1. HERa MEasurement of Spin
Collaboration of 180 phys., 33 Inst., 12 Countries
Introduction to
polarised DIS
Prerequisites
Polarised
structure functions
The Spin of the Nucleon
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

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 | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

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
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

4. What is Spin ? Spin and Symmetry: [S.Hawkins: A brief history of time]
2x360o
spin: spin: 1
math:
antisymmetric
wave function
180o o
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

5. is spin important ? Pauli principle … MATTER FORCES
obey Pauli principle
antisymmetric under exchange
of identical particles
Fermi-Dirac statistics:
Fermions
half integer SPIN
MATTER
don’t care for Pauli principle
symmetric
Bose-Einstein statistics:
Bosons
integer SPIN
FORCES
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

6. how to study the proton spin ?
… deep-inelastic scattering (DIS)
“deep” high resolution:
“inelastic”
 proton
has structure
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

7. DIS cross section leptonic part of the xsection
hadronic part of the xsection
 contains info on proton structure
+ strong interaction effects
leptonic part of the xsection
 independent of proton structure
 can be calculated explicitely
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

8. hadronic tensor parametrised by structure functions
(Lorentz symmetry, current conservation, parity, ecc.)
momentum distribution of quarks
QPM:
helicity distribution of quarks
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

9. 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 | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

10. the nucleon spin structure
gluons are important !
don’t forget the orbital angular momentum!
QPM:
EMC (‘88) DS=0.123 ± ...
Spin Puzzle
SLAC, CERN, DESY:
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

11. polarised deep inelastic scattering
inclusive dis
exclusive dis
inclusive
hadrons
polarised beam
and/or
polarised target
semi-inclusive
DIS
flavour separation
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

12. Hermes @ DESY Stern-Gerlach separation self-polarised electrons: e
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

13. how to measure xsections / asymmetries
q = const.
E’ = const.
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

14. how to measure g1 virtual photon asymmetry:
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

15. how to measure g1
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

16. the integral of g1 helicity distributions
(polarised quark distributions)
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

17. sum rules for g1 violated Bjorken sum rule: (isospin symmetry)
Bjorken sum rule 8% C.L.
violated
Ds=0
Bjorken sum rule:
(isospin symmetry)
fundamental QCD prediction
related to axial charges of proton:
measured in weak baryon decays
Ellis-Jaffe sum rule:
Ds=0
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

18. Dq from g1(x,Q2) parameterised one step further: evaluate parameter
minimisation :
evaluate
parameter
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

19. Dq and DG from g1(x,Q2) Duv Du Ds Ds Ddv Dd
Duv and Ddv (quite) well determined
Duv Du Ds Ds
Ddv Dd
Dq and DG weakly constraint by data
need more direct probes
flavour separation DG
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

20. 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 | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

21. polarised semi-inclusive DIS
polarised parton distribution functions !
known quantities
hadron asymmetries to be measured
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

22. 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________

23. quark/anti-quark helicity distributions
PURITY is an unpolarised quantity
needs at least six independent asymmetry sets A1h(x) to
determine six unknown helicity distributions: Du, Du, Dd, Dd, Ds, Ds
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

24. measured hadron asymmetries
proton
incl p+ h+
deuteron p- h+ h- p+ p- K+ K-
incl h- h- p-
K- us all sea objects x x
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

25. purities
conditional probability that g* hits 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 | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

26. quark/anti-quark helicity distributions
u quarks large positive polarisation
d quarks negative polarisation
sea quark (u, d, s ,s) compatible with 0 no indication for Ds < 0 -
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

27. ? where do we stand the (spin) structure of the nucleon … HERMES:
first glimpse
H1, ZEUS,++
HERMES
CERN
RHIC
SLAC ?
HERMES, ++
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

28. don’t forget the orbital angular momentum
hard exclusive processes…
exclusive dis
polarised beam
and/or
polarised target g
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

29. missing mass technique: Mx2=(p+q-Pg,p )2  s(Mx)~0.8 GeV
2005++ e+
detected
missing mass technique: Mx2=(p+q-Pg,p )2  s(Mx)~0.8 GeV
NOT detected
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

30. ? ? where do we stand the nucleon puzzle is going to be completed
the (spin) structure of the nucleon …
HERMES:
first glimpse
H1, ZEUS,++
HERMES
CERN
RHIC
SLAC
HERMES
CERN
RHIC
JLab
KEK
…ecc.
transversity ?
UPCOMING:
HERMES
JLab
lecture by its own ?
HERMES, ++
Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon
___Delia Hasch _______________________________________________________________Spin Physics at HERMES________

31. outlook to further HERMES activities
what happens in a nuclear medium:

32. outlook to further HERMES activities
what happens in a nuclear medium:
reduction of multiplicity of fast hadrons
 hard partonic + soft hadron interaction
cold hot
nuclear matter

33. outlook to further HERMES activities
exotic states

34. template
Thank you !