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Transversity and inclusive 2π production M. Radici - Pavia chiral-odd partner Collins effect k £ P h ¢ S T 2h asymmetry R £ P h ¢ S T Dihadron Fragmentation Functions (DiFF) quark spin analyzer jet handedness Efremov et al. (92) Collins et al. (94) Collins & Ladinsky (94) Artru & Collins (96) 1998 Jaffe asymmetry in 2π SIDIS s-p interference predicted sign m ρ Jaffe et al. (98) Pavia twist 2 DiFF analysis 1 st model calculation predicted no sign change Bianconi et al. (’00) Radici et al. (’02) (LM) analysis Bacchetta & Radici (03) twist 3 DiFF Bacchetta & Radici (04) e+e- & pp Boer, Jakob, Radici (03) Bacchetta & Radici (04) 2005-… new data SIDIS e+e- (Belle) A-A Majumder et al. (05)

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QCD N'06 Transversity and 2 pion production 2 Kinematics of e p " ! e’ (h 1 h 2 ) X RTRT partial wave (LM) 12 LM scattering plane

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QCD N'06 Transversity and 2 pion production 3 leading-twist cross section (LM)(L’M’) from e + e - ( Boer, Jakob, Radici P.R. D67 (03) Belle ) pp collisions ( Bacchetta & Radici P.R. D90 (04) RHIC2 )

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QCD N'06 Transversity and 2 pion production 4 color-gauge invariance and universality inserting all unsuppressed A - gluons makes the nonlocal q-q correlator color-gauge invariant leading-twist projections are semipositive definite in Dirac space ! probabilistic interpretation

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QCD N'06 Transversity and 2 pion production 5 e+e- p-p collision p p " ! ( ) X p p ! ( ) C ( ) D X Bacchetta & Radici P.R. D90 (04) Boer, Jakob, Radici P.R. D67 (03) Belle same in SIDIS as in e+e- at twist 2 1 st check of universality

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QCD N'06 Transversity and 2 pion production 6 single spin asymmetry (following Trento conventions!) (here) (previous work) ( Hermes analysis? )

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QCD N'06 Transversity and 2 pion production 7 published models ( Jaffe, Jin, Tang, P.R.L. 80 (98) 1166 ) ep " ! e’ ( + - ) X no calculation of q I (z) → “figure of merit” s-p interference from - elastic scattering phase shifts only; sign change from Re[ ] (Radici, Jakob, Bianconi, P.R. D65 (02) ) spectator model interference ~ (s) – I m[ ] uncertainty band from different f p / f s strength ratio PDF input P. van der Nat DIS2005 Trento conventions ! (– 8/ = )

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QCD N'06 Transversity and 2 pion production 8 improved model ( Bacchetta & Radici, in preparation ) ep " ! e’ ( + - ) X PYTHIA output on HERMES kinematics: GeV GeV 2 excludes elastic and single/double diffractive events → semi-inclusive 2. q X 2 + - X 2 (14.81%) 3. q X 3 + - X 3 (0.31%) 4. q X’ 4 + - ( 0 X’ 4 ) (8.65%) 5. q X’ 5 + - ( X X 5 ) (2.05%) 6. q K 0 X 6 + - X 6 (3.41%) 1. All – (2+..+6) = background (70.77%) events events events Total ( + - ) pairs MhMh

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QCD N'06 Transversity and 2 pion production 9 spectator model approximation 2. q X 2 + - X 2 3. q X 3 + - X 3 4. q X’ 4 + - ( 0 X’ 4 ) X 2 = X 3 = X 4 = X p-wave channel = coherent sum | | Warning: [( ) L=1 ] J=1 1. background q + - X no resonance real s-wave channel max number of ( + - ) pairs in s-p interference ~ I m [ p-wave channel ] s-wave p-wave parameters X4X4

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QCD N'06 Transversity and 2 pion production 10 fit of PYTHIA distributions in invariant mass and z MhMh z p-wave 1. background s-wave Total Total

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QCD N'06 Transversity and 2 pion production 11 models for transversity u d Strat Soffer, Stratmann, Vogelsang P.R. D65 (02) Kor Korotkov, Nowak, Oganessian E.P.J. C18 (01) 639 Sch Schweitzer et al. P.R. D64 (01) Wak Wakamatsu P.L. B509 (01) 59 from Q 2 = 2.5 GeV 2 x

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QCD N'06 Transversity and 2 pion production 12 prediction of max spin asymmetry MhMh z

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QCD N'06 Transversity and 2 pion production 13 MhMh z “fit” of spin asymmetry HERMES PRELIMINARY 6.6% scale uncertainty ( + - ) 0 +- +- bins

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QCD N'06 Transversity and 2 pion production 14 spin COMPASS MhMh z deuteron 0.004

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QCD N'06 Transversity and 2 pion production 15 spin COMPASS proton 0.004

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