1. Spin structure of the nucleon
Delia Hasch
introduction to polarised DIS
prerequisites
quark polarisation
gluon polarisation
the (spin) structure of the nucleon

2. fascinated by spin …. N. Bohr W. Pauli
“You think you understand something? Now add spin…” -- R. Jaffe
W. Pauli
N. Bohr
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

3. what is spin ? Stern-Gerlach (1921): Uhlenbeck, Goudsmit: (1925)[
Stern-Gerlach (1921):
Uhlenbeck, Goudsmit:
(1925)
explanation of atomic spectra
quantum number: ms=1/2
Pauli : exclusion principle
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

4. how to study the nucleon structure ?
… deep-inelastic scattering (DIS)
 Q2 determines the resolution
“deep” high resolution:
 nucleon
has a structure
“inelastic”
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

5. the nucleon spin structure
gluons are important ! DG
sea quarks: Dqs
don’t forget the orbital angular momentum!
QPM:
EMC 1988:
DS=0.123 ± ...
Spin Puzzle
SLAC, CERN, DESY: DS 
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

6. helicity densities Dq
because of helicity conservation, the virtual photon can
couple only to a quark of opposite helicity
by changing the orientation of target nucleon spin or the helicity of incident lepton beam we can select q+(x) or q-(x)  Dq
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

7. experimental prerequisites (Hermes)
resolution: dp/p~2%, dq<1 mrad
particle ID: lepton ID with e~98%, hadron contamination <1%
RICH: p, K, p ID within 2<Eh<15 GeV
Stern-Gerlach separation
self-polarised electrons: e
27.5 GeV (e+/e-)
<Pb>~ 0.53±0.03
Stern-Gerlach separation
pure nuclear-polarised atomic gas,
flipped at 90s time intervals, <Pt>~0.85 ±0.04
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

8. DIS cross section leptonic part of the cross section
hadronic part of the cross section
 contains information on nucleon structure
 cannot be calculated from first principles
leptonic part of the cross section
 independent of nucleon structure
 can be calculated explicitely
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

9. hadronic tensor parametrised by structure functions
(symmetry considerations, conservation laws)
momentum distribution of quarks
QPM:
helicity distribution of quarks
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

10. how to measure cross sections / asymmetries
q = const.
E’ = const.
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

11. quark helicity distributions
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

12. Dq and DG from inclusive data (QCD fit)
one step further (evolution equations):
parameterised
minimisation :
evaluate
parameters
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

13. Dq and DG from inclusive data
Duv and Ddv (quite) well determined:
Duv >0, Ddv <0
Dq and DG weakly constraint by data
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

14. how to further proceed ?
unpolarised DIS
Dq and DG from inclusive DIS data: via evolution equations
requires wide kinematic
range in Q2 and x
only fixed target spin
experiments so far …
need polarised collider to
extend kinematic coverage
need more direct
probes
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

15. polarised semi-inclusive DIS
, z=Eh/n
probability that struck quark
of flavour f fragments into
hadron of type h with energy
fraction z
flavour tagging
p+ ud
fragmentation
function
K- us
p- ud
distribution
function
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

16. polarised quark distributions
flavour separation by flavour tagging
flavour content of final state hadrons
related to flavour of struck quark via
fragmentation functions
Dqh not well known at √s~5-20 GeV of current polarised DIS experiments 
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

17. particle identification
double radiator RICH for p / K / p separation
aerogel: n=1.03
C4F10: n=1.0014
Cerenkov light emission:
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

18. purity analysis @ HERMES
Delia Hasch Physics at Hermes Trieste (Italy),

19. measured hadron asymmetries
proton
HERMES
incl p+ h+
deuteron
HERMES p- h+ h- p+ p- K+ K-
incl h- h- p-
K- us all sea objects x x
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

20. purities p+ p- u u d d s s K+ K-
probability that g* hit a quark of flavour q when hadron of type h was detected u u d d s s p+ K+ p- K-
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

21. quark/anti-quark helicity distributions
[HERMES, PRL92(2004), PRD71(2005)]
u quarks large positive polarisation
d quarks negative polarisation
sea quarks (u, d, s ,s) compatible with 0 -
first direct 5-flavour separation of
polarised PDFs
new data from COMPASS/RHIC coming
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

22. how to measure the gluon polarisation DG
…reminder: from scaling violation
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

23. direct measurement of DG
method: photon-gluon fusion q
t  ħ/2mq
open charm production
(hard scale: mass of c-quark)
 theoretically very clean: c g g* D
cc-bar  D* , D0
g*p  D0 D0-bar X 
 experimentally very challenging:
 vertex reconstruction
inside massive target
 S/B
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

24. direct measurement of DG
method: photon-gluon fusion q
t  ħ/2mq
hadron pairs with high transv.
momenta (hard scale: PT)
 experimentally very clean g g* h1 h2
 highly model dependent
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

25. G from high-pT hadron pairs
3 main contributions to *p  h+h- X : h2 h2 h2 * q q * * q V q g p g q q h1 h1
QCDC
VMD
PGF h1
AQCDC ~ q/q
AVDM = 0
APGF  G/G
Contributions shown from paper: Pythia 5 … ! Infinite systematic error ! :-o
 applicable at HERMES (COMPASS) ? : kine / resolved photons / intrinsic k_T
 new Pythia 6 tuned to HERMES multiplicities: f_PGF much smaller
 first time: sys. error estimated (Patty thesis) -- new paper in preparation
 HERMES: quasi-real photoproduction
estimate their relative
contributions: Monte Carlo…
0.5 -1
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

26. G from high-pT hadron pairs
3 main contributions to *p  h+h- X : h2 h2 h2 * q q * * q V q g p g q q h1 h1
QCDC
VMD
PGF h1
AQCDC ~ q/q
AVDM = 0
APGF  G/G
Contributions shown from paper: Pythia 5 … ! Infinite systematic error ! :-o
 applicable at HERMES (COMPASS) ? : kine / resolved photons / intrinsic k_T
 new Pythia 6 tuned to HERMES multiplicities: f_PGF much smaller
 first time: sys. error estimated (Patty thesis) -- new paper in preparation
 HERMES: quasi-real photoproduction
[PRL84(2000)]
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

27. G from high-pT hadron pairs
first glimpse:
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

28. G from high-pT hadron pairs
first glimps:
complementary
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

29. pp  p0X is sensitive to gg gg and gq gq
G from p0 at RHIC
pp  p0X is sensitive to gg gg and gq gq
STAR
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

30. pp  p0X is sensitive to gg gg and gq gq
G from p0 at RHIC
pp  p0X is sensitive to gg gg and gq gq
fractional contributions:
uncertainty still large ...
dramatic improvement by lumi and
beam polarization (~70%)
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

31. future G measurements (2010)
COMPASS :
 open charm
 high PT
first glimps:
HERMES :
 high PT on d
RHIC :
 p0
 jets
 prompt g
 charm/bottom
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05

32. Gluon Polarization at RHIC
Longitudinal double spin asymmetry in :
Dominant processes:
 or 
photon
 or 
(heavy flavor)
Direct photon production
Di-jet production

33. ? ? where do we stand the nucleon puzzle is going to be completed
the (spin) structure of the nucleon …
HERMES:
first glimpse
NMC,BCDMS,E665,
H1, ZEUS
COMPASS
RHIC
HERMES
COMPASS
RHIC
JLab
KEK
…ecc.
exclusive processes
first results:
HERMES
JLab
transversity ?
HERMES
(SMC, SLAC)
 Compass
 RHIC
seminar by its own ?
seminar by its own
preface | introduction to polarised DIS | prerequisites | quark polarisation | gluon polarisation | the (spin) structure of the nucleon
Delia Hasch spin structure of the nucleon GK: Freiburg-University 06/07/05