1. Transversity: New Developments in Nucleon Spin Structure
ECT*, June 2004
Transversity
&
Friends
Next: Frascati June 2006

2. SIDIS:Theory Amsterdam group (Mulders,Boer,Pijlman..)
Classifiacation of TMDs up to twist-3 (theory overview and developments)
INFN (Anselmino,Kotzinian,D’Alesio,Radici…)
Fenomenology of kT dependence for cross sections, asymmetries
Bochum-Regensburg (Metz,Goeke,Bacchetta,Schweitzer…)
Universality,Sivers and Collins functions
Collins (factorization,universality)
BHS (Brodsky, Hwang,…)
FSI, relations between TMDs and GPDs
Others (Penn State,NMSU,Boston,Genova, Portland,DESY..)
transversity,Sivers,twist-3…
Mariland (Ji, Yuan, Ma,…)
Dubna (Efremov, Teryaev,..)
Others (Osaka,Peking,JLab,..)

3. A.Miller

4. R. Joosten

5. Many theory talks on 2p production as an alternative to access transversity in SIDIS!!!
Also accessible at CLAS!
P. van der Nat

6. C. Aidala

7. Universality of Distribution & Fragmentation functions
J. Collins
3 soft blobs make the gauge-link topology complex
Metz
Cancellations give the same Collins fragmentation function in DIS and e+e- annihilation
We cannot (yet) model the Collins FF reliably
enough to use it to extract h1!!!
pion loop
gluon loop
kT-dependent distribution and fragmentation functions are universal !
H. Avakian, JLab June 27, 2004

8. ➡ quarks from “far” surface should dominate
Understanding the Sivers mechanism
D. Sivers
Parton energy loss considerations suggest quenching of jets from “near” surface of target
➡ quarks from “far” surface should dominate
M.Burkardt
\phi_S = +90^\circ,\ \phi_h = 0^\circ \ \rightarrow\ \mathrm{predict}\ \langle \sin(\phi_h-\phi_S)\rangle_\mathrm{UT}^{\pi+} < 0
Asymmetric u-quark distribution+ FSI result in SSA

9. TMD distributions and SSA
Beam SSA
Introducing a new twist-3 distribution function g1┴ arising due to unaccounted before gauge link. Factorization of twist-3 contributions not proved yet!
Fetze Pijlman
Single spin asymmetries ALU and AUL observed at HERMES and CLAS described in one framework a la Afanasev-Carlson and their relation to new twist-3 distribution functions.
Marc Schlegel
Leonard Gamberg
Calculate and via 1-gluon
Exchange in quark-diquark
\phi_S = +90^\circ,\ \phi_h = 0^\circ \ \rightarrow\ \mathrm{predict}\ \langle \sin(\phi_h-\phi_S)\rangle_\mathrm{UT}^{\pi+} < 0
Only 5 from 8 twist-2 functions functions are independent. Some chiral-odd functions are equal to chiral-even functions (h1L=g1).
Not confirmed by others!
Elvio Di Salvo

10. With kT-effects in pp scattering pQCD works for E704
U. D’Alesio
add kT

11. E704 SSA: Sivers effect Analyzing power:
Analysis by Anselmino et al, E704
Sivers effect only
can explain the data
Collins effect alone
Can’t explain the data
(result of account of kT)

12. Hadron transverse momentum dependence
A. Kotzinian

13. Results: p on P & D targets
A.Kotzinian
Only Sivers effect
is enough to describe
the HERMES AUL

14. A.Kotzinian

15. SIDIS
A.Kotzinian
If Sivers dominates, the same SSA with “-” sign should be in the target fragmentation region

16. Modified LEPTO MC predictions for JLAB SSA
A. Kotzinian
Opposite signs of asymmetry in the target and current fragmentation
In principle, one can check origin of by measuring it in the TFR

17. End of Story?
A.Kotzinian
Zoology of FracFun

18. M. Diehl: Generalized Parton Distributions & Transversity
GPD’s and Lattice QCD
N.Makins (summary talk)
M. Diehl: Generalized Parton Distributions & Transversity
● But now there are 8 GPD’s:
(please!)
● We thought there were 4 GPD’s:
● New GPD gives transversity in forward limit
... but if you go off-forward, gluons can contribute! (via L)
Important point: GPD’s and kT-dependent PDF’s
give complementary information
GPD’s = distribution of partons in transverse space
TMD PDF’s = distribution of partons in transverse momentum
H, \tilde{H}, E, \tilde{E}(x,\xi,t)
H_T, \tilde{H}_T, E_T, \tilde{E}_T(x,\xi,t)
\xi \rightarrow 0,\ t \rightarrow 0
Alternative to Wigner distributions → kT-unintegrated GPDs
Sivers function and GPD E have similar structure but come from different “mother” functions

19. Future Expreiments Delia Hash (Frascati) Lepton facilities
Physics: transversity++ (including sin2f in AUL and ALU )
near / mid term : HERMES @DESY <2010
BELLE @KEK
far term: >2010
“dream” future: EIC @RHIC >2015
(high intensity m
Frank Rathmann (Juelich) Hadron facilities (polarized antiprotons for transversity measurements)

20. Open discussions on experiment and theory
Exclusive r and SIDIS (CLAS,HERMES,COMPASS)
HT effect (1/Q6), important by itself
Theory:
Universality of Fragmentation functions
Trento convention:
1) azimuthal angles and spin directions
2) Sivers function definitions
M.Diehl, P. Mulders, A. Bacchetta and A. Miller
Put together a hep-ph with all definitions
H. Avakian, JLab June 27, 2004

21. Conclusions & Outlook N.Makins (summary talk)
Trento2004 featured a splendid theoretical synthesis of field-theoretic analysis (rigour) and phenomenological thinking (intuition)
New data from DESY, CERN, JLAB directly related to kT-dependent structures within the proton are already teaching us new things about non-perturbative QCD
Understanding of the new results is proceeding at a rapid rate, but much work is still required ⇒ global analysis
The new data are just the first trickle of a great wealth of upcoming information on transversity and the new kT-dependent distribution / fragmentation functions
Warmest thanks to all the organizers for the superb organization and stimulating agenda!

22. (sorry, only hall with a logo!)
Trento 2004: New data!
(sorry, only hall with a logo!)
Universality questions: are the new kT-dependent functions process-dependent or not?
The new data: do we have a qualitative understanding?
Modelling: toward a quantitative understanding
Other avenues: GPD’s and Lattice QCD