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Transversity and inclusive 2-pion production

Transversity and inclusive 2-pion production. TJNAF, 18-20 May 2005. Marco Radici. Pavia. In collaboration with: A. Bacchetta (Univ. Regensburg). how to extract transversity (at leading twist) ?. no inclusive DIS !. chiral-odd partner in. initial state ! polarized Drell-Yan.

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Transversity and inclusive 2-pion production

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

  2. how to extract transversity (at leading twist) ? no inclusive DIS ! chiral-odd partner in initial state!polarized Drell-Yan final state!semi-inclusive (SIR) double polarized DY(Ralston-Soper ’79) : p" p"! l+ l- X only transversity involved, no other unknowns, but ATT small (NLO) by Soffer inequality (Martin, Schaefer, Stratmann, Vogelsang ’98 Barone, Calarco, Drago, ‘97) presumably h1 for antiquarks in p is small ! use antiprotons: HESR@GSI doable with s=200 GeV2 MonteCarlo simulation (A. Bianconi and M.R., P.R. D71 (2005) 074014 and hep-ph/0504261 )

  3. SIR ? polarization of quark ! intuitively search for ? polarized final hadrons production : e p"!" X , p p"!" X (E704,RHIC) Double Spin Asymmetry (DSA) HESR@GSI can help in selecting models which mechanism ?! {pq, q, kq} not all collinear transfer q" to orbital motion of h !Collins effect asymmetry in sin /k£Ph¢ST chiral-odd Collins function H1? : extract it at e+e- facilities (Belle@RHIC)

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

  5. Superposition of effects : take reaction explain SSA data with Collins effect observe ? momenta in final state in initial state Sivers effect third possibility : in initial state Boer ‘99 generalized factorization scheme proof for Drell-Yan and low-pT SIDIS (Ji, Ma, Yuan, P.L. B597 (’04) 299 ) universality still under debate ; evolution ? search for effects ! SSA , but surviving sdkT

  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 sdkT 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. Interference Fragmentation Functions for q ! (h1,h2) X with unpolarized h1,h2 hadronic tensor Ph=P1+P2 R=(P1-P2)/2 functions of ( z,  =z1/z1+z2, Mh2, kT2, kT¢RT )! ( z, , Mh2 ) ( twist-2 Bianconi, Boffi, Jakob, M.R., 2000 ; twist-3 Bacchetta, M.R., 2004)

  8. RT e p"! e’ (h1h2) X leading-twist d - no specific weight for - no admixture with other effects - easier factorization proof ; universality unknown but … (e+e-, pp) - RT soft scale: evolution ? most general ! (L,M)

  9. (e+e-) ? from e+e-! ()jet 1 ()jet 2 X (Artru, Collins ‘96; Boer, Jakob, M.R. ‘03) 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 (back)

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

  11. FSI from interference of ()@L=0 and () @ L=1 (Jaffe, Jin, Tang, ’98) X|,Xih,X|~|()L=0ih()L=1| + |()L=1ih()L=0| fragmentation in helicity basis collinear ep"! e’ (+-) X not general (z,Mh2) dependence ! 2h c.m. frame |RT| = |R|(M1,M2,Mh) sin  = a(M1,M2,Mh) + b(M1,M2,Mh) cos IFF(z, (cos),Mh2) = n IFFn(z,Mh2)Pn (cos)

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

  13. ep"! e’ (+-) X at leading twist (Jaffe, Jin, Tang, 1998) spectator model • no calculation of qI (z) • ,  stable particles • interference from - phase shifts only (Radici, Jakob, Bianconi, 2002) spectator model uncertainty band from: • different fp / fs strength ratio • f1(x), h1(x) from spectator model • f1(x), h1(x)=g1(x) from GRV98 & GRSV96 • f1(x), h1(x) = (f1+g1)/2 from “ “ Trento conventions ! reverse sign!

  14. New model calculation (A. Bacchetta and M.R., in preparation) spectator model in  : off-shell spectator : partial-wave analysis PRELIMINARY HERMES guess on [M(+-)] corrected for acceptance p wave: incoherent sum of resonant 0!+- and s d0 [ !+-0 ] s wave: incoherent sum of direct production and K0S!+- (sdcos d)

  15. form factor Breit-Wigner m, , m,  , mK0 , K0 from PDG + same for K0S fit parameters + h.c.

  16. spectator model ! flavor symmetry ´

  17. fit [GeV] PRELIMINARY removes all elastic, single and double diffractive events ! only semi-inclusive (def. of AUT)

  18. PRELIMINARY f1, h1 from spectator model f1, h1=g1 from GRV98 & GRSV96

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

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