Jim Stewart DESY Measurement of Quark Measurement of Quark Polarizations in Transversely Polarizations in Transversely and Longitudinally Polarized and Longitudinally Polarized Nucleons at HERMES Nucleons at HERMES for the Hermes collaboration • Introduction Introduction • The HERMES Experiment The HERMES Experiment • Measurement of the Quark Helicity Distributions Measurement of the Quark Helicity Distributions • Transversity Measurements at HERMES Transversity Measurements at HERMES • Summary Summary
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Jim Stewart DESY Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Nucleons at HERMES for the Hermes collaboration Introduction.
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Jim StewartDESY
Measurement of Quark Polarizations in Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Transversely and Longitudinally Polarized
Nucleons at HERMESNucleons at HERMES
for the Hermes collaboration
•IntroductionIntroduction•The HERMES ExperimentThe HERMES Experiment•Measurement of the Quark Helicity DistributionsMeasurement of the Quark Helicity Distributions•Transversity Measurements at HERMESTransversity Measurements at HERMES•SummarySummary
August 2004August 2004J. StewartJ. Stewart
Semi-Inclusive Deep Inelastic ScatteringSemi-Inclusive Deep Inelastic Scattering
2
lab
2
lab
22
had
(k k )
E
Q
Qx
2ME
z
E
q
The cross section can be expressed as a convolution of a The cross section can be expressed as a convolution of a
distribution function and a fragmentation function.distribution function and a fragmentation function.
3 distribution functions survive the integration over transverse quark momentum3 distribution functions survive the integration over transverse quark momentum
Virtual Photon Asymmetry - Path to Virtual Photon Asymmetry - Path to qq
3/ 2
N
N q
~ q(x)
S S 3/ 2
S S
"1/ 2
N
N q
~ q(x)
S S 1/ 2
S S
•Virtual photon can only couple to quarks of opposite helicityVirtual photon can only couple to quarks of opposite helicity
•Select quark helicity by changing target polarization directionSelect quark helicity by changing target polarization direction
•Different targets give sensitivity to different quark flavors Different targets give sensitivity to different quark flavors
,q (x) (x) (x)
( : , , , , , )
f f fq q
f u d s u d s
."
August 2004August 2004J. StewartJ. Stewart
Quark PolarizationsQuark Polarizations
2 2 2
1/ 2 3/ 2
2 2 21/ 2 3/
2
2
2
21 2 2
( ,Q )A ( ,Q )
( ) ( ,( ,Q ( )
(
) Q )
( ,Q )
( ,
~ ~( ,Q ) ( ,Q ) )
)
hh hf f f f
h h hf f
hq f
hq q q f
hq
f
h
f
e q x dzD z
e q x dzD
e q x dzD z
e dzD z
q
z
x
x
x
z q x
P
1, 1, 1, 1, 1,( ( ), ( ), ( ), ( ), ( ))Kp d p d pA A x A x A x A x A x
, , , ,u d u d s
Qu d u d s
Correlation between detected hadron Correlation between detected hadron and the struck quark allows and the struck quark allows flavor flavor separationseparation
Linear System in Linear System in Q
QA P
Inclusive DIS Inclusive DIS →→Semi-inclusiveSemi-inclusive →→ , , , ,u u d d s
August 2004August 2004J. StewartJ. Stewart
The HERMES ExperimentThe HERMES Experiment
•27.5 GeV polarized positron beam (<P>~53%)
•Longitudinally polarized H
•(<P>~85%)
•Transversely polarized H (<P>~78%)
August 2004August 2004J. StewartJ. Stewart
The Measured Hadron AsymmetriesThe Measured Hadron Asymmetries
Polarized parallel to the protonPolarized parallel to the proton
q x q x q x ."
u(x) 0
Polarized anti-parallel to the protonPolarized anti-parallel to the proton
d(x)<0
Good agreement with LO-QCD fitGood agreement with LO-QCD fit
u(x) and Δd(x)
u(x) and d(x) ~ 0
s < 0
No indication for No indication for
→0.028 ± 0.033 ± 0.009 0.028 ± 0.033 ± 0.009
Measured rangeMeasured range
Submitted Phys.Rev.DSubmitted Phys.Rev.D
August 2004August 2004J. StewartJ. Stewart
Properties of the Transversity DFsProperties of the Transversity DFs For non-relativistic quarks For non-relativistic quarks q(x)=q(x)=q(x)q(x)
→ q(x) probes the relativistic nature of the q(x) probes the relativistic nature of the quarksquarks
Due to Angular Momentum ConservationDue to Angular Momentum Conservation→ Different QCD evolutionDifferent QCD evolution→ No gluon componentNo gluon component
→ Predominately sensitive to valence quarksPredominately sensitive to valence quarks
BoundsBounds Soffer Bound: Soffer Bound:
T-evenT-even Chiral oddChiral odd
→ Not measurable in inclusive DISNot measurable in inclusive DIS
gives the produced hadron gives the produced hadron transverse momentumtransverse momentum
August 2004August 2004J. StewartJ. Stewart
Sivers Function fSivers Function f1T1T
(x)(x)
Distribution functionDistribution function→ Naïve T-ODDNaïve T-ODD→ Chiral evenChiral even
a remnant of the quark transverse momentum a remnant of the quark transverse momentum can survive the photo-absorption and the can survive the photo-absorption and the fragmentation processfragmentation process
Can be inherited in the transverse momentum Can be inherited in the transverse momentum component component → influence azimuthal distributioninfluence azimuthal distribution
Non-vanishing Sivers function requires quark Non-vanishing Sivers function requires quark orbital angular momentumorbital angular momentum
Cross section depends on the angle between Cross section depends on the angle between the target spin direction and the hadron the target spin direction and the hadron production planeproduction plane
August 2004August 2004J. StewartJ. Stewart
How to Measure TransversityHow to Measure Transversity
2 (1/ 2)1
2 (1/ 2)1 1
sin(
( , )
sin( )
( , )1,
( , ) ( , )
~ ( ) ( )
( ) ( )
)S
h S h S
UT ST h S h S
qq
qq TqS
N NA
S N N
e q x H z
e f x D z
Collins azimuthal momentCollins azimuthal moment
Sivers azimuthal momentSivers azimuthal moment
sin( )h
TS U
sin( )h
TS U Assuming gaussian distributions for initial Assuming gaussian distributions for initial
an final quark momentuman final quark momentum
August 2004August 2004J. StewartJ. Stewart
RESULTSRESULTSCollinsCollins
SiversSivers
u 0
usin( ) 0s
and ssin( ) 0 in( ) 0s s
Unexpected result:Unexpected result:
sin( ) sin( ) ss
- Possible interpretation:Possible interpretation:
1, 1,disf favH H
usin( ) 0 L 0s
Sivers MomentSivers Moment
More theoretical input needed to More theoretical input needed to clarify interpretationclarify interpretation
ff1T1T
(x) DIS = - f(x) DIS = - f1T1T
(x) DY (x) DY
UNIVERSALITYUNIVERSALITY
Collins MomentCollins Moment
- Same SizeSame Size
Submitted to Phys.Rev.Lett.Submitted to Phys.Rev.Lett.
August 2004August 2004J. StewartJ. Stewart
Summary and ConclusionsSummary and ConclusionsLongitudinally Polarized Target DataLongitudinally Polarized Target Data
First direct measurement of the helicity distributionsFirst direct measurement of the helicity distributions
Transversely Polarized Target DataTransversely Polarized Target Data Collins: Disfavored fragmentation functions appear to be Collins: Disfavored fragmentation functions appear to be
important and have opposite sign to the favoredimportant and have opposite sign to the favored Sivers: Amplitude is greater than zeroSivers: Amplitude is greater than zero
0, 0, , , 0u d u d s
August 2004August 2004J. StewartJ. Stewart
Polarized SeaPolarized Sea
Unpolarized data on sea shows Unpolarized data on sea shows the Gottfried sum rule is broken the Gottfried sum rule is broken