Kein%20Folientitel

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Selected Recent Results on Parton
Distribution and Fragmentation Functions
Klaus Rith University of Erlangen-Nürnberg DESY
Main HERMES research topics
Origin of nucleon spin
Details of nucleon structure
Klaus Rith
Moriond QCD
March 19, 2009


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HERMES Spectrometer
e
HERA longitudinally polarized 27.6 GeV e/e- beam
Polarized and unpolarized internal gas target
(spin flip every 90 s)
Kinematics 0.02ltxlt0.7, 1.0 GeV2ltQ2lt15 GeV2
Data taking summer 1995 June 30, 2007
1995-2000 longitudinal target polarization,
2002-2005 transverse target pol. 2006-2007
unpolarized H, D targets Recoil Detector
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Leading-twist Parton Distributions
Complete description of nucleon by quark momentum
and spin distri-butions at leading-twist 3
kT-integrated distribution functions (DF)
Transversity DF
Unpolarised DF
Helicity DF
?q(x) ? h1q(x)
q(x) ? f1q (x)
?q(x) ? g1q(x)
well known
First glimpse
known
HERMES 1995-2000
HERMES 2002-2005
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Transverse Momentum Dependent DFs
Quark distribution functions
Boer-Mulders DF
(chiral-odd)
Transversity DF
(chiral-odd)
Sivers DF (T-odd)
Fragmentation functions (FF)
D1 ? Dqh normal FF,
H1?
spin-dependent Collins FF (chiral-odd)
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Quark Distributions from SIDIS
Flavor tagging
? E - E, Q2 -q2 -(l l )2
x Q2/(2M?) fraction of nucleons longitudinal
momentum carried by struck quark
K-
q(x) quark number density
K
Leading hadron originates with large probability
from struck quark Dqh(z) Fragmentation
function (FF)
z Eh/?


zq2?q(x) Dqh(z)
ALL (x,z) ?

zq2 q(x) Dqh(z)
Measure hadron asymmetries
Targets H, D h ?, K, p (identified with
RICH)
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Quark Helicity Distributions ?q(x)
PRD 71 (2005)
012003
u quarks large positive polarisation
d quarks negative polarisation ?d(x) ? - 0.4
?u(x)
Sea quarks (u, d, s) polarisation compatible
with 0.
HERMES
x
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The Strange Sea S(x), ?S(x)
Inputs Multiplicities for K and K- from
unpolarized deuteron
d2NDDIS/dxdQ2 KU(x,Q2)5 Q(x) 2S(x)
where Q(x) u(x)u(x)d(x)d(x) and S(x) s(x)
s(x)
d2NDK?/dxdQ2 KU(x,Q2)Q(x)?DQK(z)dz S(x)
?DSK(z)dz
where DQK(z) 4DuK(z)DdK(z) and DSK(z)
2DsK(z)
Inclusive and K, K- asymmetries from polarized
deuteron
A1,D d2NDIS/dxdQ2 KLL(x,Q2)5?Q(x) 2?S(x)
A1,DK?d2NK?/dxdQ2 KLL(x,Q2)?Q(x)?DQK(z)dz
?S(x) ?DSK(z)dz
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S(x) from Kaon Multiplicities
dNK? Q(x)?DQK(z)dz S(x) ?DSK(z)dz
?DQK(z)dz
x gt 0.3

?
dNDIS 5 Q(x) 2 S(x)
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P.L. B666 (2008) 466
S(x) from CTEQ6L with ?DQK(z)dz ?DSK(z)dz as
free parameters (dotted) does not fit the data
S(x) much softer than assumed by current PDFs
(mainly based on ? N?????X)
( )
Take ?DSK(z)dz 1.27 ? 0.13 from de Florian et
al.
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?S(x) from Kaon Asymmetries
P.L. B666 (2008) 466
?S 0.037 ? 0.019(stat.) ? 0.027(syst.)
compared to
?S - 0.085 ? 0.013(stat.) ? 0.012(syst.) from
inclusive data and SU(3)
Large negative contribution from low x?
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Transverse Azimuthal Angular Asymmetries
Amplitude has 2 components
Transversity DF
2?sin(? ?S)?hUT h1q(x)?H1?q(z)
Collins FF
U unpol. e?-beam T transv. pol. Target
Unpolarised FF
z Eh/?
2?sin(? - ?S)?hUT f1T?q(x)? D1q(z)
(Requires non-vanishing orbital angular momenta
Lq of quarks)
Sivers DF
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Collins Amplitudes
Transversity DF
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
?
2?sin(? ?S)?hUT h1q(x) ? H1?q(z)
?
?
?
Collins FF
First measurement of non-zero Collins effect
Both Collins fragmentation function and
transversity distribution function are sizeable
Surprisingly large ?- asymmetry
Possible source large contribution (with
opposite sign) from unfavored fragmentation,
i.e. u? ?- H1 ?,disf ? - H1 ?,fav
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Sivers Amplitudes
Sivers DF
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
?
2?sin(? - ?S)?hUT f1T?q(x) ? D1q(z)
?
?
?
First observation of non-zero Sivers distribution
function in DIS
Experimental evidence for orbital angular
momentum Lq of quarks But Quantitative
contribution of Lq to nucleon spin still unclear
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Transverse SSA for ? - ?-
access to Sivers valence distribution
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Azimuthal Asymmetries in Unpolarised SIDIS
Boer-Mulders DF
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
?
?
?
?
transversely polarised quarks in unpolarised
nucleon
2?cos(2?h)?
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Azimuthal Asymmetries in Unpolarised SIDIS
Cahn effect
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
?
?
?
?
Intrinsic transverse quark momentum
2?cos(?h)?
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Transverse Azimuthal Asymmetry in DIS
1-photon exchange approximation TAA forbidden
(Spin-flip every 90 s)
AN ? 0 Signature of 2-photon exchange
Compatible with zero !
AN O(10-3)
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Conclusions
HERMES provides new constraints for S(x) at low Q2
HERMES made a first glimpse at various Transverse
Momentum dependent parton Distribution functions
TMDs offer a large amount of new information on
the nucleon structure They need to be explored in
detail by the next generation of experiments at
future high-luminosity e-N facilities
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Backups
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TMDs in SIDIS
le
ST
?
If1TD1
Sivers
le
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
?
SL
le
?
?
?
?
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TMDs in SIDIS
le
ST
le
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
?
le
SL
?
?
?
?
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Cahn and Boer-Mulders effect
Boer-Mulders effect
Cahn effect
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Transverse SSA for pion pairs
JHEP 06 (2008) 017
First evidence for (transversity and) chiral-odd,
naive-T-odd spin-dependent di-hadron
fragmentation function
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Transverse SSA for pion pairs
h1,q
h1,q
Trans. component of relative momentum survives
integration over the Ph- of pair Collinear
kinematics (factorization, evolution) Simple
product of unknown functions Limited statistical
power
Explicit dependence on transverse momentum of
hadron Ph- Convolution of two unknown
functions High statistical power
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Azimuthal angular asymmetries
Transverse quark spin spin-dependent
fragmentation Azimuthal asymmetry
sin(? ? S)h
COLLINS
Left-right distribution asymmetry (due to orbital
angular momentum) final state interaction
Azimuthal asymmetry sin(? - ? S)h
SIVERS
green quark
anti-green remnant
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How to measure Transversity
Need another chiral-odd object!
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Sivers Amplitudes
Sivers DF
N/q U L T
U f1 h1
L g1 h1L
T f1T g1T h1 h1T
large!
T ?
2?sin(? - ?S)?hUT f1T?q(x) ? D1q(z)
?
?
?
First observation of non-zero Sivers distribution
function in DIS
Experimental evidence for orbital angular
momentum Lq of quarks But Quantitative
contribution of Lq to nucleon spin still unclear
Final result K enhancement will be smaller, Q2
dependent?
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2-D Collins Moments for ?
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2-D Sivers Moments for ?
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Extraction of Transversity

• Global fit
• HERMES, COMPASS, BELLE

(ed-gtehX)
(ee-gthhX)
(ep-gtehX)
First extraction of transversity distribution
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Sivers Extraction
xf1T?(x)