1. Study of spin structure of nucleon in COMPASS - measurements for transversity with a transversely polarized target –
T. Matsuda – Uni. of Miyazaki, Japan
on behalf of the COMPASS collaboration
1. The COMPASS experiment at CERN
2. Transversity measurements
1-hadron asymmetries
(Collins & Sivers asymmetries)
(2) 2-hadron correlation asymmetry
(3) L polarimetry
3. Summary and outlook
Joint Meeting of Pacific Region Particle Physics Communities
(DPF2006+JPS2006)
Oct.29-Nov.03,2006 Honolulu, Hawaii, USA

2. 1. The COMPASS experiment at CERN
The aim of COMPASS (muon beam program)
★gluon polarization
★longitudinal quark polarizations
　　　 (g1d, Δq flavour decompositon)
★Transversity
Using
Longitudinal PT
Transverse PT
Also Hadron beam program is scheduled.
Data taking History
2002 muon run (Longitudinal &Transverse Pol. Target)
2003 muon run (Longitudinal &Transverse Pol. target)
2004 muon run (L&T Pol. Target and Hadron Pilot run)
2006 muon run (only Longitudinal Pol. Target)
(muon beam share: longitudinal PT 80%, transeverse PT 20%)

3. --COMPASS spectrometer--
Polarized Target
SM1
RICH
ECal1 & Hcal1
Muon　filter 1
SM2
MWPCs
Micromegas &Drift chambers
ECal2 & Hcal2
Muon filter 2
GEM & MWPCs
SciFi
GEM & Straws
Silicon
Scintillating
fibers
~50m
Beam: 160 GeV m+
m/spill
(4.8s duration/16.2s repetition)
Polarization:
m Beam: ~80%
LiD Target:<50%>
m+ beam
Common Muon and Proton Apparatus for Structure and Spectroscopy

4. ーCompass 6LiD Polarized targetー
Dynamic Nuclear Polarization
Dilution factor: ~40%
Maximum Polarization:+57%
3He – 4He Dilution Cryostat
Longitudinal orientation
beam
Transverse orientation

5. Data taking by the transversely polarized target through 2002-2004
days of data taking (19), 2 periods
days of data taking (14), 1 period
days of data taking (24), 2 periods
trigger
(large x, Q2)
DAQ,
on line filter
Reconstructed DIS events

6. 2. Transversity measurement
(0) Transversity –introduction
(1) Transversity –1-hadron asymmetries
( Collins & Sivers asymmetries)
(2) Transversity –2-hadron correlation asymmetry
(3) Transversity –L polarimetry

7. What is Transversity？ ・Nucleon structure functions
are described with 3 functions
completely at leading twist
in the parton model.
Only DTq(x) is unknown !
・Dq(x) is different from DTq(x)
because rotation does not
commute with Lorentz boost
in relativity.
(Dq(x)＝DTq(x) in non-relativity)
・Dq(x) is a chirally even function,
DTq(x) is a chirally odd function (quark helicity flip).
longitudinal
transverse
・DTq(x) does not couple with gluon structure function, then its evolution with Q2 will be unlike Dq(x).
Inqualities
(Soffer’s inequality)

8. How do we measure transversity?
Quark helicity is conserved in totally
Inclusive Deep Inelastic Scattering(IDIS)
and transversity is not measured by IDIS,
because transversity needs quark helicty flip
in a helicity base.
(The quark coupling to gluon and photon preserve chirality.)
In case of Semi-Inclusive Deep Inelastic Scattering(SIDIS)
it is possible to measure transversity, because SIDIS allows both flip and non-flip cases.
Then we measure SIDIS events to study transversity.
To measure chirally odd quark distribution functions like transversity,
we need phenomena with chirally odd fragmentation functions.
At COMPASS we measure transversity by following 3 methods.
(1) Collins asymmetry (Sivers asymmetry is measured simultaneously.)
(2) 2-hadron correlation asymmetry
(3) L polarimetry

9. Collins and Sivers asymmetries Collins angle & Sivers angle.
fS = azim. angle of inital quark spin
fS’ = azim. angle of struck quark spin
fS= p- fS’ （due to helicity conservation)
fh =azim. Angle of leading hadron
Leading hadron
Collins angle
（Azimuthal angle of a leading hadron around a struck quark spin ）
FC = fh - fS’ (= fh +fS- p)
Sivers angle
（Azimuthal angle of a leading hadron around an initial quark spin (=nucleon spin))
FS= fh - fS
Initial quark spin (Target spin)
Struck quark spin
Scattering plane
quark direction
Leading hadron
（Breit frame）

10. Collins asymmerty and Sivers asymmetry
spin independent part
FF:
PRL96(2006)232002
Collins FF measured by BELLE
spin dependent part
If the spin information of the struck quark propagates to the fragment function, we observe Collins asymmetry.
Transversity
Collins asymmetry、
Spin-dependent FF
measure
transverse spin transfer coefficient
If quarks move asymmetrically around nucleon spin orientation, we also observe Sivers asymmetry.
　Sivers asymmetry
the effect of quark orbital
motion in nucleon
measure

11. Event selection for muons

12. Event selction cont. for hadrons
z>0.2 for all hadrons
for leading hadrons

13. Collins and Sivers asymmetries for all hadrons (2002-2004 data)
To be published in NPB hep-ex/
All hadrons (z>0.2)
Collins
asymmetry
very small or compatible to zero
Sivers
asymmetry
Black:Positive hadrons
White: Negative hadrons

14. Collins and Sivers asymmetries for leading hadrons (2002-2004 data)
Leading hadrons (z>0.25)
To be published in NPB hep-ex/
Collins
asymmetry
very small or compatible to zero
Sivers
asymmetry
Black:Positive hadrons
White: Negative hadrons

15. Collins, Sivers asymmetries
PID by RICH
Collins, Sivers asymmetries
All hadron z>0.2
Leading hadron z>0.25

16. Initial quark spin (Target spin)
(2) SSA in two hadron correlation Which angle we measure?  Trento conventions
see hep-ph/
fS = azim. angle of inital quark spin
fS’ = azim. angle of struck quark spin
fS= p- fS’ （due to helicity conservation)
ΦRS = φR - φS’ (= φR +φS- p)
Initial quark spin (Target spin)
Struck quark spin RT
R=(z2P1T-z1P2T)/(z1 +z2) Ph=P1+P2
RT is the component of R Ph .
fR = azimuthal angle of RT
quark direction

17. Two hadrons correlation --the interference frgmentaion function--
spin independent part
spin dependent part
FF:
z=z1+z2
also should be measured
If the spin information of the struck quark propagates to the interference fragmentation function, we observe the following asymmetry.
Transversity
measure
transverse spin transfer coefficient
interference FF
unknown at the moment

18. Event Selection-two hadron correlation-
For hadron in order to select the current fragmentation region
zh > 0.1 (then zh1+ zh2>0.2)
xfh > 0.1
For m
same as others.
exclusive r band K0
exclusive r cut r0
We choose one positve hadron and one negative hadron.

19. 2-hadron asymmetry (2002-2004 data)
very small or compatible to zero

20. Leading + Sub-Leading hadron pairs selections
Other pairs and other combinations analysis
Leading + Sub-Leading hadron pairs selections

21. (3) L polarimetry Struck quark spin Initial quark spin (Target spin)
Polarized fragmentation function
describing the spin transfer from
the quark to the final state L.

22. L polarimetry event selection

23. L polarizarion
L polarizarion

24. 3 Summary & Outlook transversity Next experiment
Collins and Sivers SSA shown
data (to be published in NPB, hep-ex/ )
SSA in two hadron correlation shown
data (preliminary)
L polarization shown data (preliminary)
asymmetries are small and compatible with zero.
Why? Cancellation between proton and neutron ?
　　Many theoretical works have been done and are ongoing.
Next experiment
Muon program with transverse proton target will be going on in > complementary and comparable accuracy to deuteron data expected

26. x vs Q2 distribution

27. Comparison of COMPASS 2002 results with HERMES ones.
（COMPASS;deuteron, HERMES;proton）
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
-0.2
-0.2
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
-0.2
-0.2 x z x z
Note:The sign of the original definition of HERMES is opposite.

28. Comparison of COMPASS 2003-2004 results with HERMES ones.

29. Collins and Sivers asymmetries for all hadrons (2002 final results)
PRL 94(2005)202002
All hadrons(z>0.2)
0.0
0.1
0.2
-0.2
-0.1
0.0
0.1
0.2
-0.2
-0.1
Collins
asymmetry
0.0
0.1
0.2
-0.2
-0.1
0.0
0.1
0.2
-0.2
-0.1
Sivers
asymmetry
Black:Positive hadrons
White: Negative hadrons

30. Collins and Sivers asymmetries for leading hadron (2002 final results)
PRL 94(2005)202002
Leading hadrons (z>0.25)
0.0
0.1
0.2
-0.2
-0.1
Collins
asymmetry
0.0
0.1
0.2
-0.2
-0.1
Sivers
asymmetry
Black:Positive hadrons
White: Negative hadrons

31. COMPASS Collaboration
More than 220 physicists from 30 Institutes
Bielefeld, Bochum, Bonn (ISKP & PI), Erlangen, Freiburg, Heidelberg, Mainz, München (LMU & TU)
Дубна (LPP and LNP), Москва (INR, LPI, State University), Протвино
CERN
Helsinki
Warsawa (SINS),
Warsawa (TU)
Nagoya/Chubu/Yamagata
Miyazaki/KEK
Saclay
Praha
Lisboa
Torino
(University,INFN),
Trieste
(University,INFN)
Burdwan,
Calcutta
Tel Aviv