Two hadron correlations in SIDIS and e + e - annihilation reactions

Transcription

1 wo adron correlations in SIDIS and e + e - anniilation reactions YerI, Armenia & INFN, orino Collaborators: H. Matevosyan and A.W. omas University of Adelaide, Australia Introduction accessing MD DFs and FFs wit electromagnetic probe production in SIDIS (current fragmentation region, CFR) and semi-inclusive e + e - anniilation (SIA) wo adron production in CFR of SIDIS and SIA arget fragmentation region (FR) of SIDIS Correlations in artonic and Hadronic Interactions September 08, Yerevan, Armenia

2 SIDIS: CFR xf 0 d d dxdq d dzd dq ( l, ) N ( N, S ) ( l) ( ) X ( l, ) q( k, s) ( l) q( k, s) f q, s/ N, S D q, s S ' D ( z, p ) D ( z, p ) p s H ( z, p ) q, s m H was measured by BABAR and BELLE to back-to-back jets e + e - + X

3 Nucleon olarization wist- MD qdfs Quark polarization U L U f x k q (, ) k M ij j q ( xk, ) L S g q (, ) L L x k k S x k M q L L (, ) k S M q f ( x, k ) k S M g x k q (, ) S x k q (, ) k S q k ( x, k ) M M All azimutal dependences are in prefactors. MDs do not depend on tem 3

4 LO cross section in SIDIS CFR d ( x 0) x ( l, ) N ( N, S ) ( l) ( ) X F ( y) dxdq dsdzd yq cos FUU, Dnn( y) FUU cos( ) sin SLDnn( y) FUL sin( ) SLDll ( y) FLL sin( S ) F sin( ) sin( S ) U S S FU, sin( S ) Dnn( y) sin( 3 S) FU sin(3 S) cos( S) S Dll ( y) FL c os ( S) Virtual poton depolarization factors y( y) ( y) Dll ( y), D ( y) ( y) ( y) nn F F 8 terms out of 8 Structure Functions, 6 azimutal modulations 4 terms are generated by Collins effect in fragmentation S 8 structure functions F f (, ) AB f D, F H, F H, F g D q cos( ) q sin( ) q q UU, q UU q UL L q LL q f D, F H, F H, F g D sin( s ) q sin( s ) q sin(3 s ) q cos( s ) q U q U q U q L q 4

5 SIA Access to q q unpolarized fragmentation finctions Dq q(z,p ) 5

6 + SIA wo adron production in opposite emisperes: acces to Collins FF H Quarks are unpolarized, but teir transverse polarization are correlated, inducing an azimutal correlation of produced adrons in opposite jets. q q (z, p ). Obtained H (z,p ) FFs are used for transversity ( x, k ) extraction from SIDIS data. 6

7 SIDIS: CFR 7 x 0, x 0 F, F, d d dxdq d dz d dz d dq ( l, ) N ( N, S ) ( l) ( ) ( ) X ( l, ) q( k, s) ( l) q( k, s), f q, s/ N, S D q, s S, New objects: DiFFs Dqs,

8 + SIA Measured by BELLE: diadrons production in back-to-back jets in SIA Access to spin dependent DiFFs, Dqs, 8

9 Diadron FFs: pqcd definition 9

10 Number density distribution in quark to fragmentation q pol. DiFF U L D, G Unpolarized DiFF H H Longitudinal andedness Interference DiFF (IFF) Collins-like DiFF,, k, R ; s,,k,, cos RK F z D z R k sin k S s H z,,k M M R k sin RK sl G z,,k, R, cos M M R sin R S s H z,,k, R, cos M M cos, R, cos cos RK R k RK RK RK k z 0

11 Fourier moments of DiFFs We define Fourier moments of integrated over pair total momentum weigted DiFFs and

12 Access to transversity in SIDIS M. Radici, Jakob and Bianconi: RD 65, (00). d d d d sin( ) R S q q q q e ( x) H q q q q z, M e f ( x) D z, M, [0], H z M H z M, SIDIS Corrected by A. Baccetta, M. Radici: RD 69, (004). [0],, [], H z M H z M H z M, SIDIS

13 DiFFs in, SIA - q z 3

14 Access to IFF and andedness DiFF in SIA: weigted asymmetries Boer, Jacob and Radici: RD 67, (003). [0] M H [0] G z, M, SIDIS, G z, M ee H z, M H z, zm,, ee RL 07 (0) (IFF) BELLE results arxiv: (andedness) 4

15 Model calculation of FFs and DiFFs Complete self consistent formalism for spin dependent MD FFs: Bentz, AK, Matevosyan, Ninomiya, omas, Yazaki: R D94, (06) MC implementation: Matevosyan, AK, omas: One adron production, RD 95, 040 (07) wo adron production: Longitudinally polarized quark, RD 96, (07) wo adron production: ransversely polarized quark, RD 97, 0409 (08) All 8 elementary quark-to-quark spin-dependent MD FFs are taken into account H, SIDIS H z, M, ee G H, ee z, M 5

16 Rederiving diadron production cross-sections in e + e - and SIDIS Matevosyan, AK, omas: RL 0, 5, 00 (08), : arxiv: Matevosyan, Baccetta, Boer, Courtoy, AK, Radici, omas: ys. Rev. D 97, (08), arxiv: Fully differential cross section 6

17 IFFs in e + e - and SIDIS 7

18 Handedness DiFF in e + e - Matevosyan, AK, omas: RL 0, 5, 00 (08), : arxiv: Weigting break-up te convolution 8

19 New weigt to access andedness DiFF in e + e - Matevosyan, AK, omas: RL 0, 5, 00 (08), : arxiv:

20 Our MC model results 0

21 SIDIS: FR xf 0 rentadue, Veneziano 994 Graudenz 994 Collins 998, 000, 00 de Florian, Sassot 997, 998 Grazzini, rentadue, Veneziano 998 Ceccopieri, rentadue 006, 007, 008 Sivers 009 Ceccopieri, Mancusi 03 Ceccopieri 03 Applied to HERA data: D. de Glorian, R. Sassot (998), Soeibi et al (07).. d ( l) N ( N ) ( l) ( ) X ( l) q( k ) ( l) q( k) M qn / xq,, dxdq d d xf ( x) dq N Fracture function M is a Conditional robability Distribution Function (CDF) to observe te adron produced in nucleon fligt direction wen ard probe interacts wit parton carrying fraction x of nucleon momentum.

22 Quark transverse spin in ard l-q scattering Nucleon and initial quark spin s AK, ransversity worksop, Yerevan, 009 FR s γ * N CMS s ˆ l γ * Final quark spin s' CFR ( y) QED: lq l q s D ( y) s, D ( y), ( y) nn nn s s s p sin sin s s If only one adron in FR of SIDIS is detected tere is no final quark polarimetry. No access to quark transverse polarization dependent fracture functions. No Collins like modulation.

23 SIDIS FR. Spin & MD Fracture Functions xf Anselmino, Barone and AK, L B 699 (0)08; 706 (0)46; 73 (0)37 Nucleon and quark polarization are included, produced adron and quark transverse momentum are not integrated over. Classification of twist-two Fracture Functions and cross sections expressions. d d xf ( x) dxdq d d d dq N ( l, ) N ( N, S ) ( l) ( ) X ( l, ) q( k, s) ( l) q( k, s) M q, s/ N, S S 0 3

24 Karl Linney: plants classification lants were divided by it into 4 classes and 6 groups on te basis of features of a structure of teir reproductive organs. For SMD Fracture Functions I was expecting 3 (rentadue) independent structures. Fortunately for unpolarized adron production we end up wit only 6 of tem at twist-two 4

25 Quark correlator SIDIS [ ] B CFR ( x, k,, ) d d d 4 ( ) ( ) E 5 3 i( xb k ) X e 6 3 X, S (0), S ; X, S ; X (,0, ), S,, i i 5 At LO 6 independent SMD fracture functions. robabilistic interpretation at LO: te conditional probabilities to find an unpolarized, a longitudinally polarized or a transversely polarized quark wit longitudinal momentum fraction x B and transverse momentum k inside a nucleon fragmenting into a adron carrying a fraction ζ of te nucleon longitudinal momentum and a transverse momentum. FR X 5

26 Nucleon olarization SMD Fracture Functions for spinless adron production Quark polarization U L U L S û ( k ) ˆ m m L N u L k m m N Slˆ L L ˆ l t k t ij j ij j ˆ ˆ m mn SL m tˆ S k tˆ L L L mn SMD fracture functions depend on k x, k,,, S m k S m N uˆ uˆ S m k S m N lˆ lˆ S tˆ ( S ) tˆ ( k S ) tˆ m mn ( k S ) k ( S m m N k ) tˆ k k cos ( ) q azimutal dependence in fracture functions 6

27 LO cross-section for single adron production in FR d ( x 0) x ( l, ) N ( N, S ) ( l) ( ) X F 4 dxdq ds dd yq ( ) y eq q u x,, S u x,, sin( S) m y( y) S LlL x,, S l x,, co s( S ) m u ( x,, ) d k uˆ B m k u ( x,, ) d k uˆ uˆ l ( x,, ) d k lˆ B mn L B L ˆ m k l ( x,, ) d k l lˆ B mn At LO only 4 terms out of 8 Structure Functions, Only azimutal modulations No Collins-like sin(φ +φ S ) modulation No access to quark transverse polarization 7

28 Double adron production in DIS (DSIDIS): FR & CFR x 0, x 0 F F d d dxdq d dzd d d dq ( l, ) N ( N, S ) ( l) ( ) ( ) X ( l, ) q( k, s) ( l) q( k, s) M q, s/ N, S D q, s S ' D ( z, p ) D ( z, p ) p s H ( z, p ) q, s m 8

29 Unintegrated DSIDIS cross-section: accessing quark polarization N d dxdq d dzd dd ( l, ) N (, S ) ( l) ( ) ( ) X S uˆ D ( y) lˆ ll x ( y) 4 ˆ ' Qy p s t H m x S S UU L UL U ( y) 4 Q y D ll LU SL LL S L D D DSIDIS cross section is a sum of polarization independent, single and double spin dependent terms, similarly to SIDIS cross section. 9

30 wist- A LU asymmetry in DSIDIS DIS0, Anselmino, Barone and AK, LB 73 (0) 37 ˆ l D LU F k mm N sin( ) A LU F uˆ D... depend on x, z,,, and cos( ), wit One can coose as independent angles Integrating and over we obtain d d LU UU UU mm lu N F lˆ k F D ud ˆ 0 and ( ) x, z,,,, cos( ) sin( ) x, z,,,, c os( ) 30

31 A CLAS A LU ( x, z,,, ) a cos( ) a cos( ) sin( ) (, ) cos( ) cos() LU LU LU UU x, z,, auu auu p sin( ) p sin( ) Courtesy of S.isano & H.Avakian (unpublised ) CLAS RELIMINARY CLAS RELIMINARY ˆ l D LU F k mm N sin( ) resence of iger armonics indicate tat σ LU (ΔΦ) σ UU (ΔΦ) 3

32 Conclusions Azimutal correlations in diadron production in SIDIS and SIA provide a new way to study nucleon structure and adronization process In our recent work e inconsistency between IFF definitions in SIDIS and SIA was resolved e BELLE zero result in quark andedness MD FF study was explained New weigted asymmetries are proposed for measurement of tis FFs bot in SIDIS and SIA o describe FR of SIDIS 6 LO spin-dependent MD fracture functions For one adron in FR SIDIS SSA contains only a Sivers-type modulation. Observation of Collins-type SSA will indicate tat LO factorized approac fails Indication of long range correlation between te struck quark polarization and of produced in FR adron migt be important reliminary data from JLab sow nonzero A_LU We expect more news for JLab and EIC 3

33 adds 33

34 Collinear Frac.Func.: application to HERA data, D. de Glorian, R. Sassot, Leading roton Structure Function. RD 58, (998) d 3 p t arg et 4 y x p 4 y M p, Q, x,, = N ddq dx Q p x 34

35 Collinear Frac.Func.: application to HERA data, Soeibi et al, Neutron fracture functions. RD 95, 0740 (07) 35

36 DSIDIS azimutal modulations DIS0 F mm N ˆ t H kp cos( ) ˆ UU 0 nn p mm ud ˆ t H F D F m cos( ) ˆ t ˆ H t H Fkp Fp mn mm cos( ) D nn ( y) ( y) ( y) F ( )( k) ( k) MD ˆ ˆ k C M D k p k C[ Mˆ Dw] e d k d p ( z ) Mˆ ( x,, k,, ) D ( z, p ) w a () a a a Structure functions F... depend on x, z,,, and ud ˆ cos( ), wit 36

37 σ LU, σ LL, σ L ˆ l D LU F k mm N sin( ) LL F l ˆ D 0 L m N F lˆ k D cos( ) cos( S ) ˆ ˆ l D l D F0 Fk m mn S 37

38 σ UL UL mm D nn N F uˆ k L D F mm N mm m m sin( ) tˆ p L H ˆ tl H kp F sin( ) sin( ) tˆ ˆ Fk p Fp N mm L H t L H sin( ) 38

39 σ U U m N m F F uˆ D sin( ) k uˆ D uˆ D F 0 k mn S sin ( S ) ˆ ˆ ˆ t H t H t H F p F p Fkp 3 m mm mm mn sin 3 S tˆ H ˆ F kkp F t ˆ H t H kkp4 F kkp5 mm N mm N mm N 3 ˆ ˆ ˆ ˆ t H t H t H t H Fp F p Fkp F kp4 m mm mm mn mm m N sin 3 S tˆ ˆ H t H ˆ t H F kkp F kkp3 F kkp6 mm N mm N mm N 3 ˆ t H F kkp sin 3 S Dnn( y) m mn 3 3 ˆ t H tˆ H F p F kkp3 sin 3 S mm mm N ˆ t H tˆ H F p F kkp4 sin S mm mm N ˆ t H Fk p sin S mm mn ˆ t H Fkp3 sin S mm mn tˆ H F kkp sin S mm N 39