and Transversity Collins Effect in SIDIS and in e + e Annihilation

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1 7th International Spin Physics Symposium (SPIN26), Kyoto, October 2 7, 26 Collins Effect in SIDIS and in e + e Annihilation and Transversity A. Efremov, JINR, Dubna, Russia In collaboration with K.Goeke and P.Schweitzer Based on PRD 73 (26) 9425 and work in progress Overview: What is Collins effect? Collins effect in SIDIS. Emerging picture of Collins function & transversity. Transversity and Drell-Yan. Collins effect in e + e -annihilation Summary & conclusions.

2 Collins effect in SIDIS Asymmetry in transversally polarized parton fragmentation. SIDIS, transversely polarized target Epressions in LO /Q (Boer, Mulders,... 99s) k T factorization (Ji, Ma, Yuan&Collins, Met4) S q k q H zk q +K T d 3 σut ddzdφ = d3 σunp ddzdφ H (z, K2 T { + S T [ sin(φ φ S) A sin(φ φ S) }{{ UT } Sivers effect + sin(φ + φs) A S) UT }{{} Collins effect ) twist-2, chirally odd & naively T-odd (Collins 992, Efremov, Mankiewicz, Tornquist 992,...) HADRON PRODUCTION PLANE h a () twist-2, chirally odd (Ralston&Soper 979,...) l Θ h φ φ S S S P h q z ais N l LEPTON SCATTERING PLANE Collins SSA : A S) UT ha (, p2 T )H a (z, K2 T ) f a ()Da (z) ]}

3 Collins effect in e + e hh2x h jet, h2 jet 2 (Boer, Jakob, Mulders, 997) q q transversal spins correlation. P h θ 2 e e + e rest frame P h2 e + P h2 φ d 2 σ e+ e hh2x dφd cos θ2 = d2 σunp dφd cos θ2 [ sin 2 θ2 +cos(2φ a ) e2 a H a(/2) H ā(/2) + cos 2 CGauss θ2 }{{ a e2 a Da Dā } A C Gauss (z, z2) = 6 π z z2 z 2 +z2 2 Actually same angular dependence from radiative and acceptance effects Trick used at BELLE: A U A L + cos(2φ) P Universality: epect the same Collins function in e + e and SIDIS (Met2, Collins & Met5) though... not yet everybody fully convinced (Amsterdam group). ]

4 Available data SIDIS: HERMES (PRL94,22(25), hep-e/483 & AIP 792,933(25), hep-e/573) SIDIS: COMPASS (PRL94,222(25), hep-e/532) UT () for proton π + HERMES preliminary..2.3 (a) UT () for proton π - HERMES preliminary..2.3 (b) A sinφ C UT () for deuteron COMPASS data e + e BELLE (hep-e/5763). (Recently A U /AC P(z, ) for.2 < z <.3.2 (a) P(z, ) for.3 < z <.5.2 (b) positive hadrons.. P(z, ) for.5 < z <.7.2 (c) A sinφ C UT () for deuteron COMPASS data negative hadrons.. was reported (R.Seidl,QCD-N6)). (c) P(z, ) for.7 < z <.2 (d) (d) and: SIDIS: SMC preliminary (Bravar, Nucl.Phys.Proc.Suppl.79(999)52) e + e DELPHI preliminary (AE, Smirnova, Tkatchev, Nucl.Phys.Proc.Suppl.79(999)554)

5 Question : Are all these data due to the same Collins effect? Problems : HERMES & COMPASS Different scales. Unknown H evolution. Soft factors. Sudakov suppression. Unknown k T -dependence. Unknown functions H (z, K T ), h a (, p T ). Way out: SMC BELLE DELPHI Q 2 /GeV 2 Different scales compare H /D, presumably less scale-dependent. Neglect soft factors, disregard Sudakov suppression. F (, k T ) = F () G(k T )&Gaussian, if P h Q & at HERMES (D Alesio&Murgia24) h a () from chiral quark-soliton model (PRD64(2)343) about 2% accuracy. f a () from GRV98, Da (z) from Kretzer2; Kretzer,Leader,Christova2. Basically one unknown H can be etracted modulo uncertainties due to our assumptions.

6 Emerging picture of Collins function & transversity A S) = 2 UT a e2 a ha () B GaussH (/2)a (z) a e2 a f a () Da (z) H (/2)a (z) = d 2 KT KT H a (z, KT) 2 2zmπ Da (z) + p 2 h / K2 H BGauss(z) = For pions, two functions : H fav = H u/π+ = H d/π =... BGaussH (/2)fav = (3.5 ±.8) 2 H unf = H u/π = H d/π+ =... }{{} natural (?) to epect H fav H unf HERMES BGaussH (/2)unf = (3.8 ±.7) 2 }{{} H unf H fav string fragmentation (Artru,Czyżewski,Yabuki,ZPhysC73(997)527) UT () for proton π + HERMES preliminary..2.3 (a) UT () for proton π - HERMES preliminary..2.3 (b) A sinφ C UT () for deuteron COMPASS data positive hadrons.. (c) A sinφ C UT () for deuteron COMPASS data negative hadrons.. Good description of HERMES compatible with COMPASS (d)

7 Grain of salt: preliminary SMC charged hadrons Q 2 5 GeV 2,.8 z.45 and P h (.5.8) GeV Reason to worry? Data are preliminary A N in % Emerging picture of transversity from SIDIS How model dependent is our result? Compare to Vogelsang & Yuan, (PRD72,5428(25)) same B Gauss H a (different p T -dependence) but assume saturation of Soffer bound. h a () 2 (f a + ga )() Look closer: demand etracted B Gauss H to vary within -σ. Question: How much is h a () allowed to vary? h a Picture: u other h a h u } () within 3% of Soffer bound {{, } supported by lattice QCDSF h + h - h + h - proton deutron h q () u SMC preliminary our estimates..2.3 () from chiral quark soliton model () unconstrained. d

8 Emerging picture of transversity from SIDIS will improve Data on π & kaons. More data from HERMES proton & deuteron target. More data from COMPASS deuteron & proton target. Data from CLAS with transv. pol. target. Data from HALL-A, transv. 3 He neutron target, Q 2 2 GeV 2, h d () green: h d () < from chiral quark-soliton model, dashed: h d () of opposite sign, error bars: projections for 24 days of beam time (Chen, et al. nucl-e/53). UT () on neutron. π - (b) UT () on neutron. π + (c) JLab HALL A -.5 JLab HALL A

9 Transversity and Drell-Yan The best and the cleanest way to access transversity h A T T (y, Q 2 ) = Σ ae 2 ah a (, Q 2 )hā ( 2, Q 2 ) Σ b e 2 b f b (, Q 2 )f b (2, Q 2 ), /2 = Q 2 s e±y. Are planned to be measured at PAX & J-PARC. Our predictions (χqsm): (A.E.,Goeke, Schweitzer EPJC35:27(4) and work in progress) A TT (y,q 2 ) J-PARC A TT (y,q 2 ) J-PARC A TT (y,q 2 ) PAX E beam = 3 GeV -.2 E beam = 5 GeV.4 pp Q 2 = 5 GeV 2.2 Q 2 = 5 GeV Q 2 = 6 GeV Q 2 = 6 GeV y.5 y -. pp.5 Rather noticeable effect even for p p! Mostly sensitive to h u (). Allow discriminate models (e.g. popular guess h a () g () a would give AT T 3%) y

10 Collins effect in e + e C unf (a) H (/2) (z) at BELLE (b) BELLE e + e hh2x with h,2 = π ± A U (φ) A L (φ) + cos(2φ ) P with P(z, z2) = F (H fav /Hunf, Gauss) include s, s H unf (fine for D) symmetric z z2 or fav unf Best Ansatz H (/2)a = CazD a (z), other Ansätze not ecluded Best fit results: C fav =.5, C unf =.45 }{{} sign preferred by HERMES, correlated C fav -.4 fav unf or vice versa: fav unf z P (z, ) for.2 < z <.3 (a).2 P (z, ) for.3 < z <.5 (b).2 P (z, ) for.5 < z <.7 (c).2 P (z, ) for.7 < z < (d) Good description!

11 Important most recent news from BELLE (hep-e/674) New double ratio was measured, could decrease C fav, C unf correlation A U (φ) A C (φ) + cos(2φ ) Pc(H fav /Hunf, Gauss) P c (z, ) for.2 < z <.3 (a).2 P c (z, ) for.3 < z <.5 (b).2 P c (z, ) for.5 < z <.7 (c).2 P c (z, ) for.7 < z < (d) Ecellent confirmation of our picture of Collins effect! Faith in our first understanding of Collins effect strengthened. New (preliminary) data, will provide valuable constraints and improve the fits after officially released.

12 DELPHI preliminary (AE, Smirnova, Tkatchev, Nucl.Phys.Proc.Suppl.79(999)554) e + e Z hh2x, h,2 = charged hadrons dσ(e + e hh2x) = P ( + cos(2φ) P2), P2 = F (H fav + H unf ) dφ with P 2,DELPHI = (.26 ±.8)%± unknown systematics. Different scales! Assume H D one scale H D another scale H c, H b? Since m c, m b M Z : Maybe unfavoured? Maybe zero? Charged hadrons = π ±, K ±,... with lim mπ P 2, estimate ( )% H (/2)a/π D a/π = lim m K H (/2)a/K D a/k Preliminary DELPHI seems not incompatible with BELLE! Intermediate STATUS : SIDIS: HERMES & COMPASS compatible e + e : BELLE & DELPHI not incompatible } What about HERMES vs. BELLE?

13 HERMES vs. BELLE I. 2B GaussH (/2)fav D fav 2BGaussH (/2)unf D unf HERMES = (7.2 ±.7)% vs. 2H (/2)fav D fav HERMES = (4.2 ± 2.7)% vs. 2H (/2)unf D unf BELLE BELLE = ( )% = ( )%. Central values of HERMES systematically lower then of BELLE. Evolution? But:. BGauss < 2. Errors correlated! II. z-dependence at HERMES from BELLE fit for H (z). Solid lines σ-range. Dashed line unknown Gaussian widths.5. p2 h 4. K 2.5 H UT (z) for proton.2 π + HERMES preliminary (a) UT (z) for proton π - HERMES preliminary (b) z z BELLE & HERMES compatible!

14 Summary & Conclusions Collins effect: try of first global analysis of data. As good as possible at present stage, but assumptions & approimations necessary. e + e BELLE consistent with SIDIS HERMES & COMPASS, preliminary DELPHI consistent with those, preliminary SMC not. Emerging picture: H u H d possible eplanations: Artru et. al, Vogelsang & Yuan. h u > and within 3 % of Soffer bound in agreement with lattice. Other h a () unknown, to be improved: HERMES, COMPASS, JLAB & BELLE. Use emerging picture to understand other interesting data, e.g. CLAS & sin 2φ HERMES A applications (to be done). UL φ or twist-3 Asin UL φ and Asin LU Encouraging progress! (In spite of many forced theoretical uncertainties: soft factor, /Nc, scale dependence, transverse momenta,...) However, optimism! New & more precise data coming in, improved analyses necessary. We are learning! Thank you!