1. 1 The Partonic Transverse-spin Structure of the Proton Marco Radici Pavia The Partonic Structure of Hadrons ECT* (Trento), 9-14 May 2005 Barone, Drago, Ratcliffe, Phys. Rep. 359 (2002) 1 or Barone and Ratcliffe, Transverse Spin Physics (World Scientific, 2003) In collaboration with: A. Bacchetta (Univ. Regensburg) A. Bianconi (Univ. Brescia)

2. 2 Examples of large SSA Ex.: Heller et al., P.R.L. 41 (‘78) 607 Ex.: Adams et al., STAR P.R.L. 92 (‘04) 171801 Airapetian et al., HERMES P.R.L. 94 (’05) 012002 Ex.: Conway et al., E615 P.R. D39 (‘89) 92

3. 3

4. 4 helicity basis transverse basis But helicity flip suppressed in QCD collinear factorization + ~ massless quark spinors  = § 1 ) transverse spin effects ( ! SSA) suppressed in QCD

5. 5 We need transverse spin distribution (transversity) it completes the parton structure of N at leading twist DF Distribution Function in quark-N helicity basis (Jaffe) suppressed in inclusive DIS struct. function analogue in Parton Model F1F1 g1g1 ? helicity = chirality at leading twist ) helicity flip, chiral-odd dynamical breaking of chiral symmetry?

6. 6 Properties of transversity h 1 (x,Q 2 ) = g 1 (x,Q 2 ) in nonrelativistic theory because [boost, rotation] = 0 difference ) information on relativistic dynamics of quarks in hadrons no h 1 for gluons ) no mixing with gluons in evolution contrary to helicity g 1 ) non-singlet evolution of h 1 for quarks

7. 7 cont’ed tensor charge (1 st moment of h 1 ) has anomalous dimension   0 tensor charge is C-odd ) does not couple to quark-antiquark, gluons.. singlet DF ) more valence quark-like content of h 1 ? Place to test CQM ? from lattice:  f h 1 f = 0.562 § 0.088 (Aoki et al.) inequalities: |h 1 (x)|  f 1 (x) (positivity) ; |2h 1 (x)|  f 1 (x) + g 1 (x) (Soffer) nonsinglet axial charge (1 st moment of g 1 ) does not depend on scale Q 2 better place to test evolution several model calculations but QCDSF : g 1 » h 1 (Schierholz et al.)

8. 8 Hadron spin physics young field : Bacchetta, D’Alesio, Diehl, Miller, Single-Spin Asymmetries: the Trento Convention Phys. Rev. D70 (2004) 117504 I3HP VI EU Framework Programme ! I 3 H P (coordinator Guaraldo) Network Project N7 “Transversity” (coordinator De Sanctis) 1 st Network Workshop at ECT* June 2004 Transversity: New Developments in Nucleon Spin Structure report ! M.R., G. van der Steenhoven, The Transversity Council of Trento at ECT* (2004) CERN Courier 44 (2004) 51 Rich experimental program: HERMES@DESY, COMPASS@CERN, BELLE+STAR@RHIC, Hall B@JLAB, PANDA+PAX+ASSIA@GSI,...

9. 9 suppressed in inclusive DIS: how to extract transversity ? search for chiral-odd partner of h 1 constraint: leading twist process initial statepolarized Drell-Yan (DY) : final statesemi-inclusive DIS : annihilation :

10. 10 presumably h 1 for antiquarks in p is small ! use antiprotons: HESR@GSI A TT small (NLO) by Soffer inequality (Martin, Schaefer, Stratmann, Vogelsang ’98 Barone, Calarco, Drago, ‘97) search for transversity in double polarized DY : p " p " ! l + l - X (historically the 1 st : Ralston & Soper ’79) Collins-Soper frame: q T (  * ) in (xz) plane only transversity involved, no other unknowns, but

11. 11 semi-inclusive  production : which mechanism ?! e p " ! e’  + X p p " !  + X E704 RHIC semi-inclusive process ? polarization of quark intuitively search for ? polarized final hadrons Double Spin Asymmetry (DSA) depolarization (spin transfer coefficient) HESR@GSI can help in selecting models: DeGrand & Miettinen ’81 Andersson et al. ’79 Dharmaratna & Goldstein ’90 Anselmino et al. ’91....

12. 12 in seminclusive DIS {p q, q , k q } not all collinear DSA ) transfer q " not to h " final hadron (DSA), but to orbital motion of h SSA ) SSA with intrinsic P h ? dependence not integrated ) Collins effect asymmetry in sin  / k £ P h ¢ S T chiral-odd Collins function H 1 ? (z, k T ) : extract it at e + e - facilities (Belle@RHIC)

13. 13 Technical slide ! DIS : ep " ! e’hX Collins effect leading twist:  S  0,  convolution keep d  enough differential (  C =  h +  S ) to break the convolution F […] need (Boer & Mulders ’98)

14. 14 new TMD functions ( s dk T ! 0) ! new spin effects leading twist ! number density interpretation k P hT Sivers Collins polarized PFF k P hT Boer-Mulders

15. 15 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 complete proof not yet available search for effects ! SSA, but surviving s dk T

16. 16 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

17. 17 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) (18)

18. 18 Color gauge invariance ? (Boer, Mulders, Pijlman, 2003) insert all unsuppressed A - gluons and A T gluons at n + =- 1 makes the nonlocal q-q correlator color gauge invariant insert also all A T gluons makes the nonlocal q-g-q correlator color gauge invariant leading-twist projections are semipositive definite in Dirac space ! probabilistic interpretation (Bacchetta and M.R., 2004)

19. 19 quark chiral basis : P § P R/L  with P § =½  ¨  § P R/L = ½ (1 §  5 ) ( )  - ´  q’q = ½ bounds :

20. 20 RTRT e p " ! e’ (h 1 h 2 ) X leading-twist d  - no specific weight for - collinear factorization - no admixture with other effects unknown most general ! Single Spin Asymmetry

21. 21 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)

22. 22 e + e - ! (  +  - ) jet 1 (  +  - ) jet 2 X leading twist (Boer, Jakob, Radici, ’03) “Artru-Collins” azimuthal asymmetry same as in SIDIS

23. 23 (Jaffe, Jin, Tang, ’98)  X |  , X ih  , X| ~ |(   ) L=0 ih (   ) L=1 | + |(   ) L=1 ih (   ) L=0 | T-odd structure from interference of L=0 (  !   ) and L=1 (  !   ) fragmentation in helicity basis collinear ep " ! e’ (  +  - ) X collinear factorization ok, but not general ! 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 

24. 24  q’q = ½  n … P n (cos  ) (A. Bacchetta and M.R., 2003) s-p interference (Jaffe) (24)

25. 25 00 000 00 000 000 00 000 0000 sp,+1p,0p,-1 s p,+1 p,0 p,-1 (Jaffe) spin 1  !   (Bacchetta Mulders)

26. 26 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

27. 27 New model calculation (A. Bacchetta and M.R., in preparation) spectator model in  : off-shell spectator : p wave: resonant  0 !  +  - partial-wave analysis s wave: coherent sum of direct production and resonant f 0 !  +  - plus incoherent s d  0  !  +  -  0

28. 28 Parameters and fit of event distribution form factor PDG m ,  , m f0,  f0, m ,   fit [GeV] PRELIMINARY

29. 29 spectator model ! flavor symmetry PRELIMINARY f 1, h 1 from spectator model f 1, h 1 =g 1 from GRV98 & GRSV96 ( “ “ ) x 2

30. 30 Double polarized Drell-Yan with antiprotons c.m. energy invariant mass parton momenta DIS regime factorization for specific M, leading twist low  ! high s collider mode for HESR@GSI at present: 2 M ranges explored: Y 9 ¸ M ¸ 4 J/  (GeV) J/  2.5 ¸ M ¸ 1.5  ( “ )

31. 31 Monte-Carlo simulation (A. Bianconi and M.R., hep-ph/0504261) events for  +  - Drell-Yan pairs distributed with cross section NLLA QCD corrections (compensate in DSA?) factorized leptons q T dependence (Anassontzis et al. 1988) / d  0 PDF(x,M 2 ) da violation of Lam-Tung sum rule Collins-Soper frame: q T (  * ) in (xz) plane N.B.  S1,  S2 randomly distributed in Collins-Soper frame

32. 32 cuts: s=200 GeV 2 ; 4 1 GeV/c ; 60 o <  <120 o ; S T =50% sample: 80.000 events ! 40.000 ! 17.000 (A. Bianconi and M.R., hep-ph/0504261) 0.08. . 0.4

33. 33 unambiguous extraction of h 1 (x) seems possible statistical error bars from 20 repetitions cuts: s=200 GeV 2 ; 4 1 GeV/c ; 60 o <  <120 o ; S T =50%

34. 34 cuts: s=200 GeV 2 ; 1.5 1 GeV/c ; 60 o <  <120 o ; S T =50% sample: 80.000 events ! 40.000 ! 17.000 (A. Bianconi and M.R., hep-ph/0504261) 0.01. . 0.03

35. 35 unambiguous extraction of h 1 (x) seems possible cuts: s=200 GeV 2 ; 1.5 1 GeV/c ; 60 o <  <120 o ; S T =50% statistical error bars from 20 repetitions

36. 36 Conclusions interpretation of future 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