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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 1992-1996 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 change @ m ρ Jaffe et al. (98) 2000-2002 Pavia twist 2 DiFF analysis 1 st model calculation predicted no sign change Bianconi et al. (’00) Radici et al. (’02) 2003-2004 (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) 094003 - Belle ) pp collisions ( Bacchetta & Radici P.R. D90 (04) 094032 - 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) 094032 Boer, Jakob, Radici P.R. D67 (03) 094003 - 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) 074031 ) 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/ = - 2.55)

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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: 0.1 1 GeV 2 0.023 4 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%) 395 114 events 239 043 events 1 888 065 events Total 2 667 889 ( + - ) 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 |2.+3.+4.| 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 2.+3.+4. p-wave 1. background s-wave Total Total + 5.+6.

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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) 114024 Kor Korotkov, Nowak, Oganessian E.P.J. C18 (01) 639 Sch Schweitzer et al. P.R. D64 (01) 034013 Wak Wakamatsu P.L. B509 (01) 59 from GRV98-LO @ 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 0.15 0.15 0.22 1.23

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

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

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