1. 1 Transversity and inclusive 2-pion production Marco Radici Pavia TJNAF, 18-20 May 2005 In collaboration with: A. Bacchetta (Univ. Regensburg)

2. 2 how to extract transversity (at leading twist) ? double polarized DY (Ralston-Soper ’79) : p " p " ! l + l - X no inclusive DIS ! initial state ! polarized Drell-Yan chiral-odd partner in final state ! semi-inclusive (SIR) only transversity involved, no other unknowns, but A TT small (NLO) by Soffer inequality (Martin, Schaefer, Stratmann, Vogelsang ’98 Barone, Calarco, Drago, ‘97) presumably h 1 for antiquarks in p is small ! use antiprotons: HESR@GSI doable with s=200 GeV 2 (A. Bianconi and M.R., P.R. D71 (2005) 074014 and hep-ph/0504261 ) MonteCarlo simulation

3. 3  production : e p " !  " X, p p " !  " X ( E704,RHIC ) which mechanism ?! ? polarization of quark ! intuitively search for ? polarized final hadrons Double Spin Asymmetry (DSA) HESR@GSI can help in selecting models SIR {p q, q , k q } not all collinear transfer q " to orbital motion of h ! Collins effect asymmetry in sin  / k £ P h ¢ S T chiral-odd Collins function H 1 ? : extract it at e + e - facilities (Belle@RHIC)

4. 4 Technical slide ! SIDIS : e p " ! e’ h X Collins effect leading twist:  S  0,  convolution keep d  enough differential (  C =  h +  S ) to break the convolution  […] Single Spin Asymmetry needs (Boer & Mulders ’98)

5. 5 Superposition of effects : take reaction observe ? momenta in final state explain SSA data withCollins effect in initial state Sivers effect third possibility : in initial stateBoer ‘99 generalized factorization scheme proof for Drell-Yan and low-p T SIDIS ( Ji, Ma, Yuan, P.L. B597 (’04) 299 ) universality still under debate ; evolution ? search for effects ! SSA, but surviving s dk T

6. 6 Collins effect 2 hadron semi-inclusive process e p " ! e’ (  1  2 ) X p p " ! (  1  2 ) X.. ! asymmetry in the azimuthal orientation of pair plane with respect to some reference plane survives s dk T suggested for the first time by Collins, Heppelmann & Ladinski, 1994 but no twist analysis nor quantitative calculations (see also Ji 1994) then Jaffe, Jin, Tang 1998 ! suggestion of SSA from interference of (  ) partial waves and Bianconi, Boffi, Jakob, M.R., 2000 ! complete twist-2 analysis and first model calculation

7. 7 Interference Fragmentation Functions for q ! (h 1,h 2 ) X with unpolarized h 1,h 2 hadronic tensor P h =P 1 +P 2 R=(P 1 -P 2 )/2 functions of ( z,  =  z 1 /z 1 +z 2, M h 2, k T 2, k T ¢ R T ) ! ( z, , M h 2 ) ( twist-2 Bianconi, Boffi, Jakob, M.R., 2000 ; twist-3 Bacchetta, M.R., 2004)

8. 8 RTRT e p " ! e’ (h 1 h 2 ) X leading-twist d  - no specific weight for - easier factorization proof ; universality - no admixture with other effects unknown but … most general ! - R T soft scale: evolution ? (e + e -, pp) (L,M)

9. 9 or extracted self consistently also from p-p collisions (Bacchetta, M.R. 2004 ) p p " ! (  ) X p p ! (  ) C (  ) D X contains also same as for gluons available for spin ½ hadron otherwise chiral-odd  g for spin ¸ 1 ? from e + e - ! (  ) jet 1 (  ) jet 2 X (Artru, Collins ‘96; Boer, Jakob, M.R. ‘03) (e + e - ) (back)

10. 10 e + e - ! (  +  - ) jet 1 (  +  - ) jet 2 X leading twist (Boer, Jakob, Radici, ’03) “Artru-Collins” azimuthal asymmetry same as in SIDIS (back)

11. 11 (Jaffe, Jin, Tang, ’98)  X | ,X ih ,X| ~ |(  ) L=0 ih (  ) L=1 | + |(  ) L=1 ih (  ) L=0 | FSI from interference of (  ) @ L=0 and (  ) @ L=1 fragmentation in helicity basis collinear ep " ! e’ (  +  - ) X not general (z,M h 2 ) dependence ! IFF(z,  (cos  ),M h 2 ) =  n IFF n (z,M h 2 ) P n (cos  ) 2h c.m. frame |R T | = |R|(M 1,M 2,M h ) sin   = a(M 1,M 2,M h ) + b(M 1,M 2,M h ) cos 

12. 12  n … P n (cos  ) (A. Bacchetta and M.R., 2003) s-p interference (Jaffe) (models) (new model) (A UT results)

13. 13 ep " ! e’ (  +  - ) X at leading twist (Jaffe, Jin, Tang, 1998) no calculation of  q I (z) ,  stable particles interference from  -  phase shifts only (Radici, Jakob, Bianconi, 2002) uncertainty band from: different f p / f s strength ratio f 1 (x), h 1 (x) from spectator model f 1 (x), h 1 (x)=g 1 (x) from GRV98 & GRSV96 f 1 (x), h 1 (x) = (f 1 +g 1 )/2 from “ “ spectator model Trento conventions ! reverse sign!

14. 14 New model calculation (A. Bacchetta and M.R., in preparation) spectator model in  : off-shell spectator : p wave: incoherent sum of resonant  0 !  +  - and s d  0 [  !  +  -  0 ] partial-wave analysis s wave: incoherent sum of direct production and K 0 S !  +  - ( s dcos  d  ) P R E L I M I N A R Y HERMES guess on  [M(  +  - )] corrected for acceptance

15. 15 Breit-Wigner m ,  , m ,    m K0,  K0 from PDG form factor fit parameters + h.c. + same for K 0 S

16. 16 spectator model ! flavor symmetry ´

17. 17 fit [GeV] P R E L I M I N A R Y (def. of A UT ) removes all elastic, single and double diffractive events ! only semi-inclusive

18. 18 PRELIMINARY f 1, h 1 from spectator model f 1, h 1 =g 1 from GRV98 & GRSV96

19. 19 Conclusions interpretation of upcoming HERMES 2  semi-inclusive data in terms of collinear fragmentation via IFF seems reasonable and feasible; work in progress… extraction of transversity via IFF more convenient with respect to Collins effect HESR@GSI will probably offer anther tool: collinear fully polarized Drell-Yan with antiprotons Transverse spin physics without transverse momenta is a real option Transverse spin physics without transverse momenta is a real option