1. Transversity
(transverse spin and transverse motion)
(unravelling the spin-orbital motion of partons?)
Towards transversity distributions: theory and experiments
Collins mechanism
Transverse Single Spin Asymmetries
Sivers mechanism
Spin and k┴ dependent parton distributions (TMD)
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

2. Parton distributions and (or
are fundamental leading-twist quark distributions
quark distribution – well known
all equally important
quark helicity distribution – known
transversity distribution – unknown
gluon helicity distribution – poorly known
related to
chiral-even
related to
chiral-odd
positivity bound
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

3. decouples from DIS (no quark helicity flip)+ + – – + = – + + + + + – =
in helicity basis + –
decouples from DIS (no quark helicity flip) + –
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

4. – + + – + – – + – + + – – + h1 x h1 h1 x Collins function
h1 must couple to another chiral-odd function. For example: D-Y, pp → l+l– X, and SIDIS, l p → l π X, processes – +
h1 x h1 – +
J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 + – + – + –
h1 x Collins function – + + –
J. Collins, 1993
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

5. – + +1 –1 No gluon contribution to h1 simple Q2 evolution
Q2 = 25 GeV2 Q02 = 0.23 GeV2
V. Barone, T. Calarco, A. Drago
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

6. h1 in Drell-Yan processes
Q2 = M2 l– γ* qT p p qL
Elementary LO interaction:
3 planes: plane
polarization vectors, ┴
plenty of spin effects
p-γ* plane, l+l– γ* plane
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

7. h1q (x, Q2) evolution much slower than
h1 from
at RHIC
RHIC energies:
small x1 and/or x2
h1q (x, Q2) evolution much slower than
Δq(x, Q2) and q(x, Q2) at small x
Barone, Calarco, Drago
ATT at RHIC is very small
smaller s would help
Martin, Schäfer, Stratmann, Vogelsang
talk by A. Mukherjee
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

8. Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora
h1 from
at GSI
large x1,x2
GSI energies:
one measures h1 in the quark valence region: ATT is estimated to be large, between 0.2 and 0.4
PAX proposal: hep-ex/
Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

9. talks by M. Guzzi, A. Bianconi
Energy for Drell-Yan processes
"safe region":
QCD corrections might be very large at smaller values of M:
yes, for cross-sections, not for ATT K-factor almost spin-independent
Fermilab E GeV/c
H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/
V. Barone et al., in preparation
talks by M. Guzzi, A. Bianconi
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

10. s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

11. s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

12. data from CERN WA39, π N processes, s = 80 GeV2
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

13. h1 x Collins from SIDIS processes
Asymmetry in the fragmentation of a transversely polarized quark φ Sq p┴ pq
(Fundamental QCD property? D. Sivers) q’ q y
initial q spin is transferred to final q', which fragments Sq
Sq’ p┴
“Trento conventions” ΦS Φh x
Amsterdam notations
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

14. neglecting intrinsic motion in partonic distributions:
Collins function
transversity
some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h1)
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

15. fit to HERMES data on Mauro Anselmino, Como, September 7, 2005
Transversity 2005

16. Extraction of Collins functions from HERMES + BELLE data
P1 depends on
(talk by R. Seidl)
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

17. Fits to HERMES Collins data, preliminary results
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

18. Fits to BELLE Collins data, preliminary results
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

19. HERMES + BELLE: Collins function is not zero
Theory: probably universal
Collins, Metz
Amrath, Bacchetta, Metz, Kundu, Mulders, …
Models: few, in disagreement
pion-quark vertex ? loop?
assumes h1 = ∆q
disfavoured Collins functions = 0
Talk by. A. Bacchetta
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

20. Alternative accesses to transversity
Inclusive Λ production and measure of Λ polarization
transverse fragmentation function p X
COMPASS analysis in progress
Talk by A. Ferrero
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

21. Two pion production: interference fragmentation function
Talks by P. van der Nat, M. Radici
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

22. Vector meson production:
(generalized fragmentation function)
Inclusive hadronic production:
Talk by F. Murgia
Single Spin Asymmetry in D-Y processes
(Boer-Mulders distribution)
Talks by D. Boer, G. Goldstein, M. Radici
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

23. Transverse SSA S p' p – p – p' PTy p' x PT θ z p
– p
– p'
Single Spin Asymmetry in elastic scattering. Example:
6 independent helicity amplitudes
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

24. for a generic configuration:y ΦS Φ x S p' PT θ p
– p z
– p'
for a generic configuration:
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

25. large SSA observed at hadron level
needs helicity flip + relative phase + – + + x + + + +
at quark level
large SSA observed at hadron level
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

26. SSA, pp → πX BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2
E704 √s = 20 GeV < pT < 2.0
STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5
E704 √s = 20 GeV 0.7 < pT < 2.0
SSA, pp → πX
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

27. Unweighted Collins moment: Unweighted Sivers moment:
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

28. Transverse Λ polarization in unpolarized p-Be scattering at Fermilab
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

29. Mauro Anselmino, Como, September 7, 2005
Transversity 2005

30. + – S Brodsky, Hwang, Schmidt model for Sivers function p X q q
diquark
diquark
needs k┴ dependent quark distribution in p↑: Sivers function
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

31. Sivers asymmetry in SIDIS
Amsterdam notations
Sivers asymmetry in SIDIS
talk by A. Prokudin
p┴ = PT – z k┴ + O(k┴2/Q2)
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

32. M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
hep-ph/ (PRD 71, ) and hep-ph/
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

33. Deuteron target Mauro Anselmino, Como, September 7, 2005
Transversity 2005

34. First p┴ moments of extracted Sivers functions, compared with models
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
First p┴ moments of extracted Sivers functions, compared with models
data from HERMES and COMPASS
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

35. SSA in p↑p → π X E704 data, E = 200 GeV
fit to AN with Sivers effects alone
maximized value of AN with Collins effects alone
U. D’Alesio, F. Murgia
M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

36. HERMES + E704: Sivers function is not zero
Talks by M. Burkardt D. Sivers, X. Artru
Spin-k┴ partonic correlations in nucleons
Theory: not quite universal
J. Collins, a “QCD theorem”
Models: few, in fair agreement
Talk by A. Baccheta
chiral models, A. Drago, P. Pobilytsa
M. Burkardt
Sum rules: talk by O. Teryaev
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

37. Looking forward to an interesting workshop, thanks!
Mauro Anselmino, Como, September 7, 2005
Transversity 2005