1. University of Erlangen-Nürnberg & DESY
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

2. HERMES Spectrometer e
HERA longitudinally polarized 27.6 GeV e+/e- beam
Polarized and unpolarized internal gas target (spin flip every 90 s)
Kinematics: 0.02<x<0.7, 1.0 GeV2<Q2<15 GeV2
Data taking: summer 1995 – June 30, 2007
RICH:
Hadron:  ~ 98%, K ~ 88% , P ~ 85%
: longitudinal target polarization, : transverse target pol.
: unpolarized H, D targets + Recoil Detector 2

3. q(x)  h1q(x) q(x)  f1q (x) q(x)  g1q(x)
Leading-twist Parton Distributions
Complete description of nucleon by quark momentum and spin distri-butions at leading-twist: 3 kT-integrated distribution functions (DF)
Unpolarised DF
Helicity DF
Transversity DF
q(x)  h1q(x)
q(x)  f1q (x)
q(x)  g1q(x)
well known
known
First glimpse
HERMES
HERMES 3

4. Quark distribution functions Fragmentation functions (FF)
Transverse Momentum Dependent DFs
Quark distribution functions f1
Boer-Mulders DF g1
(chiral-odd) h1
Transversity DF
(chiral-odd)
Sivers DF (T-odd)
Fragmentation functions (FF)
D1  Dqh = ‚normal‘ FF, H1 = spin-dependent Collins FF (chiral-odd) 4

5. Quark Distributions from SIDIS
Flavor tagging
 = E - E‘, Q2 = -q2 = -(l – l ‘)2
x = Q2/(2M) = fraction of nucleon‘s 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) 5

6. Quark Helicity Distributions q(x)
PRD 71 (2005)
u quarks: large positive polarisation
d quarks: negative polarisation
d(x)  u(x)
Sea quarks (u, d, s): polarisation compatible with 0.
HERMES x 6

7. 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] 7

8. S(x) from Kaon Multiplicities
dNK Q(x)DQK(z)dz + S(x) DSK(z)dz DQK(z)dz
x > 0.3
= 
dNDIS Q(x) + 2 S(x)
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. 8

9. S(x) from Kaon Asymmetries
P.L. B666 (2008) 466
S =  0.019(stat.)  0.027(syst.)
compared to
S =  0.013(stat.)  0.012(syst.) from inclusive data and SU(3)
Large negative contribution from low x? 9

10. 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 10

11. Collins Amplitudes Transversity DF Collins FF
N/q U L T f1 h1 g1
h1L
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 11

12. Sivers Amplitudes 2sin( - S)hUT ~ f1Tq(x)  D1q(z)
Sivers DF
N/q U L T f1 h1 g1
h1L
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 12

13. Transverse SSA for + - -
access to Sivers valence distribution 13

14. Azimuthal Asymmetries in Unpolarised SIDIS
Boer-Mulders DF
N/q U L T f1 h1 g1
h1L
f1T
g1T
h1 h1T kT sT    
transversely polarised quarks in unpolarised nucleon
2cos(2h) 14

15. Azimuthal Asymmetries in Unpolarised SIDIS
Cahn effect
N/q U L T f1 h1 g1
h1L
f1T
g1T
h1 h1T  kT   
Intrinsic transverse quark momentum
2cos(h) 15

16. 1-photon exchange approximation: TAA forbidden
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) 16

17. HERMES provides new constraints for S(x) at low Q2
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 17

18. Backups

19. TMDs in SIDIS I[f1TD1] I[h1H1┴] le ST le SL le Sivers Transversity
& Collins
I[f1TD1] 
Sivers d le
N/q U L T f1 h1 g1
h1L
f1T
g1T
h1 h1T  SL le    

20. TMDs in SIDIS I[h1TH1┴] ┴ I[g1TD1] ┴ I[h1LH1┴] ┴ le ST le SL le d f1
N/q U L T f1 h1 g1
h1L
f1T
g1T
h1 h1T 
I[h1LH1┴] ┴ SL le    

21. Cahn and Boer-Mulders effectkT sT
Boer-Mulders effect
Cahn effect kT

22. 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

23. 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

24. Azimuthal angular asymmetries
Transverse quark spin + spin-dependent fragmentation
Azimuthal asymmetry ~ sin( +  S)h
COLLINS h q
Left-right distribution asymmetry (due to orbital angular momentum) + final state interaction
Azimuthal asymmetry ~ sin( -  S)h
SIVERS
green quark
anti-green remnant

25. ? - + - + How to measure Transversity Need another chiral-odd object!
chiral even!
Transversity
Sq(pqxPh)
chiral odd fragmentation
function + -
SIDIS:
H1 h1

26. Sivers Amplitudes large! 2sin( - S)hUT ~ f1Tq(x)  D1q(z)
Sivers DF
N/q U L T f1 h1 g1
h1L
f1T
g1T
h1 h1T
large!
2sin( - S)hUT ~ f1Tq(x)  D1q(z)
T    
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? 12

27. 2-D Collins Moments for ±
x vs z
z vs Ph ┴
x vs Ph ┴

28. 2-D Sivers Moments for ±
x vs z
z vs Ph ┴
x vs Ph ┴

29. Extraction of Transversity
Global fit
HERMES, COMPASS, BELLE
(ep->ehX)
(ed->ehX)
(ee->hhX)
A. Prokudin at Transversity 2008
First extraction of
transversity distribution
Consistent picture
Also with new proton
data from COMPASS

30. Sivers Extraction
xf1T(x)
E. Boglione at Transversity 2008