Outline: The Belle detector unpolarized fragmentation function measurements Understanding the systematics for precision measurements at high z Expected precision The Collins function measurements Access to transversity over Collins fragmentation function Collins function measurements at Belle Interference fragmentation function measurements Light quark and spin dependent fragmentation function measurements at Belle Fragmentation workshop, Trento, February 26, 2008 M. Grosse Perdekamp (University of Illinois) M. Leitgab (University of Illinois) A. Ogawa (BNL/RBRC) R. Seidl (RBRC) representing the Belle collaboration

Fragmentation workshop, Trento, February 26 th KEKB: L>1.7x10 34 cm -2 s -1 !! Asymmetric collider 8GeV e GeV e + √s = 10.58GeV (  (4S)) e + e -   (4S)  B  B Continuum production: GeV e + e -  q  q (u,d,s,c) Integrated Luminosity: >700 fb -1 >60fb -1 => continuum 2 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Fragmentation workshop, Trento, February 26th Belle detector KEKB

 / K L detection 14/15 lyr. RPC+Fe C entral D rift C hamber small cell +He/C 2 H 6 CsI(Tl) 16X 0 Aerogel Cherenkov cnt. n=1.015~1.030 Si vtx. det. 3/4 lyr. DSSD TOF conter SC solenoid 1.5T 8 GeV e  3.5 GeV e  Belle Detector Good tracking and particle identification!  (K)~85%,  (   K)<10%

Fragmentation workshop, Trento, February 26 th Single hadron cross section 4 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle Process: e + e -  hX At leading order sum of unpolarized fragmentation functions from quark and anti-quark side e-e- e+e+ h

Fragmentation workshop, Trento, February 26 th Systematic studies Momentum scale and smearing – understood Particle identification: create PID efficiency matrix for K, ,p,e,   Unfolding –Use D *   D 0   K for K,  identification –Use    P for P,  identification Acceptance correction 5 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle REAL Particles Reconstructed particles  Kp  e  K p  e

Fragmentation workshop, Trento, February 26 th PDG2007 Unpolarized FF as important input for all precise QCD measurements Statistics limited at low-Q 2 and high-z  important for evolution Huge amount of Belle data can help Student working on unpol. FF extraction Favored/Disfavored disentangling by detecting hadron pairs (as in Collins analysis)? Also plans to measure  and  6 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle MC simulation, ~1.4 fb -1 2.

Fragmentation workshop, Trento, February 26 th Event Structure for Hadron pairs 7 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle = 6.4 Far-side: h j, j=1,N f with z j e + e - CMS frame: e-e- e+e+  Spin averaged cross section: Jet axis: Thrust Near-side Hemisphere: h i, i=1,N n with z i

Fragmentation workshop, Trento, February 26 th Collins fragmentation in e + e - : Angles and Cross section cos(  1 +  2 ) method 8 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle       2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins  e + e - CMS frame: e-e- e+e+ [D.Boer: PhD thesis(1998)]

Fragmentation workshop, Trento, February 26 th Collins fragmentation in e + e - : Angles and Cross section cos(2  0 ) method 9 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle  2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins  Independent of thrust-axis Convolution integral I over transverse momenta involved e + e - CMS frame: e-e- e+e+ [Boer,Jakob,Mulders: NPB504(1997)345]

Fragmentation workshop, Trento, February 26 th Applied cuts, binning Off-resonance data –60 MeV below  (4S) resonance –29.1 fb -1  Later also on-resonance data: 547 fb -1 Track selection: –pT > 0.1GeV –vertex cut: dr<2cm, |dz|<4cm Acceptance cut –-0.6 < cos  i < 0.9 Event selection: –Ntrack  3 –Thrust > 0.8 –z 1, z 2 > R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Hemisphere cut Q T < 3.5 GeV z1z1 z2z = Diagonal bins z1z1 z2z2

Fragmentation workshop, Trento, February 26 th Examples of fits to azimuthal asymmetries 11 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N(  )/N 0 No change in cosine moments when including sine and higher harmonics 22     ) Cosine modulations clearly visible P1 contains information on Collins function

12 Fragmentation workshop, Trento, February 26thR.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Methods to eliminate gluon contributions: Double ratios and subtractions Double ratio method: Subtraction method: Pros: Acceptance cancels out Cons: Works only if effects are small (both gluon radiation and signal) Pros: Gluon radiation cancels out exactly Cons: Acceptance effects remain 2 methods give very small difference in the result

Fragmentation workshop, Trento, February 26 th Testing the double ratios with MC Asymmetries do cancel out for MC Double ratios of  +  + /  -  - compatible with zero Mixed event pion pairs also show zero result Asymmetry reconstruction works well for t MC (weak decays) Single hemisphere analysis yields zero  Double ratios are safe to use 13 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle uds MC (U/L double ratios) uds MC (U/C double ratios) U : Unlike sign pion pairs L : Like sign pion pairs C : all charged pion pairs Data (         )

More than 540 fb -1 of on_resonance data  (4S) is just small resonance More than 75% of hadronic cross section from open quark-antiquark production What about the data under the resonance? Fragmentation workshop, Trento, February 26th14R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle

Fragmentation workshop, Trento, February 26 th Why is it possible to include on_resonance data? Different Thrust distributions 15 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle e + e -  q  q (u d s) MC  (4S)  B + B - MC  (4S)  B 0  B 0 MC Charm-tagged Data sample (used for charm correction) also increases with statistics Largest systematic errors reduce with more statistics e + e -  qq ̅, q∈uds e + e -  cc ̅

Fragmentation workshop, Trento, February 26 th Improved systematic errors (UC) Tau contribution PID error MC double ratios Charged ratios (  +  + /  -  - ) higher moments in Fit difference double ratio- subtraction method 16 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle reweighted MC-asymmetries:  cos      asymmetries underestimated due to thrust axis reconstruction  rescaled with 1.21 Correlation studies:  statistical error rescaled by1.02 (UL) and 0.55 (UC) Beam polarization studies  consistent with zero Correction for charm events A 0 (cos(2   )) moments A 12 (cos(       )) moments

Fragmentation workshop, Trento, February 26 th Final charm corrected results for e + e -   X (29fb -1 of continuum data) Significant non-zero asymmetries Rising behavior vs. z cos(  1 +  2 ) double ratios only marginally larger UC asymmetries about 40-50% of UL asymmetries First direct measurements of the Collins function 17 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Final results Preliminary results

Fragmentation workshop, Trento, February 26 th Charm corrected results for e + e -   X (547 fb -1 ) Significance largely increased Behavior unchanged Reduced systematic errors due to statistics Precise measurements of the Collins function 18 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle PRELIMINARY

Fragmentation workshop, Trento, February 26 th Collins asymmetries II: sin 2  /(1+cos 2  ) binning (UL) Nonzero quark polarization ~ sin 2  Unpolarized de- nominator ~ 1+cos 2  Clear linear behavior seen when using either thrustz or 2nd hadron as polar angle Better agreement for thrust axis (~approximate quark axis) UC plots similar 19 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle thrustz   PRELIMINARY

20 Fragmentation workshop, Trento, February 26thR.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Towards a global transversity analysis SIDIS experiments (HERMES and COMPASS, eRHIC) measure  q(x) together with either Collins Fragmentation function or Interference Fragmentation function RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x) There are always 2 unknown functions involved which cannot be measured independently Spin dependent Fragmentation function analysis in e + e - Annihilation yields information on the Collins and the Interference Fragmentation function ! Universality understood Evolution ?

Fragmentation workshop, Trento, February 26 th Global analysis by Anselmino et al: Phys.Rev.D75:054032,2007) 21 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle HERMES p data: PRL 94, (2005) 2005 data not yet included in fit COMPASS d data: PRL 94, (2005) and 2005 and identified hadron data not yet included in fit: Nucl.Phys.B765:31-70,2007

Fragmentation workshop, Trento, February 26 th Global Analysis- Belle Collins function: asymmetries for double ratios of  unlikesign /  likesign for 29 fb R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Anselmino et al: Phys.Rev.D75:054032,2007, data: RS et al.(Belle collaboration), PRL 96, (2006) +inclusion of  (4S) data:  >540 fb -1 (not yet included in global fit) PRELIMINARY

Fragmentation workshop, Trento, February 26 th First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins data HERMES AUT p data COMPASS AUT d data Belle e+ e- Collins data Kretzer FF  First extraction of transversity (up to a sign) 23 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Anselmino et al: Phys.Rev.D75:054032,2007

Fragmentation workshop, Trento, February 26 th Interference Fragmentation – thrust method e + e -  (  +  - ) jet1 (     ) jet2 X Stay in the mass region around r-mass Find pion pairs in opposite hemispheres Observe angles  1 +  2 between the event-plane (beam, jet-axis) and the two two-pion planes. Transverse momentum is integrated (universal function, evolution easy  directly applicable to semi-inclusive DIS and pp) Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] 24 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

Fragmentation workshop, Trento, February 26 th Interference Fragmentation – “  0 “ method Similar to previous method Observe angles  1R +  2R between the event-plane (beam, two-pion-axis) and the two two-pion planes. Theoretical guidance by Boer, Jakob, Radici 25 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle  R2  R1

Fragmentation workshop, Trento, February 26 th Different model predictions for IFF 26 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of  - phaseshift analysis  sign change at  mass -originally no predictions on actual magnitudes -Tang included some for RHIC-Spin Radici et al. [Phys. Rev. D65 (2002)] : Spectator model in the s-p channel  no sign change observed (updated model has Breit-Wigner like asymmetry) PRELIMINARY f 1, h 1 from spectator model f 1, h 1 =g 1 from GRV98 & GRSV96

Fragmentation workshop, Trento, February 26 th Summary and outlook Continue to measure precise spin dependent fragmentation functions at Belle –kT dependence of Collins function –Favored/disfavored disentanglement –Interference Fragmentation function measurements (started) Measure precise unpolarized fragmentation functions of many final states  Important input for general QCD physics and helicity structure measurements Measure other interesting QCD- related quantities at Belle: –Chiral-odd  -fragmentation function –Event shapes –R-ratio with ISR 27 R.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle A first successful global analysis of transversity data using the HERMES,COMPASS and published Belle data Belle Collins data largely improved from 29  547 fb -1 Significant, nonzero asymmetries  Collins function is large Long Collins paper is nearly finished

28 Fragmentation workshop, Trento, February 26thR.Seidl: Light quark and spin dedpentent fragmentation function measurements at Belle Backup Slides

Fragmentation workshop, Trento, February 26 th R.Sei dl: Towa rds a meas urem ent of the tenso r charg e 29 Collins fragmentation in e + e - : Angles and Cross section cos(2   ) method  2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins  Independent of thrust-axis Convolution integral I over transverse momenta involved e + e - CMS frame: e-e- e+e+ [Boer,Jakob,Mulders: NPB504(1997)345]

Fragmentation workshop, Trento, February 26 th R.Sei dl: Towa rds a meas urem ent of the tenso r charg e 30 Similar to previous method Observe angles  1R  2R between the event-plane (beam, two-pion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici Interference Fragmentation – “   “ method  R2  R1

Fragmentation workshop, Trento, February 26 th R.Sei dl: Towa rds a meas urem ent of the tenso r charg e 31 Applied cuts, binning Off-resonance data –60 MeV below  (4S) resonance –29.1 fb -1  Later also on-resonance data: 547 fb -1 Track selection: –pT > 0.1GeV –vertex cut: dr<2cm, |dz|<4cm Acceptance cut –-0.6 < cos  i < 0.9 Event selection: –Ntrack  3 –Thrust > 0.8 –Z 1, Z 2 >0.2 Hemisphere cut Q T < 3.5 GeV z1z1 z2z = Diagonal bins z1z1 z2z2

Fragmentation workshop, Trento, February 26 th R.Sei dl: Towa rds a meas urem ent of the tenso r charg e 32 Other Favored/Unfavored Combinations  charged pions or   Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored)  ±   pairs (favored + unfavored) x (favored + unfavored) P.Schweitzer([hep-ph/ ]): charged  pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.  Build new double ratios:  Unlike-sign/ charged  pairs (UC) UL UC

Fragmentation workshop, Trento, February 26 th R.Sei dl: Towa rds a meas urem ent of the tenso r charg e 33 What would we see in e + e - ? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m1  m2  “ Jaffe ”“ Radici ”