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Transversity and inclusive 2 π production

Transversity and inclusive 2 π production. M. Radici (Pavia). with A. Bacchetta (DESY). (LM). (L’M’). Di hadron F ragmentation F unctions ( DiFF ). chiral-odd partner. 2h asymmetry P 1 £ P 2 ¢ S T. Collins effect k £ P h ¢ S T. Spin asymmetry in e p " ! e’ (h 1 h 2 ) X.

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Transversity and inclusive 2 π production

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  1. Transversity and inclusive 2π production M. Radici (Pavia) with A. Bacchetta (DESY) (LM) (L’M’) Dihadron Fragmentation Functions (DiFF) chiral-odd partner 2h asymmetry P1£P2¢ST Collins effect k£Ph¢ST Transversity and 2 pion production

  2. Spin asymmetry in e p"! e’ (h1h2) X at leading twist following Trento conventions, spin asymmetry is ? ? LM from e+e- → (h1h2) (h1’ h2’) X (BELLE) or models ! 1 2 check universality in SIDIS and e+e- at twist 2 (Boer, Jakob, Radici P.R. D67 (03) 094003) partial wave (LM) then d or in pp collisions (Bacchetta & Radici P.R. D90 (04) 094032) see later… Bacchetta & Radici P.R. D67 (03) 094002 Transversity and 2 pion production

  3. ep"! e’ (+-) X published models (Jaffe, Jin, Tang, P.R.L. 80 (98) 1166) • no calculation of δqI (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) – Im[] • uncertainty band from • different fp / fs strength • ratio • PDF input P. van der Nat DIS2005 Trento conventions !£ (– 8/) Transversity and 2 pion production

  4. improved model ( Bacchetta & Radici, hep-ph/0608037 ) ep"! e’ (+-) X PYTHIA output on HERMES kinematics: 0.1<y<0.85 Q2 > 1 GeV2 0.023<x<0.4 W2>4 GeV2 excludes elastic and single/double diffractive events → semi-inclusive Mh 2. q →  X2 → +- X2 (14.81%) 395 114 events 3. q →  X3 → +- X3 (0.31%) 239 043 events 4. q →  X’4 → +- (0 X’4) (8.65%) 5. q → η X’5→π+π- (X X5) (2.05%) Total 2 667 889 (π+π-) pairs 6. q → K0 X6→π+π- X6 (3.41%) 1. All – (2+..+6) = background (70.77%) 1 888 065 events Transversity and 2 pion production

  5. spectator model approximation 1. background ≡ q →π+π- X1 no resonance → real s-wave channel 2. q →ρ X2→π+π- X2 X1 = X2 = X3 = X4 = X p-wave channel = coherent sum |2.+3.+4.| 3. q →ω X3→π+π- X3 4. q →ω X’4→π+π- (π0 X’4) Warning: ω→ [(ππ)L=1π]J=1 X4 max number of (π+π-) pairs in s-p interference ~ Im [ p-wave channel ] parameters s-wave p-wave Transversity and 2 pion production

  6. fit of PYTHIA distributions in invariant mass and z 2.+3.+4. p-wave 1. background s-wave Total Total + 5.+6. Mh z Transversity and 2 pion production

  7. models for transversity Strat Soffer, Stratmann, Vogelsang P.R. D65 (02) 114024 Kor Korotkov, Nowak, Oganessian E.P.J. C18 (01) 639 Schw Schweitzer et al. P.R. D64 (01) 034013 Wak Wakamatsu P.L. B509 (01) 59 u d x from GRV98-LO @ Q2 = 2.5 GeV2 Transversity and 2 pion production

  8. spin asymmetry 0.023<x<0.4 ; 0.1<y<0.85 Q2>1 GeV2 s=56.2 GeV2 HERMES 6.6% scale PRELIMINARY uncertainty ρ → π+π- ω → (π+π-) π0 Mh bins 0.15 0.15 0.22 1.23 Mh Transversity and 2 pion production

  9. spin asymmetry @ COMPASS deuteron 0.1<y<0.9 Q2>1 GeV2 s=604 GeV2 0.004<x<0.4 Mh Joosten – DIS2005 0.03<x<0.4 Mh z Transversity and 2 pion production

  10. proton 0.1<y<0.9 Q2>1 GeV2 s=301 GeV2 spin asymmetry @ COMPASS 0.004<x<0.4 ….. Mh 0.03<x<0.4 Mh z Transversity and 2 pion production

  11. p-p collision possible at RHIC, GSI and JPARC Bacchetta & Radici P.R. D90 (04) 094032 p p"! (ππ) X self-consistent extraction of p p ! (ππ)C (ππ)D X Transversity and 2 pion production

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