Transversity and dihadron fragmentation functions Alessandro Bacchetta Regensburg

Transversity and dihadron fragmentation functions Alessandro Bacchetta Regensburg University 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions

• Work funded by http: //www. avh. de/ • In collaboration with M. Radici, Università di Pavia 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 2

Outline • • • Introduction Dihadron FF to probe transversity Dihadron FF in DIS Dihadron FF in e+e- annihilation Dihadron FF in pp scattering 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 3

Why is fragmentation into two hadron interesting? • They can be used for TRANSVERSITY MEASUREMENT (the relative transverse momentum of the two hadrons can replace in single-pion production) • They reveal SPIN TRANSFER EFFECTS IN HADRONIZATION (the angular distribution of two hadrons can be sensitive to the spin of the quark) 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 4

Collinear single-hadron fragmentation p quark The only relevant variable is the fraction of longitudinal momentum (z) For unpolarized hadrons, the only fragmentation function at leading twist is 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 5

Noncollinear single-hadron fragmentation p The relevant variables are the fraction of longitudinal momentum (z) AND the transverse momentum quark For unpolarized hadrons at leading twist there are two fragmentation functions and Collins FF: relation between quark spin and k. T 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 6

“Collinear” dihadron fragmentation No transverse momentum of the pair center of mass. h 1 fraction of longitudinal momentum carried by the pair invariant mass of the pair quark polar angle of the hadrons in their center of mass frame h 2 azimuth angle of the pair plane There are two fragmentation functions at leading twist: 14. 10. 2004 and A. Bacchetta - Dihadron fragmentation functions 7

“Collinear” dihadron fragmentation No transverse momentum of the pair center of mass. h 1 quark h 2 Interference fragmentation function: relation between quark spin and RT 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 8

The dihadron interference fragmentation function is a chiral odd object that can be used to probe transversity • Collins, Heppelmann, Ladinsky, NPB 420, 565 • Collins, Ladinsky, hep-ph/9411444 • Ji, PRD 49, 114 • Jaffe, Jin, Tang, PRL 80, 1166, hep-ph/9709322 • Radici, Jakob, Bianconi, PRD 65, 074031, hep-ph/0110252 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 9

Interpretation of function h 1 h 2 _ quark h 1 h 2 Collins function h _ quark h 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 10

Interpretation of function Cut-diagram representation Lz Orbital angular mom. Quark helicity Lz-1 _ + The orbital angular momentum projection has to change one unit, e. g. s-p wave interference p-p wave interference 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 11

Dependence on Considering only s and p waves (at low invariant mass) A. Bacchetta, M. Radici, PRD 67, 094002 Each one of these functions contains different and interesting physics. . . 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 12

Dependence on Breit-Wigner shape See next talk by P. van der Nat R. Jaffe, X. Jin, J. Tang, PRL 80 (1997) 14. 10. 2004 Radici, Jakob, Bianconi, PRD 65, 074031 A. Bacchetta - Dihadron fragmentation functions 13

Dihadron FF in semi-inclusive DIS two- hadr o l n pla ne l' sc att er in y gp z lan e x 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 14

AUT asymmetry A. Bacchetta, M. Radici, PRD 69, 074026 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 15

Comparison with single-hadron l had ron l' sc att pla ne y er in gp z lan e x 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 16

AUT in single-hadron production Drawbacks: • Several terms • Convolutions • Evolution • Universality 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 17

Dihadron FF in e+e- annihilation RCT PD P 1 D Boer, Jakob, Radici, PRD 67, 094003 e- RDT P 1 C PC e+ 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 18

Dihadron FF in RCT pp FR scattering PA C SB P 1 C FS PC B PB Bacchetta, Radici, hep-ph/0409174 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 19

Dihadron FF in unpolarized pp scattering Bacchetta, Radici, hep-ph/0409174 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 20

Conclusions • Dihadron interference fragmentation functions are good candidates to “probe” h 1(x) • They are easy to deal with from theoretical and maybe also from the experimental point of view • They can be measured in SIDIS (HERMES, CLAS, COMPASS), in e+e- annihilation (BELLE, BABAR), in pp collisions (PHENIX, STAR, GSI, LHC, TEVATRON) 14. 10. 2004 A. Bacchetta - Dihadron fragmentation functions 21