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Transversity and inclusive 2-pion production

Collaboration with A. Bacchetta on extracting transversity at leading twist without inclusive DIS, exploring polarized Drell-Yan final states, semi-inclusive double polarized DY, use of antiprotons at HESR@GSI, and Monte Carlo simulations for SIR. Discusses the search for polarization of quarks and hadrons, Collins effect asymmetry, SSA data explanation, and SSAs surviving sdkT. Explores effects on various mechanisms and models, such as DSA, Collins function, and twist analyses. Discusses azimuthal asymmetries, interference fragmentation functions, and chiral-odd effects in e.p"! process. Details the evolution of universal factors and the potential for generalized factorization schemes in Drell-Yan and SIDIS processes. Provides insights into the azimuthal orientation of pair planes, the twist analysis, and quantitative calculations in the context of 2-hadron semi-inclusive processes.

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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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