1. Polarization phenomena in the target fragmentation region of SIDIS
Aram Kotzinian
Uni&INFN, Torino
YerPhI, Armenia
Hadronization in SIDIS
LUND model and LEPTO
Longitudinal Λ polarization in TFR
SIDIS azimuthal asymmetries in the CFR and TFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

2. SIDIS in one photon exchangel l'
xF1 > 0 – current fragmentation region (CFR)
xF2 < 0 – target fragmentation region (TFR)
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

3. CFR in QCD factorized approachl l'
Well classified TMD distr. and fragm. functions
Target remnant doesn’t taken into account
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

4. INT Workshop, Seattle, September 24, 2010
TFR in LO QCD N q h l l'
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=Eh/EN
Scattered quark doesn’t taken into account
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

5. INT Workshop, Seattle, September 24, 2010
FragFun FracFun
Factorization proof Yes No
Evolution equation Yes Yes
QCD definition Yes No
SPRES: find k
But Trentadue &Veneziano “Cited 156 times”
TMD classification Yes No
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

6. INT Workshop, Seattle, September 24, 2010
Gauge link
2015 years ago
Graf from Ted Rogers talk
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

7. INT Workshop, Seattle, September 24, 2010
LEPTO MC Generator
Parton DF, hard X-section & Hadronization are factorized h TR q N l l'
For hadrons in TFR can be considered as a model for FracFun
Here scattered quark is taken into account
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

8. LUND String Fragmentation
Soft Strong Interaction qq q
Rank from diquark
Rank from quark h
No polarization effects
Dream is to have
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

9. Longitudinal Λ polarization in TFRq Λ z l l'
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

10. INT Workshop, Seattle, September 24, 2010
Meson cloud model
Melnitchouk & Thomas (1995) N K+ Λ l l'
correlated
quarks
Zero polarization for unpolarized target
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

11. Intrinsic Strangeness Model
Ellis, Karliner, Kharzeev , Sapozhnikov, Alberg, AK
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
“Spin crisis”:
Polarized proton:
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

12. INT Workshop, Seattle, September 24, 2010
Spin flow N Λ z
TFR
CFR N Λ z
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

13. INT Workshop, Seattle, September 24, 2010
Spin transfer in TFR
J.Ellis, D.Naumov&AK (2002)
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

14. INT Workshop, Seattle, September 24, 2010
Spin transfer models qq q 
Rank from diquark
Rank from quark
Struck quark
Remnant diquark
Rq= (A)
Rqq>Rq (B)
Rqq= (A)
Rq>Rqq (B)
NOMAD (43.8 GeV)
COMPASS (160 GeV)
No clean separation of the quark and diquark fragmentation
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

15. Λ polarization in quark & diquark fragmentation
Λ polarization from the quark fragmentation
Λ polarization from the diquark fragmentation
I – nonrelativistic SU(6) wave functions
II – flavor SU(3) & polarized DIS data
for baryon octet:
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

16. 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:
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

17. INT Workshop, Seattle, September 24, 2010
Results
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

18. CLASS preliminary (from H. Avakian)6
Lambda polarization for 5.75 GeV with proton target (predictions for 5.75 GeV from Ellis, Kotzinian and Naumov)

19. INT Workshop, Seattle, September 24, 2010
CLAS12 projections
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

20. INT Workshop, Seattle, September 24, 2010
Predictions for EIC
5 GeV/c electron + 50 GeV/c proton,
Good separation of the quark and diquark fragmentation allows to distinguish between
different spin transfer mechanisms in the quark fragmentation
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

21. INT Workshop, Seattle, September 24, 2010
General expression for 1h production cross-section
Valid for SIDIS CFR, TFR
and exclusive reactions
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

22. Parton model for SIDIS in CFR
At twist-two
Often used:
Yerevan, June 22, 2009
Aram Kotzinian

23. INT Workshop, Seattle, September 24, 2010
Cahn effect
Unpolarized quark hard scattering and hadronization
1/Q kinematic correction
CFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

24. INT Workshop, Seattle, September 24, 2010
Sivers effect
Leading order effect in
unpolarized quark hard scattering and hadronization
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

25. Initial quark kT in MC generators PYTHIA and LEPTO
- Generate virtual photon – quark scattering in collinear configuration:
- Before
- After hard scattering
- Generate intrinsic transverse momentum of quark (Gaussian kT)
- Rotate in l-l’ plane
- Generate uniform azimuthal distribution of quark
- Rotate around virtual photon
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

26. 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
A.K. hep-ph/
Cahn:
Sivers:
Generate the final quark azimuth
according to distributions
M.Anselmino, M.Boglione, U.D’Alesio, A.K., F.Murgia and A.Prokudin:
PRD 71, (2005);
Parameters were extracted from combined analysis of HERMES and COMPASS data
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

27. INT Workshop, Seattle, September 24, 2010
Results: Cahn effect
Charged hadrons azimuth
EMC Collaboration (280GeV)
Imbalance of measured
in TFR and CFR: neutrals?
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

28. Results: Sivers effect
Predictions for xF-dependence at JLab 12 GeV
Red triangles with error bars – projected statistical accuracy for 1000h data taking
(H.Avakian).
z, xBj and PT dependences
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

29. Results: Sivers JLab 12 GeV
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

30. Quark transverse spin in hard scattering
QED:
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

31. Collins effect in the string model
goes to the left
Second rank hadron will have opposite sign asymmetry with larger amplitude
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

32. Target remnant polarization state
JETSET is based on SU(6) quark-diquark model
(ud)1,1 u- d+
1 rank
proton
2 rank
pion k┴
k'┴ ST s' d- s
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

33. Transverse pseudo vectors
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

34. INT Workshop, Seattle, September 24, 2010
h1T contribution s s'
TFR
CFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

35. INT Workshop, Seattle, September 24, 2010
contribution
TFR
CFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

36. INT Workshop, Seattle, September 24, 2010
contribution
TFR
CFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

37. INT Workshop, Seattle, September 24, 2010
contribution
TFR
CFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

38. Quark transverse spin effects in TFR of SIDIS
Spin quantization axis for final quark and diquark
In contrast to CFR no sideway spin flip
no factor, which appears due to
magnitude of s' in Collins fragmentation of scattered quark
2) the only modulation induced by combined effect of
target remnant transverse polarization and Collins
fragmentation at leading order is
Same type of contribution as Sivers effect
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

39. Ed. Berger criterion for independent hadronization
The typical hadronic correlation length in rapidity is
Illustrations from P. Mulders:
HERMES: ~4 GeV; COMPASS: ~11 GeV; EIC(5+50, y>0.4): ~24GeV
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

40. INT Workshop, Seattle, September 24, 2010
Discussion
Some questions:
Will Λ polarization follow predictions of intrinsic strangeness model in TFR of electroproduction?
Are there sin(Φh+ Φs), sin(3Φh- Φs), sin(2Φh) leading twist modulation in TFR?
At which xF occurs transition from Collins like to Sivers like modulation?
Is there influence of target remnant state on hadrons in CFR (and vice versa) at low W? COMPASS W-dependence for Sivers modulation amplitude: can be influence of Collins effect of target remnant?
Data on Cahn and Sivers asymmetries in the CFR can be described by modified LEPTO
The measured Cahn effect in the TFR is not well described
It is important to perform measurements of Cahn, Sivers and other azimuthal asymmetries in the TFR (JLab, COMPASS, Electron Ion Colliders)
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

41. INT Workshop, Seattle, September 24, 2010xF 1 -1
CFR
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

42. INT Workshop, Seattle, September 24, 2010xF 1 -1
Larger phase space
higher W, z, x
different asymmetries
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

43. INT Workshop, Seattle, September 24, 2010xF 1 -1
Better resolution,
higher statistics, Q2
Better understanding
of underlying physics
Wilson links…
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

44. INT Workshop, Seattle, September 24, 2010xF 1 -1
TFR with good
resolution etc
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian

45. INT Workshop, Seattle, September 24, 2010xF 1 -1
Full picture can be
surprising and
beautiful
Thank
You
INT Workshop, Seattle, September 24, 2010
Aram Kotzinian