Measurement of TMDs in Semi-Inclusive DIS Rainer Joosten University of Bonn
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Transcript of Measurement of TMDs in Semi-Inclusive DIS Rainer Joosten University of Bonn
R. Joosten, Oct. 7, 2008
Measurement of TMDs in Semi-Inclusive DIS
Rainer JoostenUniversity of Bonn
Charlottesville, VA, October 7, 2008
R. Joosten, Oct. 7, 2008
Content of the talk
• SIDIS Experiments with transversely polarised target HERMES and COMPASS
• Transverse momentum in SIDIS
• Results• Unpolarized cross section
(Cahn effect, Boer-Mulders)• Sivers Distribution Function• Transversity Distribution Function, Collins Function• Other TMD Distribution Functions
• Conclusions
R. Joosten, Oct. 7, 2008
Perspective of the talk
I will focus on SIDIS reactions in one photon exchange
Kinematical Variable:
Q2 = -q2 @ 4 E E' sin2θ/2 resolution n = (El – El') photon energy xBj = Q2/2Mn momentum of the struck quark
z = Eh/n
exclusivity
l N l h X l q l qd DF d FF
(E,k)g* q=(n,q )
nucleon
<
R. Joosten, Oct. 7, 2008
Perspective of the talk
Also I will focus on 1 hadron production up to NLO
using different targets (p, d, n) and identifying the final hadron one can perform flavour separation
unique feature of SIDIS
R. Joosten, Oct. 7, 2008
SIDIS Experimentstransverse spin effects are an important part of the program ofthe experiments
JLAB experimentselectron beam, energy 6 GeV to be upgraded to 12 GeV
HERMES at DESYelectron beam, energy 27.5 GeV
COMPASS at CERN
long pol m beam, energy 160 GeV
R. Joosten, Oct. 7, 2008
results are coming from
Q2 – x range
COMPASS2002-2004
transverse data
CLAS
HERMES
results arecoming from
given the different beam energies, the Q2 – x range is different complementary
information, needed to study energy dependence and to disentangle higher order effects
R. Joosten, Oct. 7, 2008
HERMES
RICH PID: p, K, p ID
27.5 GeV e = 7 GeVs
Pure hydrogen gas target:
flipped at high frequency (60- 90 s)
1H→ <|Pt|> ~ 85 ±3.8 %2H→ <|Pt|> ~ 84 ±3.5 %
1H <|Pt|> ~ 74 ±4.2 %
R. Joosten, Oct. 7, 2008
SM1
SM2
m beam
MuonWall
MuonWall
E/HCAL E/HCAL
RICH
Polarised Target
COMPASS
two stage spectrometer Large Angle Spectrometer (SM1), Small Angle Spectrometer (SM2)
PID RICH in LAS
• high energy beam• large angular acceptance• broad kinematical range
beam:
160 GeV/c longitudinal polarisation -76% intensity 2·108 µ+/spill (4.8s/16.2s)
Polarized Target:
6LiD (PT ≈ 50%) or
NH3 (PT ≈ 85%)solid target cellsPolarization reversal: once a week
R. Joosten, Oct. 7, 2008
running with transversely polarized target2002-2004: 6LiD only
11 days(19)
9 days(14)
14 days(24)
proton only SIDISevents(106)
2007: NH3 target (protons)
Analyzed so far:
10·106 SIDIS events
(~20% of data)
For latest H
ERMES results,
see M. Contalbrig
o talk
in this session
For latest C
OMPASS proton
data, see H. Wollny‘s talk
in this session
R. Joosten, Oct. 7, 2008
How does transverse momentum enter?
- collinear QPM
DTq(x) = qT(x) – qT
(x)
Transversity
Integrated over kT: three quark distribution functions contribute in leading order
Dq(x) = q+(x) – q-(x)
Helicity
q(x) = q+(x) + q-(x)
f1(x)
g1(x)
h1(x)
R. Joosten, Oct. 7, 2008
Transverse momentum in the QPM
- collinear QPM - quark transverse momentum kT
Additional physics!
R. Joosten, Oct. 7, 2008
Transverse momentum
• … can be the transverse momentum kT of the quarks in the struck nucleon. It enters the PDFs (e.g. the Sivers PDF)
• … can be the transverse momentum of the fragmenting quark (and the produced hadron). It enters the PFF (e.g. the Collins FF)
• … can create kinematical effects (Cahn effect)
l N l h X l q l qd DF d FF
R. Joosten, Oct. 7, 2008
Full SIDIS cross-section in NLOA B
acchetta, M D
iehl, K G
oeke, A Metz, P
Mulders, M
Schlegel (06)
8 modulations(4 LO)
Sivers
Collins “Pretzelosity”
Cahn and Boer-Mulders
Unpolarized target
longitudinally polarized target
transversely polarized target
Kotzinian, NP B441 (1995) 234
Mulders and Tangermann, NP B461 (1996) 197
Boer and Mulders, PR D57 (1998) 5780
Bacchetta et al., PL B595 (2004) 309
Bacchetta et al., JHEP 0702 (2007) 093
NLO
General expression:
also valid for exclusive reactions and for entire phase space of SIDIS
18 structure functions
R. Joosten, Oct. 7, 2008
Kinematical corrections: Cahn effectl N l h X l q l qd DF d FF
Leading order QED with kT 0
After fragmentation:contributes to cos h and cos 2 h moments
Access to <kT>
R.N. Cahn PL B78 (1978) 269-273 …
R. Joosten, Oct. 7, 2008
SIDIS cross-section: PDFs and PFFsl N l h X l q l qd DF d FF
“Pretzelosity”
11 Hh
Boer Mulders
SiversCollins
1T1 Df 1T1 Hh 11 Hh
1T1 Dg ),( 2
Tkx
),( 2hPz
R. Joosten, Oct. 7, 2008
down
up
Boer Mulders effect
Relation to transverse space
proton
quarks
Side view Front view
A distortion in the distribution of quark spin in transverse space can give rise to a Boer-Mulders function Burkardt, hep-ph/0510408
Quark spin can be unevenly distributed in transverse space
A. Bacchetta
11 , Hh
Convoluted with Collins function
Contributes to cos h and cos 2 h moments
11cos
UUcos
UU , HhFF 2
R. Joosten, Oct. 7, 2008
Unpolarised Target SIDIS Cross-Section
Cahn effect, Boer-Mulders DF and pQCD
Boer- Mulders Collins FF, Cahn effect and pQCD
pQCD and beam polarisation
R. Joosten, Oct. 7, 2008
the azimuthal distributions have to be corrected by the apparatus acceptance
dedicated MC simulations for L and T target polarisation data
acceptance
final azimuthal distribution
the corrected azimuthal distributions are fitted:
Unpolarised Azimuthal Asymmetries
data sample: - part of the 2004 data- L and T target polarisation- each with both target configurations
to cancel possible polarisation effects
R. Joosten, Oct. 7, 2008
Deuteron target
Unpolarised Azimuthal Asymmetries cos modulation (Cahn + Boer-Mulders)
cosΑ
error bars: statistical errors
bands: systematical errors
First determination of charge dependent cos moments
R. Joosten, Oct. 7, 2008
Unpolarised Azimuthal Asymmetries cos modulation
comparison with theory
Effect up to 40%
NOT in agreement with predictions
R. Joosten, Oct. 7, 2008
Unpolarised Azimuthal Asymmetries cos2 modulation (Cahn + Boer-Mulders)
cos2Α
error bars: statistical errors
bands: systematical errors
First determination of charge dependent cos2 moments
Deuteron target
R. Joosten, Oct. 7, 2008
Unpolarised Azimuthal Asymmetries
cos2 modulation
comparison with theory
• pQCD charge independent
• Cahn charge independent(if kT
u = kTd )
• Boer–Mulders charge dependent
Effect up to 10%
Well in agreement with predictions
Indication for non-vanishing Boer-Mulders function
R. Joosten, Oct. 7, 2008
HERMES results on Cahn and Boer Mulders
Analysis is under way!
See F. Giordano‘s talk later to
day!
R. Joosten, Oct. 7, 2008
LO target transverse spin asymmetries
sin( )1 1
h s q hUT T qA f D sin( )
1 1h s q h
UT qA h H
cos( )1 1
h s q hLT T qA g D sin(3 )
1 1h s q h
UT T qA h H
Sivers Collins
8 Structure Functions for target transverse spin part, 4 LO
Pretzelosity“Boostisity”
R. Joosten, Oct. 7, 2008
Sivers effect
Distortions in transverse space
A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers function
The presence of spin can distort the distribution of quarks in transverse space (needs orbital angular momentum of quarks)
down
up
proton
quarks
Side view Front view
A. Bacchetta
1T1 , Df 1T1
)sin(UT
sh DfF
The Sivers asymmetry: ∑∑
q
hq
2q
q
hqT
qT1
2q
Siv )()(
)(),(
zDxfe
zDkxfeA
R. Joosten, Oct. 7, 2008
COMPASS Results: Sivers Effect
only statistical errors shown
Deuteron target
preliminary
preliminary
final results from 2002-2004 data [arXiv:0802.2160]
K0
Data are compatible with 0 !
Strong indication of cancelation of u and d quark Sivers Functions in deuteron target
Constrains d quark contribution in global fit
duT1T1Siv ffA
R. Joosten, Oct. 7, 2008
Sivers asymmetries
p are substantial and positive:
Evidence for a non-zero Sivers function
K: 2.3±0.3 times larger than p
Surprising for u-quark dominance expectations
large sea quark contribution?
)()( 1T1 zDxf
Proton target
p,K are compatible with 0
R. Joosten, Oct. 7, 2008
new results using latest HERMES (p) and COMPASS (d)
pion and kaon data
)()(A 1T1)sin
UTS zDxf qq(
usual unpolarised fragmentation function
extracting the Sivers function
R. Joosten, Oct. 7, 2008
h
h
q q
The Collins FF correlates the
transverse spin of the fragmenting quark and the
transverse momentum Ph of produced hadron h
Collins-effect
:),( Tq
1 pzH
11 Hh 11)sin(
UTsh HhF
The measured asymmetry AColl gives access to the transversity distribution times the Collins fragmentation function:
∑∑
q
hq
q2q
q Tq
1q1
2q
Coll )()(
),()(
zDxfe
pzHxheA
R. Joosten, Oct. 7, 2008
Collins asymmetries
• p asymmetries positive – u-quark dominance
• p large negative asymmetries – suggests
)()( fav,1
disfav,1 zHzH
• K+: consistent with p
• K of opposite sign from p – all-sea object
)()( 11 zHxh
Proton target
• p0 fulfills isospin symmetry
R. Joosten, Oct. 7, 2008
preliminary
COMPASS Results: Collins Effect
only statistical errors shown
Deuteron target
preliminary
final results from 2002-2004 data [arXiv:0802.2160]
K0Asymmetries compatible with 0 !
Again indication of cancelation of u and d Quark contribution for a deuteron target
Access to d quark contribution in global fit
du11Col hhA
R. Joosten, Oct. 7, 2008
)(1 zH
extracting transversity
l N l h X l q l qd DF d FF
Xqqee 2jet1jet pp
spin-dependent fragmentation
function
)(1 xh
hep-ex 0805.2975
See A. Vossen‘s talk later today!
R. Joosten, Oct. 7, 2008
Fits to Data
new results using latest HERMES (p)
COMPASS (d)
pion data,
and BELLE
data
A. Prokudin: Transversity 08, Ferrara
See A. Prokudin‘s talk
on Thursday!
fav1
fav1
2DH
unf1
unf1
2DH
R. Joosten, Oct. 7, 2008
……. Sivers
transversity
Transverse target spin asymmetries (4 LO)
by now all measured by COMPASS on deuteron (and proton)
pretzelosity
R. Joosten, Oct. 7, 2008
Target transverse spin results – (LO)
“Pretzelosity”
Avakian, Efremov, Schweitzer, Yuan, hep-ph/0808.3982
Estimate on the basis of the positivity limit
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g1T is the only parton DF which ischiral-even, T-even, leading twist function
in addition to the unpolarised DF and to the helicity DF
again cancellation between the u and d quarks in the deuteron ?
Target transverse spin results – (LO)
R. Joosten, Oct. 7, 2008
UUUU)2cos()cos( fixed parameters for:
unbinned Maximum Likelihood fitto the log of the weighted PDF :
definition of angles + asymmetries acc. to “Trento convention”
i
wi
iFL )(
)sin()sin(2)sin()sin(2[ Sh
UTSSh
UTSP
1,,,...,)sin( Sh
UTSi PF
)2sin()2sin(2)3sin()3sin(2 Sh
UTSSh
UTS
])sin()sin(2 Sh
UTS
…takes into account cross contamination of moments
[PRD70(2004),117504]
HERMES results on transverse target spin asymmetries
Accessible in the HERMES data!
Talk by Delia Hasch @ IWHSS 2008
R. Joosten, Oct. 7, 2008
target transverse spin dependent asymmetries (NLO)
R. Joosten, Oct. 7, 2008
target transverse spin dependent asymmetries (NLO)
R. Joosten, Oct. 7, 2008
CONCLUSIONS • Transversity, Collins Function and Sivers Function
Great progress in determining transversity, Sivers and Collins function based on pion and kaon data by
HERMES, Belle and COMPASS
• Boer Mulders Function and Cahn effect <kT>First COMPASS (d) data on charge dependent cos and cos 2 moments: Indication of non vanishing Boer-Mulders
functionHERMES data and COMPASS proton data underway
• Transverse Target Spin asymmetries (Pretzelosity, g1T)COMPASS transverse target spin asymmetries ondeuteron target available (LO and NLO):
no significant asymmetriesHERMES data on proton (LO) should be available soonCOMPASS proton data (LO and NLO) underway
R. Joosten, Oct. 7, 2008
Outlook
• We have abundant and good data on tape!
• There is more to come from COMPASS and JLAB(SIDIS, Drell-Yan, DVCS)
• Now we have to analyze all data and learn as much as possible from it!
See also A. Bacchetta’s talk on Thursday!
Thank You !!
R. Joosten, Oct. 7, 2008
R. Joosten, Oct. 7, 2008
Backup Slides
R. Joosten, Oct. 7, 2008
error bars: statistical errors
bands: systematical errors
2s y)(11y12y
ε
Unpolarised Azimuthal Asymmetries
ssin ε/Α
sin modulation
Effect well in agreement with 0 !
Deuteron target
R. Joosten, Oct. 7, 2008
Unpolarised Azimuthal Asymmetries sin modulation
Effect very small !
hep-ex/0612059v1
Proton target
R. Joosten, Oct. 7, 2008
p0 Collins asymmetries
neutral pions:results for the three pion charge
states are consistent with isospin symmetry
R. Joosten, Oct. 7, 2008
SIDIS kinematics
R. Joosten, Oct. 7, 2008
Full cross-section in NLO
NLO
R. Joosten, Oct. 7, 2008
Transversity
Boer-Mulders
Sivers
Pretzelosity
Parton distribution functions with transverse spin
11, Hh
11 , Hh
1T1 , Df
1T1 , Hh
R. Joosten, Oct. 7, 2008
Collins Asymmetry – Proton Datacomparison with M. Anselmino et al. predictions
statistical errors only; systematic errors ~ 0.3 stat
R. Joosten, Oct. 7, 2008
COMPASS proton datacomparison with the most recent predictions from M. Anselmino et al.
statistical errors only; systematic errors ~ 0.5 stat
R. Joosten, Oct. 7, 2008
R. Joosten, Oct. 7, 2008
R. Joosten, Oct. 7, 2008
)(1 zH
extracting transversity
l N l h X l q l qd DF d FF
Xqqee 2jet1jet pp
spin-dependent fragmentation
function
)(1 xh
hep-ex 0805.2975
See A. Vossen‘s talk later today!