Transverse momentum in semiinclusive DIS Alessandro Bacchetta Essential

Transverse momentum in semi-inclusive DIS Alessandro Bacchetta

Essential literature • Mulders, Tangerman, NPB 461 (96) [no T-odd distribution functions, no Trento conventions] • Boer, Mulders, PRD 57 (98) [subleading twist not complete, no Trento conventions] • Bacchetta, Mulders, Pijlman, PLB 595 (04) [no transverse polarization, no Trento conventions] • Goeke, Metz, Schlegel, PLB 618 (05) [no cross sections] A. B. , Diehl, Goeke, Metz, Mulders, Schlegel, JHEP 02 (2007) 093 DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 2

Outline • Inclusive and semi-inclusive DIS • Cross section in terms of structure functions • Selected examples of structure functions in terms of transverse-momentum-dependent (TMD) partonic functions • Conclusions DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 3

Inclusive DIS proton lepton DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 4

Semi-inclusive DIS (SIDIS) proton lepton pion DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 5

Vectors and angles involved DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 6

Vectors and angles involved SIDIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 7

DIS cross section Any other modultation (e. g. ) is a sign of two-photon exchange DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 8

Full SIDIS cross section Kotzinian, NPB 441 (95) Diehl, Sapeta, EPJC 41 (05) 18 structure functions 10 already some measurements DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 9

Regime Ph Q • Factorization proof (leading twist) Ji, Ma, Yuan, PRD 71 (04) • Subleading twist is included, even though factorization is not guaranteed • Structure functions can be interpreted as convolutions of TMD parton distribution functions – 8 PDFs are leading twist and occur in 8 structure functions – 16 PDFs are subleading twist and occur in 8 structure functions – 2 structure functions are sub-subleading twist • For large Ph see talks by Koike, Tanaka DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 10

Structure functions FUU, T & FUU, L DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 11

Structure function FUU, T Access intrinsic transverse momentum DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 12

Structure function FUU, T Koike, Nagashima, Vogelsang, NPB 744 (06) h fragmentation q q p. QCD intrinsic See talk by C. P. Yuan (Structure functions) DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 13

Unpolarized beam and target Cahn effect ZEUS, hep-ex/0608053 Boer-Mulders DIS 2007 Collins Alessandro Bacchetta - TMD functions in SIDIS See talk by Gamberg 14

Longitudinally pol. beam CLAS, PRD 69 (04) HERMES, PLB 622 (05) HERMES, PRL 84 (00), PLB 562 (03) DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 15

Longitudinally pol. beam & target • Nontrivial interplay between spin and transverse momentum • Orbital angular momentum involved • Differences between flavors H. Avakian, QCD-N’ 06, Frascati DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 16

Transversely pol. target Sivers Transversity HERMES, PRL 94 (05) COMPASS, NPB 765 (07) DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS See talks by Diefenthaler, Bressan, D’Alesio 17

Transversely pol. target (cont. ) • Similar to Sivers function measurement • Sensitive to orbital angular momentum + 4 more See talk by Kotzinian DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 18

Transversely pol. target (cont. ) Integrated over Ph In inclusive DIS 0 DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 19

Conclusions • In one-particle-inclusive DIS there are 18 structure functions to be measured • Some information about 10 of them is already available • The structure functions can be interpreted in the lowtransverse-momentum regime in terms of transversemomentum-dependent partonic functions • Constant progress in experiments, phenomenology and theory • A lot remains to be done DIS 2007 Alessandro Bacchetta - TMD functions in SIDIS 20