
q
d f x d D z T Tk s ;S p s
Well classified correlations in TMD distr. and fragm. functions
1ˆ Tf T TS (p×k ) Sivers distribution
1ˆ h T Ts (p×k ) Boer distribution
1Lg L LS s Helicity distribution
1ˆ H h
T Ts (q×p ) Collins effect in quark fragmentation
( )q Nf x N
( )hqD z
h
p
1( ) Lh T T Lk s S Mulders distribution
JLab, May 27, 2005 Aram Kotzinian 6
SIDIS in LO QCD: TFR
( , )qh NM x z N
q
h
( , )lN lhX lq lq qh N
q
d d M x z
( , , , ; )q hh N q NM x zT Tk s ; p S
1994: Trentadue & Veneziano; Graudenz; … Fracture functions: conditional probability of finding a parton q with momentum
fraction x and a hadron h with the CMS energy fraction z
More correlations for TMD dependent FracFuncs
; s
( ) ...
h h
h
L T T L T T
T T T T
S (p ×k ) (p ×k )
S p (s ×k )
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Ed. Berger criterion (separation of CFR &TFR)
The typical hadronic correlation length in rapidity is
Illustrations from P. Mulders:
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LUND String Fragmentation
( , , ) ( , , , ; )q hh N q F
lN lhX lq lqq q N
qNd xd H xf x TT Tk s ; k pS s ; S
u
( ud)
R
R
R
u
u
d
d
d
s
d
s
+ρ
0π
-π
+K
Soft
Str
ong
Inte
ract
ion
q
Ran
k f
rom
diq
uark
Ran
k f
rom
qu
ark
h
Parton DF, hard X-section & Hadronization are factorized
Implemented in LEPTO + JETSET (hadronization)
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Flavor separation using SIDIS
0.028 0.033 0.009s
Leader & Stamenov, 2003:
Non-negative strange quark
polarization is almost
impossible
HERMES analysis
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Purity method for flavor separation
Purities are calculated using LEPTO
( )q Nf x N
( )hqD z
h
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LO SIDIS in LEPTO- Before
- After
-Example: valence struck quark
quarkTarget remnant
Natural question: does Lund hadronization exactly correspond to independent quark fragmentation in the CFR with z>0.2? (A.K.2004)
The important property of FFs is universality:
1. Independence of Bjorken variable x2. Target type independence3. Process type independence ),,(
),,(),(
2/
2,/2
QzxN
QzxNQzD
DISNq
SIDIShNqh
q
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Bjorken variable dependence of “FFs” in LEPTO
2 2
0.1
1.5
x
Q GeV
2 2
0.1
3.4
x
Q GeV
2
2
F
Cuts:
Q 1
W 10
y<0.85;
0.023<x<0.6
E >3.5
0.2
x >0.1
GeV
GeV
GeV
z
The dependence of “FFs” on x
cannot be attributed to Q2 evolution
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Target type dependence of “FFs” in LEPTO
Example oftarget remnant: removed valence u-quark:
( )p u ud ( )n u dd
There is dependence of “FFs” on the
target type at 10% level
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The primary hadrons produced in string fragmentationcome from the string as a whole, rather than from
an individual parton.
LUND string fragmentation
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Even for meson production in the CFR the hadronization in LEPTO is more complicated than SIDIS description with independent FFs
Hadronization Functions (HF)
More general framework -- Fracture Functions (Teryaev, T-odd, SSA…)
We are dealing with LUND Hadronization Functions:
),,(),(),,( 2/
22/ QxxHQxqQxxM F
hNqF
hNq
),,( 2/ QxxM F
hNq
LEPTO is a model for Fracture Functions:
The dependence on target flavor is due to dependence on target remnant flavor quantum numbers. What about spin quantum numbers?
Violation of naïve x-z factorization and isotopic invariance of FF
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Dependence on target remnant spin state (unpolarized LEPTO)
Example: valence u-quark is removed from proton. Default LEPTO: the remnant (ud) diquark is in 75% (25%) of cases scalar (vector)
Even in unpolarized LEPTO there is a dependence on targetremnant spin state
0{( ) }, 1.ud u w
1{( ) }, 1.ud u w
(ud)0: first rank Λ is possible(ud)1: first rank Λ is impossible
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Target remnant in Polarized SIDIS
JETSET is based on SU(6) quark-diquark model
Probabilities of different string spin configurations depend on quark and target polarizations, target type and process type
90% scalar
100% vector
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Polarized SIDIS & HF-- spin dependent cross section and HFs
These Eqs. coincide with those proposed by Gluk&Reya (polarized FFs). In contrast with FFs, HFs in addition to z depend on x and target type
hN Nl
hNq Nq
H /and
0hq NH double spin effect, as in DFs.
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For validity of purity method most important is the second relation
),,(),(
),,(),(1),,(),(
),,(
),,(
),(),(
),,(),(
),,(
2/
2
2/
22
/22
2/
2/
2
22
/22
21
QzxHQxq
QzxHQxqQzxHQxqe
QzxH
QzxH
QxqQxq
QzxHQxqe
QzxA
hNq
hNq
q
hNqq
hNq
hNq
q
hNqq
h
Asymmetry
The standard expression for SIDIS asymmetry is obtained when
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Toy model (A.K.2003)u
( ud)
In JETSET there is a pointer indicating whether produced
hadron is coming from quark or diquark end of the string.
Symmetric LUND fragmentation: each string breaking
starting with equal probabilities from q or qq end.
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PEPSI MCModel A: default PEPSI
Model B: neglect contribution of events to asymmetries
with hadrons originated from diquark
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Beam Energy Dependence
Situation is different for higher energies:
dependencies of “FFs” extracted from MC
on x, target type and target remnant quantum numbers
are weaker
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LUND MC is proved to be capable to describe data in a wide range of kinematics.The new concept of (polarized) hadronization is introduced and studied using LEPTO event generator
The hadronization in LEPTO is more general than simple LO x-z factorized picture with independent fragmentation, for example, it describes well TFR.
It necessary to modify PEPSI MC event generator by including polarization in hadronization.
The purity method have to be modified to include polarized HFs. Within this new approach one can include all hadrons (CFR+TFR) for flavor separation analysis.
More studies on the accuracy of different methods of the polarized quark DF extraction using SIDIS asymmetries are needed.Alternative measurements are highly desirable
SIDIS at different beam energies: COMPASS, JLab, EICW production in polarized p+p collisions (Anti)neutrino DIS on polarized targets (Neutrino Factory)
Conclusions 1
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Melnitchouk & Thomas: Meson Cloud Model
100 % anticorrelated with target polarization contradiction with neutrino data for unpolarized target
Longitudinal polarization of Λ in the TFR
Λ-polarization in TFR
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Karliner, Kharzeev , Sapozhnikov, Alberg, Ellis & A.K. Nucleon wave function contains an admixture with
component:
π,K masses are small at the typical hadronic mass scale: a strong attraction in the − channel.
pairs from vacuum in state
Intrinsic Strangeness Model
ss
qq 0
3P
Polarized proton:Spin crisis: 1.0s
0PJ
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J.Ellis, A.K. & D.Naumov (2002)
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qq q
Rank from diquark
Rank from quark
NOMAD (43.8 GeV) COMPASS (160 GeV)
No clean separation of the quark and diquark fragmentation
Λ parent
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Λ polarization in quark & diquark fragmentation
Λ polarization from the diquark fragmentation
Λ polarization from the quark fragmentation
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Spin Transfer
We use Lund string fragmentation model incorporated in LEPTO6.5.1 and JETSET7.4.
We consider two extreme cases when polarization transfer is nonzero:
model A: the hyperon contains the stuck quark: Rq = 1
the hyperon contains the remnant diquark: Rqq = 1
model B: the hyperon originates from the stuck quark: Rq ≥ 1
the hyperon originates from the remnant diquark: Rqq ≥ 1
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Fixing free parameters
We vary two correlation coefficients ( and ) in order to fit our models A and B to the NOMAD Λ polarization data.
We fit to the following 4 NOMAD points to find our free parameters:
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Results
Predictions for JLab 5.75 GeV
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Predictions for CLAS
Predictions for xF-dependence at JLab 12 GeVRed squares with error bars – projected statistical accuracy for
1000h data taking (H.Avagyan).
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Predictions for EIC
5 GeV/c electron + 50 GeV/c proton, 9.04.0 GeV/c, .1 ,1 2
Beam yQP
Good separation of the quark and diquark fragmentation allows to distinguish betweendifferent spin transfer mechanisms from quark and diquark
JLab, May 27, 2005 Aram Kotzinian 34
Conclusions 2
Predictions for Λ polarization are very sensitive to production mechanism
A phenomenological polarized intrinsic strangeness + SU(6) model is able to describe all available data on longitudinal polarization of Λ in full kinematic range
New measurements at different energies will serve as a test for proposed models
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Unpolarized SIDIS & Cahn effect
frame CM * P
x & z are light cone variables defined with respect z & axesz
No exact factorization !Bj hx z
M.Anselmino, M.Boglione, U.D’Alesio, A.K., F.Murgia and A.Prokudin: PRD 71,
074006 (2005)
A.K.: arXiv:hep-ph/0504081
JLab, May 27, 2005 Aram Kotzinian 36
Unpolarized SIDIS & Cahn effect
)/O( QkT
Ji et al: QCD factorization holds for QkP QCDTT
Quadratic in
Linear in and proportional to 2k
hz
hz
approximation
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Comparison with data
Non Gaussian tail; x, z and flavor dependence of intrinsic and fragmentation transv. momentum
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Brodsky, Hwang & Schmidt, 2002: FSI
+
2
( , ) 0NTq P
f x k
Collins, 2002; Belitski, Ji &Yuan, 2003: Wilson gauge link
Boer, Mulders & Teryaev, 1997: twist three gluonic pole
In standard approach the effective treatment of the Sivers effect isadopted as correlation in quark distribution in transversely polarized nucleon
ˆT TS (p×k )
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Parameterization for Sivers effect
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Data
JLab, May 27, 2005 Aram Kotzinian 41
New HERMES data
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Quark intrinsic transverse momentum in LEPTO
- Generate virtual photon – quark scattering in collinear configuration:
- Before
- After hard scattering
- Rotate in l-l’ plane
- Generate intrinsic transverse momentum of quark (Gaussian kT)
- Generate uniform azimuthal distribution of quark (flat by default)
- Rotate around virtual photon
Tk z
q
zplane ll
JLab, May 27, 2005 Aram Kotzinian 43
Implementing Cahn and Sivers effects in LEPTO
The common feature of Cahn and Sivers effects Unpolarized initial and final quarks
Fragmenting quark-target remnant system is similar to that in default LEPTO but the direction of is now modulated
Cahn:
Sivers:
Generate the final quark azimuth according to above distributions
z
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Results: Cahn
Imbalance of measured in TFR and CFR: neutrals?
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Results: Sivers
Predictions for xF-dependence at JLab 12 GeV
Red triangles with error bars – projected statistical accuracy for 1000h data taking
(H.Avagyan).
z and xBj-dependences
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Results: Sivers JLab 12 GeV
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SSA in PP-interactionsE704. Curves: by Anselmino et al, STAR (hep-ex/0505024)
Both the active quark and the polarized proton remnant are flying in forward direction.
Which final hadrons provide transverse momentum balance?
h
P
( )hqD z
P( )q Nf x
( , )q N
f x Tk
( )hqD z
ST
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Conclusions 3Both Cahn and Sivers effects are implemented in LEPTO. Possible effects of polarized hadronization were neglected.
Existing data in CFR are well described by modified LEPTOThe measured Cahn effect in the TFR is not well described
Is there an universal mechanism describing SSA in SIDIS and PP interactions?
It will be interesting to implement Cahn and Sivers effects in PHYTIA
It is important to perform new measurements of both effects in the TFR (JLab, HERMES, Electron Ion Colliders)
This will help better understand hadronization mechanism Do the neutral hadrons compensate Cahn effect in CFR?Multihadron final states distributions can enhance effects Is there a similarity with PP-reaction?
Fracture Function“Global” analysisClassification of spin and TMD dependent correlations in Fracture Functions
JLab, May 27, 2005 Aram Kotzinian 49
Conclusions
Spin phenomena in SIDIS can play very important role for modeling and understanding the QCD dynamics
Access to TFR opens a new field both for theoretical and experimental investigations
JLab@12 GeV is ideally placed to make important breakthroughs over a wide spectrum of discovery in nucleon structure and hadronization dynamics
Thanks for hospitality
@ JLab
JLab, May 27, 2005 Aram Kotzinian 50
Support Slides
JLab, May 27, 2005 Aram Kotzinian 51
HERMES check