1. on behalf of the COMPASS collaboration
New target transverse spin dependent azimuthal asymmetries from COMPASS experiment
Bakur Parsamyan
INFN & University of Turin
on behalf of the COMPASS collaboration
SPIN - Praha
Prague, July 08 – 14, 2007

2. Outline General expression of polarized SIDIS cross-section
Target transverse spin asymmetries
COMPASS experimental setup
Event selection
Extraction
1D method
Systematic checks
2D method
Correlation Coefficients
Results
asymmetry, comparison with the model
Conclusions
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

3. General expression of polarized SIDIS cross-section
A.Kotzinian, Nucl. Phys. B441, 234 (1995).
Bacchetta, Diehl, Goeke, Metz, Mulders and Schlegel JHEP 0702:093,2007
This is a general,
model independent expression
which is also valid for exclusive reactions and for entire phase space of SIDIS (TFR, CFR)
Azimuthal modulations:
2 polarization independent
1 single beam polarization dependent
2 single target longitudinal polarization dependent
1 double beam + target longitudinal polarization dependent
5 single target transverse polarization dependent
3 double beam + target transverse polarization dependent
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

4. Target transverse spin dependent azimuthal modulations
General expression of polarized SIDIS cross-section
Target transverse spin dependent azimuthal modulations
Published by HERMES & COMPASS
For Collins and Sivers asymmetries from COMPASS see next talk by Girisan Venugopal
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

5. Transverse spin dependent azimuthal modulationsLT
8 – modulations.
5 – single spin
3 – double spin
ST - target polarization, Pbeam – beam polarization
– Depolarization factor
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

6. Twist-2 + kT/Q kinematical corrections:
Interpretation of the transverse asymmetries
Twist-2:
double spin
single spin
Twist-2 + kT/Q kinematical corrections:
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

7. Definition of the UT asymmetries
“raw” – indicates number event asymmetry extracted as an amplitude of the corresponding modulation
f - target dilution factor, ST - target polarization
– Depolarization factor
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

8. Definition of the LT asymmetries
f - target dilution factor, ST - target polarization
– Depolarization factor
- Single Spin Asymmetries
- Double Spin Asymmetries
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

9. COmmon Muon Proton Apparatus for Structure and Spectroscopy
The COMPASS Experimental Setup
COmmon Muon Proton Apparatus for Structure and Spectroscopy
Longitudinally polarized µ+ beam (160 Gev/c).
Longitudinally or Transversely polarized 6LiD target
Momentum, tracking and calorimetric measurements, PID
High energy beam
Large angular acceptance
Broad kinematical range
CERN SPS North Area.
Two stages spectrometer
Large Angle Spectrometer (SM1)
Small Angle Spectrometer (SM2)
Hadron & Muon high energy beams.
Beam rates: 108 muons/s, 5·107 hadrons/s.
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

10. Polarized target 2002-2004 6LiD: Target Polarization ±50%
superconductive
Solenoid (2.5 T)
Dipole (0.5 T)
LiD:
Target Polarization ±50%
dilution factor f ≈ 0.4
~20% of the time transversely polarized
For transverse runs polarization reversal in two cells each ~ 5days
Two 60 cm long 6LiD cells with opposite polarization
Data collected simultaneously for the two target spin orientations.
Longitudinal polarization Transverse polarization
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

11. Event selection (2002-2004 deuteron data)
DIS cuts :
Q2 > 1 GeV2
0.1 < y < 0.9
W > 5 GeV
All Hadrons :
z > 0.2
pt > 0.1 GeV/c
Year
Period
Positive hadrons
Negative hadrons
2002
P2B/P2C
0.71·106
0.59·106
P2H
0.48·106
0.40·106
2003
P1G/P1H
2.46·106
2.03·106
2004
W33/W34
2.12·106
1.74·106
W35/W36
2.75·106
2.26·106
Sum
8.52·106
7.02·106
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

12. The number-of-event asymmetries Azimuthal modulations
Extraction of the asymmetries
The number-of-event asymmetries
8 modulations combinations of φh and φS
Independent angles
Azimuthal modulations
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

13. Double Ratio method (NP B765 (2007) 31)
For each data taking period, each cell and polarization state the Φj distribution of the number of events can be presented like:
u - Up Stream cell, d - Down Stream cell,
+/- - target polarization
“ratio product” quantities
Under the reasonable assumption on the ratio of the acceptances -
to be constant before and after polarization reversal in each Φj bin:
Acceptance differences cancel out
minimizes acceptance effects
spin independent terms cancel at 1st order (Cahn)
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

14. 1-D fitting procedure (MINUIT with minimization method)
9 – XBj, 8 – z, 9 - PhT bins and 16 Φj bins.
Fitting the “ratio product”
quantities
Newly extracted Collins & Sivers asymmetries gave the same result as published (NP B765 (2007) 31)
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

15. Periods compatibility
Systematic checks
Periods compatibility
Asymmetries from each period were compared with the weighed mean from all periods.
Par[0] test
Extracted from the fit par[0] ≈ 1 (acceptance cancellation)
Stability of the acceptance in Φj angles
The quality of the fit
- distribution
(acceptance assumption)
Systematic errors are smaller than statistical
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

16. 2-D fitting procedure (9 parameter fit using MINUIT)
9 – XBj, 8 - z, 9 - PhT bins and 8x8 – φh,φS bins.
Fitting function
Fitting the “ratio product” quantities
Results from 1D and 2D fits are in good agreement, only 1D results have been released
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

17. Correlation Coefficients (positive hadrons, x)
- Correlation between Collins and Sivers asymmetries
For the most of the pairs of parameters
ρ≈0 and always < 0.4
Only some correlation coefficients are larger than 0.1
Correlations are small or negligible x
preliminary
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

18. Correlation Coefficients (+/- hadrons, x, z and PT)
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

19. Results for (2002-2004 deuteron data, 1D fit)
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

20. Results for (2002-2004 deuteron data, 1D fit)
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

21. Results for (2002-2004 deuteron data, 1D fit)
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

22. asymmetry (PRD73:114017,2006)
First estimations by A.Kotzinian & P.Mulders, PRD 54, 1229 (1996)
A.Kotzinian, B.Parsamyan & A.Prokudin, PRD73:114017,(2006)
Deuteron
Proton
Lorentz Invariance Relations:
Deuteron
Proton
Predicted for COMPASS kinematical range and
deuteron target asymmetry is small ≈ 1-2%
Measured is small, compatible with zero.
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

23. ALT asymmetry (COMPASS) PRD73:114017,(2006)
Kinematical cuts: Q2>1.0 (GeV/c)2, W2>25 GeV2, 0.05<xBj<0.6, 0.5 < y < 0.9, 0.4 < z < 0.9
The predicted asymmetries are small (few % for deuteron target) in COMPASS “preferable” (with sizable statistics) kinematical regions.
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

24. ALT asymmetry (HERMES & JLab) PRD73:114017,(2006)
Kinematical cuts (HERMES): - Q2>1.0 (GeV/c)2, W2>10 GeV2, 0.1<xBj<0.6, < y < 0.85, 0.4 < z < 0.9
Kinematical cuts (JLab): - Q2>1.0 (GeV/c)2, W2>4 GeV2, 0.2<xBj<0.6, 0.4 < y < 0.7, 0.4 < z < 0.7
The predicted asymmetries can reach up to ~10% for proton target and up to ~6-7% for deuteron target with high x, y, z and pT cuts at HERMES and JLab kinematics.
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

25. Conclusions
6 new asymmetries were measured in COMPASS ( deuteron data)
Analysis was done using 1 dimensional and 2 dimensional fitting procedures
Asymmetries obtained from both methods are in agreement and point to the same physical result.
Only 1D results have been released
Correlation coefficients obtained from 2 dimensional fit are negligible or small
In most of the cases ρ ≈ 0 and always < 0.4
Results have been checked for systematic effects
Systematical errors appears to be smaller than statistical
All measured asymmetries are compatible with zero within statistical accuracy…
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

26. The end
Thank you!!!
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

27. Additional slides
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

28. All ingredients (DFs & FFs) are known!
ALT asymmetry PRD 54, 1229 (1996)
First estimations by A.Kotzinian & P.Mulders, PRD 54, 1229 (1996)
Weighted asymmetry is related to the first kT-momentum of g1T:
There exists a relation between first momentum of g1T and g2
(follows from Lorentz invariance, Tangerman & Mulders) :
All ingredients (DFs & FFs) are known!
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

29. ALT asymmetry PRD73:114017,(2006)
A.Kotzinian, B.Parsamyan & A. Prokudin, Phys.Rev. D73 (2006)
From analysis of unpolarized PhT dependence and Cahn effect
Naïve positivity constraint:
N is fixed by
holds if
Predictions done for:
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan

30. ALT asymmetry, kinematical cuts PRD73:114017,(2006)+
Low
x, y, z & pT
High
ATMD=
GRV98+GRSV2000 LO, std DFs Kretzer FFs
COMPASS - Q2>1.0 (GeV/c)2, W2>25 GeV2, 0.05<xBj<0.6, 0.5 < y < 0.9, 0.4 < z < 0.9, |Ph,T| > 0.5GeV/c
HERMES - Q2>1.0 (GeV/c)2, W2>10 GeV2, 0.1<xBj<0.6, < y < 0.85, 0.4 < z < 0.9, |Ph,T| > 0.5GeV/c
JLab - Q2>1.0 (GeV/c)2, W2>4 GeV2, 0.2<xBj<0.6, 0.4 < y < 0.7, 0.4 < z < 0.7, |Ph,T| > 0.5GeV/c
SPIN – Praha – 2007, July 08-14
Bakur Parsamyan