1. Transverse Spin Phenomena in Lepton Scattering Anna Martin Trieste University and INFN Trieste
October 4, 2006

2. in this field FANTASTIC PROGRESS SINCE SPIN2004
EXPERIMENTS:
Collins mechanism has been firmly established and there is a first check of universality
 transversity can be measured in SIDIS
Sivers mechanism is real
THEORY: important developments on
connection between Sivers effect
and Orbital Angular Momentum
assessing universality (lN vs pp)
... and many new ideas ...
VERY ACTIVE FIELD:
many interesting theoretical & experimental talks at
a lot of material: I will not be able to show all the results
Anna Martin

3. Content of this talk Polarised DIS and Experiments
Transversity Distribution Function
new results
Sivers Distribution Function
Other TMD Distribution Function
Conclusions
HERMES
COMPASS
CLAS
verificare numero talks
Anna Martin

4. Deep Inelastic Scattering
key role in investigating the partonic structure of the necleons
only the final lepton
is detected
inclusive DIS P
inclusive
hadrons
Q2 >> M2, W2>> M2
q= four momentum transferred to the nucleon
nu= lepton’s energy loss in the nucleon rest frame (sometimes ν = q · P). Here, E and E are the initial and final lepton energies in the nucleon rest frame
x =in the parton model, fraction of the nucleon’s momentum carried by the struck quark.
y=fraction of the lepton’s energy lost in the nucleon rest frame.
W2=is the mass squared of the system X recoiling against the scattered lepton.
W2 = (P + q)2 = M2 + 2Mν − Q2
in addition, detection of
final hadrons
semi-inclusive DIS
(SIDIS)
Anna Martin

5. Polarised SIDIS Experiments
transverse spin effects are an important part of the program of
the present experiments
HERMES at DESY
electron beam,
energy 27.5 GeV
internal H↑ gas target
( )
COMPASS at CERN
long pol m beam,
energy 160 GeV
solid state target
( with 6LiD↑)
JLAB experiments
electron beam,
energy 6 GeV to be upgraded to 12 GeV (long pol target, till now)
Anna Martin

6. CLAS 0.15 < x x 0.004 < x < 0.4 0.02 < x < 0.6 50 10050
100
Q2 [GeV/c]2
0.004 < x < 0.4
10 -3
10 -2
10 -1 1 x
Anna Martin

7. Content: Polarised DIS and Experiments
Transversity Distribution Function
new results
Sivers Distribution Function
Other TMD Distribution Function
Conclusions
Anna Martin

8. Spin Structure of the Nucleons
three quark distribution functions (DF) are necessary to describe the structure of the nucleon at LO
q(x)
f1q (x)
unpolarised DF
quark with momentum xP in a nucleon
well known – unpolarised DIS
helicity DF
quark with spin parallel to the nucleon spin in a longitudinally polarised nucleon
known – polarised DIS
Dq(x)
g1q(x)
DTq(x) = q↑↑(x) - q↑↓(x)
h1q(x),
dq(x),
dTq(x)
transversity DF
quark with spin parallel to the nucleon spin in a transversely polarised nucleon
still unkown
ALL 3 OF EQUAL IMPORTANCE
Anna Martin

9. Transversity Distribution Function
DTq(x), h1q(x), dq(x), dTq(x) , q=uv, vv, qsea
contribution of the quarks to the transverse spin of the nucleon
Properties:
is chiral-odd: decouples from incl DIS because helicity of quark must flip
probes the relativistic nature of quark dinamics
no contribution from the gluons  simple Q2 evolution
positivity (Soffer) bound
first moments: tensor charge
sum rule for transverse spin
Bakker, Leader, Trueman, PRD 70 (04)
Anna Martin

10. Transversity DF: how to measure it
the Transversity DF is chiral-odd:
observable effects are given only by the product of Tq (x) and an other chiral-odd function
can be measured in SIDIS on a transversely polarised target
via “quark polarimetry”
“Collins” asymmetry
“Collins” Fragmentation Function
hadron-pair asymmetry
“Interference” Fragmentation Function
Λ polarisation
Fragmentation Function of q↑Λ ….
Anna Martin

11. “Collins asymmetry” in
Measurement of the Transversity DF in SIDIS
“Collins asymmetry” in
the chiral-odd partner is the Collins Fragmentation Function
the “quark polarimetry” relies on the Collins effect (J. Collins, 93)
a quark moving “horizontally” and polarized “upwards” would emit the leading meson preferentially on the “left” side of the jet
 the fragmentation function has a spin dependent part
“Collins” FF:
unknown …
Anna Martin

12. Collins effect in SIDIS
distribution of the hadrons:
± refer to the opposite orientation of the transverse spin of the nucleon
PT is the target polarisation;
DNN is the transverse spin transfer coefficient initial  struck quark
the “Collins angle” is
C = h - s’ = h + S - p
C = h + S (Trento) C
h,s’,S azimuthal angles of hadron momentum, of the
spin of the fragmenting quark and of the nucleon
from the azimuthal distribution
of the hadrons one measures
the “Collins Asymmetry”
J. Collins, Nucl. Phys. B396 (1993) 161
F. Baldrachini, N.S. Craigie, V. Roberto, M. Socolovsky, Fortschritte der Physik 29 (1981) 505
using different targets (p, d, n) and identifying the final hadron one can perform flavour separation
unique feature of SIDIS
Anna Martin

13. What have we learnt over the past 2 years ? Collins Effect
great news from BELLE
measurement of the correlation between the azimuthal angles of p‘s in the near jet and in the far jet from e+e– annihilation
( … no results yet at ) j1
j2-p Q e- e+ A0
Final results
A12
spin2004
ref?
significant non-zero asymmetries, rising behavior with z z1
Collins effect is a real phenomenon
spin dependent FF can be measured in e+e– annihilation z2
Anna Martin

14. What have we learnt over the past 2 years
What have we learnt over the past 2 years ? Collins Asymmetry - p+ and p- asymmetries from HERMES
proton target
NEW RESULTS
(DIS2005)
data
unexpected large p-
positive p+ and negative p- asymmetries
confirmed with larger statistics:
the Collins FF is ≠ 0,
transverity is ≠ 0
Anna Martin

15. What have we learnt over the past 2 years
What have we learnt over the past 2 years ? Collins Asymmetry - h+ and h- asymmetries from COMPASS
deuteron target
PRL 94, (2005)
hadrons: mostly pions
2002 data
cancellation between p and n ?
NEW RESULTS
data
(DIS2006)
asymmetries
compatible
with zero
within the smaller
statistical errors
preliminary
preliminary
Anna Martin

16. What have we learnt over the past 2 years ? Collins Asymmetry
naïve interpretation of the data (parton model, valence region)
new proton data
preliminary
asymmetry for p+ ~ opposite to asymmetry for p-
 unfavored Collins FF ~ opposite favored Collins FF
at variance with unpolarised case
 u quark dominance
new deuteron data
preliminary
some (small) effect expected even if
 cancellation between Tu (x) and Td (x) handle on Td (x)
Anna Martin

17. What have we learnt over the past 2 years ?
recent theoretical work
Vogelsang Yuan, PRD 72, (2005)
Soffer bound
Efremov et al, PRD 73, (2006)
chiral quark-soliton model
Anselmino et al, BNL UM 2006
Soffer bound
& Tq = q
favored Collins FF ~
– unfavored Collins FF
u-dominance
agreement with Belle
comparison with the new COMPASS prelim data
RICH + AGS annual Users’ Meeting June 6,
2006, ags/users meetings/workshops/basp , and paper in
preparation.
Vogelsang and Yuan
preliminary COMPASS
Efremov et al
preliminary COMPASS
Anselmino et al, Tq = q
preliminary COMPASS
Anselmino et al, SB
preliminary COMPASS
Anna Martin

18. Also new: Collins asymmetry for K±
together with different targets, relevant for flavour decomposition
there are very recent results for the Collins asymmetry
on proton for K+ and K– (HERMES, DIS2006)
on deuteron for p+ and p– , K+ and K– (COMPASS, GPD06)
Aerogel n=1.03
C4F10 n=1.0014
C4F10
Anna Martin

19. Collins Asymmetry for Pions and Kaons
HERMES
preliminary
data
proton
COMPASS
sign
convention
COMPASS preliminary
data
deuteron
very recent results; comparison with phenomenological calculations already available (M. Anselmino et al)
Anna Martin

20. hadron-pair asymmetries
Measurement of the Transversity DF in SIDIS
hadron-pair asymmetries
alternative way to access transversity
measurement from HERMES using longitudinally polarised target data
NEW RESULTS:
measurements from HERMES and COMPASS
on transversely polarised proton and deuteron targets
more on Friday Session 2B R. Joosten, M. Contalbrigo, M. Radici
Anna Martin

21. Two Hadron Asymmetries
in inclusive production of hadron pairs, one can define the angle f R┴
and measure an azimuthal asymmetry from the modulation of the
number of events in fRS= fR┴ - fs’ or fRS= fR┴ + fS
presently unknown
can be measured in e+e- (BELLE)
expected to depend on the hadron pair invariant mass
Anna Martin

22. also these data can be described by models
What have we learnt over the past 2 years ? Two Hadron Asymmetries
NEW RESULTS deuteron target
NEW RESULTS proton target
data all +/- pairs x
data all +/- pairs
preliminary
A. Bacchetta, M. Radici hep-ph/ model for DiFF (expected to be overestimated)
proton
HERMES kin
deuteron COMPASS kin
positive moments for all invariant mass bins
first evidence for non-zero FF
 small errors (order of ~%)
 small asymmetries! cancellation?
similar results ordering in pTh, z inspired to the string fragm. model
also these data can be described by models
0.004<x<0.4
AND deuteron target
1/10
Anna Martin

23. Measurement of the Transversity DF in SIDIS
polarimetry
alternative way to access transversity
no results
NEW RESULTS from COMPASS presented here for the first time
more on Friday Session 2A A. Ferrero
Anna Martin

24. L polarimetry S
x 10 all Q2
Anna Martin

25. L polarimetry NEW systematic errors not larger than statistical errors
RICH ID not used yet
Anna Martin

26. Content: Polarised DIS and Experiments
Transversity Distribution Function
new results
Sivers Distribution Function
Other TMD Distribution Function
Conclusions
Anna Martin

27. Measurement of the Sivers DF in SIDIS
presently, the most studied in SIDIS together with the Transversity DF
it is one of the TMD parton distribution functions
is related to an intrinsic asymmetry in the parton transverse momentum distribution induced by the nucleon spin
requires final/initial-state interactions quark rescattering via soft gluon exchange
should change sign from SIDIS to DY
it is related to the parton orbital angular momentum in a transversely polarized nucleon
on its properties and the relation with angular momentum  talks by Budkart, Vogelsan, and several others in the next days
Anna Martin

28. Sivers Asymmetry S = h - S S
appears in SIDIS as a modulation in the “Sivers angle” S S
S = h - S
h azimuthal angle of hadron momentum
S azimuthal angle of the spin of the nucleon
J. Collins, Nucl. Phys. B396 (1993) 161
F. Baldrachini, N.S. Craigie, V. Roberto, M. Socolovsky, Fortschritte der Physik 29 (1981) 505
the “Sivers angle” S and the “Collins angle” C are independent
 the Collins and Sivers asymmetries can be disentangled and
extracted from the same data in SIDIS
Anna Martin

29. What have we learnt over the past 2 years ? Sivers Asymmetry
NEW RESULTS
data
proton target
data
Sivers moments as function of x, z and $P_{h\perp}$. The error band represents the maximal systematic uncertainty due to acceptance and detector smearing effects and due to a possible contribution from the $\cos\phi$ moment in the unpolarised cross section. The common overall scaling uncertainty is due to the target polarisation uncertainty. The average values of the asymmetry are pi+: A= / / and pi-: A= / / and for the kinematics the same as given in
 significant positive asymmetry for positive pions
with a factor ~4 in statistics p+ asymmetry > 0 p– asymmetry compatible with 0
the Sivers effect is a real effect
Anna Martin

30. What have we learnt over the past 2 years ? Sivers Asymmetry
deuteron target
2002 data
PRL 94, (2005)
hadrons: mostly pions
cancellation between p and n ?
NEW RESULTS
data
preliminary COMPASS
factor ~7 in statistics:
asymmetries still compatible with zero
Anna Martin

31. What have we learnt over the past 2 years ? Sivers Asymmetry
naïve interpretation of the data (valence region)
new proton data
preliminary
asymmetry for p+ > 0, asymmetry for p- ≈ 0
 Sivers DF for d-quark ≈ - 2 Sivers DF for u-quark 2
new deuteron data
preliminary
the measured asymmetries compatible with zero suggest
Anna Martin

32.  F. Bradamante talk, yesterday
What have we learnt over the past 2 years ? Sivers Asymmetry
also, the measured asymmetry on deuteron compatible with zero has been interpreted as
Evidence for the Absence of Gluon Orbital Angular Momentum in the Nucleon
S.J. Brodsky, S. Gardner
SLAC-PUB-12062, Aug Subm. Phys.Lett.B, hep-ph/
 F. Bradamante talk, yesterday
Anna Martin

33. first qualitative picture of the Sivers functions
What have we learnt over the past 2 years ? Sivers Asymmetry
recent theoretical work on the interpretation of the data
use of the new HERMES results to exctract the Sivers DF
Vogelsang Yuan (2005), Anselmino et al (2005), Collins et al (2006)
good fits to the new proton from HERMES
comparison (or fit) with the deuteron COMPASS 2002 data ok
with
Vogelsang, Yuan
Anselmino et al
Collins et al
RICH + AGS annual Users’ Meeting June 6,
2006, ags/users meetings/workshops/basp , and paper in
preparation.
Anselmino et al., hep-ph/
first qualitative picture of the Sivers functions
to progress more data from the experiments are vital
Anna Martin

34. Also new: Sivers Asymmetry for K±
HERMES
preliminary
K+ and K– on proton
(DIS06)
COMPASS preliminary
p+ and p– , K+ and K–
on deuteron
(GPD06)
very recent results; phenomenological calculations already available (M. Anselmino et al)
Anna Martin

35. Content: Polarised DIS and Experiments
Transversity Distribution Function
new results
Sivers Distribution Function
Other TMD Distribution Function
Conclusions
Anna Martin

36. other Azimuthal Asymmetries in SIDIS
related to TMD PDF and/or FF (LO)
inclusive DIS
Boer-Mulders, 98
long. polarized target
transv. polarized target
polarized beam and target
inclusive DIS
Anna Martin

37. TMD Asymmetries in SIDIS (LO)
AColl ~ sin(fh + fS) Collins asymmetry already seen
ASiv ~ sin(fh - fS) Sivers asymmetry
~ sin(3fh - fS) inverstigated at HERMES and COMPASS
~ cos(fh - fS) g1T and FF inverstigated at COMPASS
~ cos2fh “Boer-Mullders” DF and Collins FF
results from CLAS also for
and other higher order TMD Asymmetries
no preliminary
results yet
Anna Martin

38. (Boer – Mulders DF) can be measured in HERMES, COMPASS, CLAS, H1, ZEUS
correlation between the transverse momentum and transverse
spin of quarks in an unpolarised nucleon
times Collins FF
can be measured in HERMES, COMPASS, CLAS, H1, ZEUS
Barone et al. Phys.Lett. B632,277 (2006)
Anna Martin

39. CLAS 5.7 GeV (preliminary)
(Boer – Mulders DF)
difficult to measure
background higher twist terms (f. i. Cahn)
radiative correction, acceptance
+ …
M.Osipenko
CLAS 5.7 GeV (preliminary)
Anna Martin

40. Content: Polarised DIS and Experiments
Transversity Distribution Function
new results
Sivers Distribution Function
Other TMD Distribution Function
Conclusions
Anna Martin

41. Future measurements in SIDIS
“SHORT” TERM
Collins and Sivers asymmetries
more statistics from HERMES (2005 data)
p0 asymmetries (HERMES)
weighted asymmetries (HERMES and COMPASS)
Boer-Mulders, and other hadron asymmetries from HERMES, COMPASS, JLAB
Proton data from COMPASS (2007)
Neutron (p, d) data from JLAB (upgrade at 12 GeV)
“LONGER” TERM
the present experiments can not precisely map all transverse
spin effects in SIDIS
COMPASS program after 2010
polarized ep collider
Anna Martin