1. Transversity New Results from COMPASS
Christian Schill Universität Freiburg
Graduiertenkolleg
Mainz, 7. Nov. 2007

2. Contents Introduction: Spin Structure of the Nucleon
The COMPASS experiment
COMPASS results on asymmetries
Transversity distribution function
Sivers distribution function
Other TMD distribution functions
Conclusions

3. Deep-Inelastic Scattering
Q² = negative transferred four-momentum squared
Investigation of the
proton structure
1955 Hofstadter: Radius 0,8 fm Nobel Prize 1961
1968 Friedman, Kendall, Taylor: Quarks in the proton Nobel Prize 1990
DESY: highest Q²
Quarks and gluons are the elementary constituents

4. Deep-Inelastic Scattering
inclusive
hadrons
semi-inclusive scattering:
detection of final hadrons
y = relative energy loss of scattered lepton
Q² = negative four-momentum transfer squared
x = Momentum fraction of the proton carried by the quark

5. Cross-Section in Deep-Inelastic Scattering
inclusive
hadrons
y = relative energy loss of scattered lepton
Q² = negative four-momentum transfer squared
x = Momentum fraction of the proton carried by the quark

6. Structure functions partons are point-like particles quark carries
1/3 of momentum

7. Structure functions partons are point-like particles parton carries
all momentum
quark carries
1/3 of momentum
x = Fraction of momentum carried
by the parton

8. Structure functions partons are point-like particles parton carries
all momentum
quark carries
1/3 of momentum
x = Fraction of momentum carried
by the parton

9. Structure functions partons are point-like particles parton carries
all momentum
gluons
reduce quark
momentum
contribution
quark carries
1/3 of momentum
with sea-quarks
x = Fraction of momentum carried
by the parton

10. Structure functions partons are point-like particles parton carries
all momentum
gluons
reduce quark
momentum
contribution
quark carries
1/3 of momentum
with sea-quarks
x = Fraction of momentum carried
by the parton

11. scattering on spin ½ particles scattering on point-like objects
Structure functions
scattering on spin ½ particles
Scale invariance
scattering on point-like objects
larger Q²
better Resolution
more Gluons and see-quarks
Q² dependence is described
by QCD x

12. Parton Distribution Functions
Parton model:
Parton Distribution Functions:

13. Polarized Deep Inelastic Scattering
Experimental Asymmetry:
g1: Spin structure function
Δqi: Polarized parton distribution function

14. Polarized Parton Distribution Functions
Parton model:

15. Transverse Spin Physics
At leading order, the inner structure of the nucleon can be described with
three Parton Distribution Functions:
q(x) Momentum distribution
Δq(x) Helicity distribution
ΔTq(x) Transversity distribution
Well known – Unpolarized DIS
known – Polarized DIS
Largely unknown

16. Transversity Distribution Function
DTq(x) = q↑↑(x) - q↑↓(x)
q=uv, dv, qsea
quark with spin parallel to the nucleon spin in a transversely polarized nucleon
Properties:
probes the relativistic nature of quark dynamics
positivity (Soffer) bound
sum rule for transverse spin
Bakker, Leader, Trueman, PRD 70 (04)

17. How to Measure Transversity?
Optical theorem:
leptonic
hadronic
Cross-section of
inclusive deep-
inelastic scattering:
Imaginary part of amplitude
of forward Compton scattering:
* + N  X
* + N  * + N

18. Structure Functions in Forward Compton Picture+ -
F1(x)  - +
g1(x)  - +
not possible in
inclusive deep-inelastic
scattering because of
quark helicity flip
ΔTq(x) 

19. Measuring Transversity
Only in Semi-inclusive
deep-inelastic scattering
DTq(x) FF
proton
quark
hadron(s)
Fragmentation
process into
hadrons responsible for
quark spin flip
Measured in COMPASS

20. Measuring Transversity
Can be measured in semi-inclusive deep-inelastic scattering on a transversely polarized target via “quark polarimetry”:
“Collins” asymmetry
“Collins” Fragmentation Function
Two-hadron asymmetry
“Interference” Fragmentation Function
Λ polarization
Fragmentation Function of q↑Λ

21. Collins Fragmentation - Model
Collins Effect in String Fragmentation
(X. Artru)

22. Collins Fragmentation - Model

23. Collins Asymmetry
SIDIS on a transversely polarized target: l N  l´h X
Fragmentation of a transversely polarized quark into hadrons
 azimuthal asymmetry:
The Collins angle Coll
is defined as:

24. Collins Asymmetry
The measured asymmetry AColl gives access to the transversity distribution
times the Collins fragmentation function:
f: Dilution factor
Dnn: Depolarization factor
Dnn=2(1-y)/(1+(1-y)2)
PT: Target polarization
Transversity distribution
Collins fragmentation
function (measured
in e+e- at BELLE)

25. Contents Transverse spin physics The COMPASS experiment
COMPASS results on asymmetries
Transversity distribution function
Sivers distribution function
Other TMD distribution functions
Conclusions

26. The COMPASS experiment
COmmon Muon Proton Apparatus for Structure and Spectroscopy
(270 physicists, 25 institutes, 11 countries)
high luminosity: ~ 4 ٠ 1032 cm-2 s -1
fixed target
160 GeV µ+ beam
Investigation of the spin
structure of the nucleon:
LHC
COMPASS
SPS

27. The COMPASS spectrometer
μ Filter
Calorimeters
50 m
Ring Imaging
Cherenkov detector
Straws
MWPC
Target
Gems
coverage of wide kinematical range:
SciFi
Detect 2 hadrons with Q=200 mrad acceptance
Excellent K/p separtion
Precise D0 mass reconstruction
High luminosity
Quasi dead time free DAQ capable of high rates
Drift chambers
10-5 < x < 0.5
10-3 < Q2 < 100 GeV2
μ beam
Micromegas
Silicon
from Germany: FR, MZ, ER, BN, BO, M, BI

28. The polarized 6LiD-Target
Two 60 cm long target cells
with opposite polarization
Superconducting
Dipole (0.5 T)
3He – 4He dilution
refrigerator
Vertex distribution:
T=50mK
Transverse target polarization:
Reversed once a week
Polarization 50 %
Dilution factor 0.38

29. Ring Imaging Cherenkov Detector
Identification of π, K and protons
Cherenkov thresholds: π ≈ 3 GeV/c
K ≈ 9 GeV/c
p ≈ 17 GeV/c
2σ π/K separation at 43 GeV/c
6 m
5 m
3 m
Radiator:
C4F10
Mirror
wall
CsI
MWPC

30. Transversity Data Sample
transversely polarized deuteron target
~ 20% of the running time
2002
2002
11 days
11 days
of data taking
of data taking (19),
2 periods
trigger (large x, Q2)
2003
2003
9 days
9 days
of data taking
of data taking (14),
1 period
+ PID (ECAL, RICH)
2004
2004
14 days
14 days
of data taking
of data taking (24),
2 periods
reconstructed
reconstructed
DIS events
DIS events
10 Mill.
DIS events
(10
(10 6 6 ) )

31. Contents Transverse spin physics The COMPASS experiment
COMPASS results on asymmetries
Transversity distribution function
Sivers distribution function
Other TMD distribution functions
Conclusions

32. COMPASS Results: Collins Effect
Deuteron
target  K
preliminary
only statistical errors shown (systematical errors considerably smaller)

33. Interpretation Parton model, valence region: isospin-symmetric
deuteron target
D1: favored FF
D2: disfavored FF
HERMES (DESY): Proton asymmetries  0
BELLE (KEK-B): Fragmentation functions  0
Small asymmetries  cancellation ΔTu(x) ≈ - ΔTd(x)

34. Collins: Interpretation
Global fit (COMPASS, HERMES, BELLE):
COMPASS data
Anselmino et al. hep-ph/

35. Collins: Global Fit HERMES data Global fit (COMPASS, HERMES, BELLE):
Anselmino et al. hep-ph/

36. Collins: Global Fit BELLE data Global fit (COMPASS, HERMES, BELLE):
Anselmino et al. hep-ph/

37. Results for Transversity
global fit
Soffer bound
Anselmino et al.
hep-ph/

38. Collins Fragmentation Function
Favored and
unfavored FF
with opposite sign
Anselmino et al.
hep-ph/

39. Measuring Transversity
Can be measured in semi-inclusive deep-inelastic scattering on a transversely polarized target via “quark polarimetry”:
“Collins” asymmetry
“Collins” Fragmentation Function
Two-hadron asymmetry
“Interference” Fragmentation Function
Λ polarization
Fragmentation Function of q↑Λ

40. Transversity in Hadron-Pair Production
Collins-Angle replaced by:
RS = R + S - π
R= angle between lepton
scattering plane and
two-hadron plane
(A. Bacchetta, M. Radici, hep-ph/ )
(X. Artru, hep-ph/ )

41. Azimuthal Asymmetry for Hadron-Pair Production
Target single spin asymmetry ARS(x,z,Mh2):
z=z1+z2
(X. Artru, hep-ph/ )
Two-hadron interference fragmentation function
presently unknown
can be measured
in e+e- (BELLE)
expected to depend on the hadron
pair invariant mass

42. Hadron Pairs Invariant Mass Spectra
all hadron pairs: M

43. COMPASS Results for Hadron Pairs
systematic uncertainty considerably smaller than statistical error

44. COMPASS Result for All Hadron Pairs
deuteron target

45. Interpretation Two-hadron Asymmetry: On a deuteron target:
Independent measurement from Collins asymmetry
with different fragmentation functions.
Data suggest as well: ΔTuv(x) = - ΔTdv(x)

46. Model Calculations
Model calculations for COMPASS kinematics (M. Radici, QCDN 06,
hep-ph/ ):
Model for transversity:
Soffer, Stratmann, Vogelsang,
P.R. D65 (02)
Korotkov, Nowak, Oganessian,
E.P.J. C18 (01) 639
Schweitzer et al.,
P.R. D64 (01)
Wakamatsu
P.L. B509 (01) 59
ΔTq(x)
xBj
Prediction for COMPASS:
small asymmetries
on the deuteron
ARS Mh

47. Model Predictions for a Proton Target
COMPASS kinematics
Proton Target
A.Bacchetta, M.Radici
PRD74(2006)114007
Model for Di-Hadron
Fragmentation Function
new data on a proton target have been already taken this year!

48. Contents Transverse spin physics The COMPASS experiment
COMPASS results on asymmetries
Transversity distribution function
Sivers distribution function
Other TMD distribution functions
Conclusions

49. The Sivers Distribution Function
most famous transverse momentum
dependent parton distribution function
describes an intrinsic asymmetry in the
parton transverse momentum distribution
induced by the nucleon spin
transverse
nucleon spin x
nucleon
momentum
it is related to the parton orbital
angular momentum in a transversely
polarized nucleon
quark density
M. Burkardt, PRD, 66, (2002)

50. Measurement of Sivers Asymmetry
The “Sivers angle” is
S = h - S
Independent from Collins angle,
possible to measure both effects in
the same data
h,,s azimuthal angles of the hadron,
transverse spin of the initial quark

51. COMPASS: Sivers Asymmetries K
only statistical errors shown (systematical errors considerably smaller)

52. Interpretation Parton model, valence region:
Small asymmetries suggest Δ0Tdv(x)  -Δ0Tuv(x)

53. Global Fit: Sivers Asymmetry
M. Anselmino et.al hep-ph/

54. Global Analysis: Sivers function
Extraction of the Sivers function from COMPASS & HERMES:
Δ0Tq(x)
Anselmino et al
Collins et al
Anselmino et al. hep-ph/

55. Contents Transverse spin physics The COMPASS experiment
COMPASS results on asymmetries
Transversity distribution function
Sivers distribution function
Other TMD distribution functions
Conclusions

56. Beyond Collins and Sivers Mechanism
SIDIS cross-section in one-photon exchange approximation:
8 transverse target spin dependent azimuthal modulations
...
Sivers
Collins
6 further
modulations
M. Diehl, S. Sapeta,
Eur.Phys.J C41 (2005)
hep-ph/
-photon flux

57. Results beyond Collins and Sivers
all transverse target spin asymmetries on the deuteron ≈ 0

58. Conclusions Compass results for Collins effect and Sivers effect
on the deuteron
Together with the Collins Fragmentation Function (BELLE)
and data on the proton (HERMES+COMPASS 2007):
TRANSVERSITY CAN BE MEASURED
First global analyses being done

59. Conclusions ΔTu(x) > 0 and Both ΔTu(x) and 2007 COMPASS data
ΔTd(x) < 0
Both ΔTu(x) and
ΔTd(x) do not saturate
Soffer bound
2007 COMPASS data
on a proton target
will allow us to
determine ΔTu(x) and
ΔTd(x) with greater
precision!

60. COMPASS 2007 Proton Transversity Run
Data taking just finished,
waiting for the first results…

61. Thank you!