! how important for transverse spin studies Villa Olmo (Como), 7 - 10 Sept 2005 Alternative approaches to transversity: how convenient and feasible are they ? ! how important for transverse spin studies Marco Radici Pavia In collaboration with: A. Bacchetta (Univ. Regensburg) A. Bianconi (Univ. Brescia)

Some alternative ways to transversity search for chiral-odd partner of h1 constraint: leading twist process initial state polarized Drell-Yan (DY) : DIS : final state Collins effect semi-inclusive annihilation : Interference Fragmentation Functions

Drell-Yan HESR@GSI: COMPASS ? always valence quarks higher statistics Collins-Soper frame (P.R. D16 (’77) 2219) c.m. energy invariant mass parton momenta in plane DIS regime

Leading twist cross section D. Boer, P.R. D60 (’99) 014012 Tangermann & Mulders, P.R. D51 (’95) 3357 fitted against data (Conway et al., P.R. D39 (‘89) 92) MC Asym h1? Sivers

Generate the asymmetry cross sect. Summing upon qT, , x1, for some fixed S1 and S2 for each x2´ xp accumulate events with F[, S1, S2] > 0 $ U F[, S1, S2] < 0 $ D SSA (x2) = (U-D) / (U+D) For assume flavor symmetry and select For each case, repeat simulation independently for 20 times ! build mean value and variance of SSA for each x2 and test when SSA (x) reflects the same differences within error bars ) extraction h1(x) , h1? (x) is statistically possible Bianconi & M.R., P.R. D71 (’05) 074014; hep-ph/0504261, P.R. D in press

8000 events with dilut. factor = 0.85 Bianconi & M.R., P.R. D71 (’05) 074014

s » 200 (GeV)2 statistical error bars from 20 repetitions unambiguous extraction seems possible Bianconi & M.R., P.R. D71 (’05) 074014

Monte Carlo sample Program ! total  for absorption of antiprotons per nucleon producing Drell-Yan event in the selected kinematics luminosity L x  = # of “good” Drell-Yan events per N and per sec. mode s (GeV)2 M (GeV) tot (nb/N) events/month collider 200 1.5 ¥ 2.5 2.4 60K 4 ¥ 9 0.1 2.5K fixed target 30 0.8 20K 4 x 10-4 10 L=1031 (cm-2s-1) after cuts dilution factor polarized events HESR@GSI 8K collider 40K fixed target 0.85 0.25 6.8K 10K COMPASS 500K fixed target 125K

statistical error bars from 10 repetitions cross sect. s » 200 (GeV)2 statistical error bars from 10 repetitions unambiguous extraction seems possible Bianconi & M.R. in preparation

Model assumptions for Sivers Anselmino et al. P.R. D71 (05) 074006 q = u,d hep-ph/0507181

statistical error bars from 10 repetitions s » 200 (GeV)2 Anselmino et al. P.R. D71 (05) 074006 xF Anselmino et al. hep-ph/0507181 statistical error bars from 10 repetitions

s » 200 (GeV)2 PRELIMINARY statistical error bars from 10 repetitions

First message combination of unpolarized / single- / double-polarized Drell-Yan with antiproton beams can give information on h1(x), h1? (x) (violation of Lam-Tung sum rule), and f1T? (Sivers) at GSI the collider mode is highly preferable because for s ¼ 200 GeV2 the phase space is more populated; for luminosity 1031 (cm-2s-1) and 9 ¸ M ¸ 4 GeV a reasonable statistics is reached after 3 months of data taking at COMPASS in fixed target mode, s ¼ 200 GeV2 can be reached with 100 GeV pion beams; statistics of pion-induced events can be much better than antiproton one ! more precise and unambiguous information

Transversity from SIDIS : Collins effect generalized factorization scheme proof for Drell-Yan and low-pT SIDIS only (Ji, Ma, Yuan, P.L. B597 (’04) 299 ) ; universality “still under debate” ; evolution ? search for effects ! SSA , but surviving sdpT dPhT 2 hadron semi-inclusive process e p" ! e’ (1 2) X p p" ! (12) X .. Collins effect disadvantages: need kT dependence => no factorization proof, evolution? Universality? Need mechanism to get same goal without pT explicit dependence => IFF. asymmetry in the azimuthal orientation of pair plane 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 Bianconi, Boffi, Jakob, M.R., 2000 ! complete twist-2 analysis and first model calc. Bacchetta, M.R. ! partial wave expansion () L ; twist-3 ; pp collisions…

functions of ( z,  = z1/z1+z2 , Mh2, kT2, kT¢RT ) ! ( z, , Mh2 ) Interference Fragmentation Functions for q ! (h1,h2) X with unpolarized h1,h2 (LM) (L’M’) Ph=P1+P2 R=(P1-P2)/2 Not enter details. Just the qq correlator is similar to 1h production case, just for the intermediate final state. Then twist 2 projections give unpol D1 , long-pol G1 and 2 transv-pol H1perp e H1angle. Only D1 and H1angle survive after kT integration => dependence on z,zeta,Mh . Put bottom references. functions of ( z,  = z1/z1+z2 , Mh2, kT2, kT¢RT ) ! ( z, , Mh2 ) ( twist-2 Bianconi, Boffi, Jakob, M.R., P.R. D62 (2000) 034008 ; twist-3 Bacchetta, M.R., P.R. D69 (04) 074026; partial waves P.R. D67 (03) 094002 )

- no admixture with other effects e p" ! e’ (h1h2) X RT leading-twist d - no admixture with other effects - easier factorization proof ; universality - no specific weight ! easier SSA from e+e- ! (+-)jet 1 (+-)jet 2 X (Boer, Jakob, M.R. P.R. D67 (03) 094003 ) AUT

ep" ! e’ (+-) X at leading twist (Jaffe, Jin, Tang, P.R.L. 80 (98) 1166) spectator model no calculation of qI (z) ,  stable particles interference from - phase shifts only (M.R., Jakob, Bianconi, P.R. D65 (02) 074031 ) 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!

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

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

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

Second message extraction of transversity via IFF more convenient with respect to Collins effect : - integration upon PhT makes leading twist cross section very simple: unpolarized term + transversity x IFF no “contamination” with other (Sivers-like) effects - factorization proof and evolution should be easier interpretation of upcoming HERMES 2 semi-inclusive data in terms of collinear fragmentation via IFF seems reasonable and feasible for COMPASS data work is in progress… extraction of IFF from Belle data ; no asymmetric background from hard gluon radiation ! please, put it at top of shopping list !