Precision fragmentation function measurements at BelleFreiburg, June 6 2007

R. Seidl (University of Illinois and RBRC) Outline:Why QCD and spin physics?Transversity and the Collins functionTransversity as thirsd leading twist distribution functionAccess to transversity over Collins fragmentation functionCollins function measurements at BelleThe Belle detectorImproved statistics with on_resonance dataFirst global analysis from SIDIS and Belle dataInterference fragmentation function measurementsunpolarized fragmentation function measurements

Why QCD and spin physics?QCD as the right theory of quarks and gluons,Perturbative part well understoodNucleon as simplest bound state of QCD poorly understood (though building block of most matter in universe)Significant surprises when including spin:

Spin crisis: Quarks contribute only ~30% to nucleon spin Large transverse single spin asymmetries which are forbidden by perturbative QCD observedYou think you understand something? Now add spin ... R. Jaffe

The (spin) structure of the NucleonLongitudinal Spin Sum Rule:Transverse Spin (BLT) Sum Rule?Double Spin Asymmetries (pp,SIDIS)W-production (pp)Exclusive processes (DVCS,etc)Chiral-odd Fragmentation functions (Collins,IFF,L)Sivers effect??Color Glass condensate ??

Quark distributionsSum of quarks with parallel and antiparallel polarization relative to proton spin(well known from Collider DIS experiments)

Dq(x), DG(x)Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton(known from fixed target (SI)DIS experiments)

q(x),G(x)dq(x)Difference of quarks with parallel and antiparallel polarization relative to transversely polarized proton(first results from HERMES and COMPASS with the help of Belle)

Unpolarized distribution function q(x)Helicity distribution function Dq(x)Transversity distribution function dq(x)

Cross sections in (semi)inclusive pp and DIS, factorizationfq(x1) fq(x2) s Dh(z) fq(x1) s Dh(z) Hard scales PT and Q2Convolution integrals over all involved momentaFactorization of involved distribution and fragmentation functions(kT)-dependent distribution and fragmentation functionsk kQ

Transversity propertiesHelicity flip amplitudeChiral odd Since all interactions conserve chirality one needs another chiral odd objectDoes not couple to gluons adifferent QCD evolution than Dq(x)Valence dominateda Comparable to Lattice calculations, especially tensor charge

Positivity bound:

Soffer bound:

Finding another chiral odd object in SIDIS a Collins fragmentation functionCross section factorizes: sepgehX = Sqqpgq(x) sQED Dqgh(z)Transverse momentum dependent Distribution functionsTransverse momentum dependent Fragmentation functionsBoth Sivers and Collins Effect create azimuthal asymmetries

Azimuthal asymmetries in SIDISSivers and Collins effect are not distiguishable with longitudinally polarized targetHigher Twist effects are kinematically favored in longitudinal caseWith transversely polarized target a 2nd angle allows to distinguish effectsU: unpolarized beamT: transversely polarized target

J.C. Collins, Nucl. Phys. B396, 161(1993)qCollins Effect:Fragmentation with of a quark q with spin sq into a spinless hadron h carries anazimuthal dependence:

Collins effect in quark fragmentation

The Collins effect in the Artru fragmentation model+ picks up L=1 tocompensate for thepair S=1 and is emittedto the right.String breaks anda dd-pair with spin-1 is inserted.A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation:In Artru Model: favored (ie up+) and disfavored (ie up-) Collins function naturally of opposite sign

Towards a global transversity analysisSIDIS experiments (HERMES and COMPASS, eRHIC) measure dq(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 appears to be proven in LO by Collins and Metz:[PRL93:(2004)252001 ]+most recent work from Amsterdam Group

KEKB: L>1.6x1034cm-2s-1 !!Asymmetric collider8GeV e- + 3.5GeV e+ s = 10.58GeV (U(4S))e+e-U(4S)BBOff-resonance: 10.52 GeVe+e-qq (u,d,s,c)Integrated Luminosity: >700 fb-1 >60fb-1 => off-resonance

Good tracking and particle identification!

e- e+ Jet axis: Thrust = 6.4Near-side Hemisphere: hi , i=1,Nn with zi Far-side: hj , j=1,Nf with zj

QEvent Structure at Bellee+e- CMS frame:Spin averaged cross section:

Collins fragmentation in e+e- : Angles and Cross section cos(f1+f2) methodj1j2-pj1j22-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment oftransverse quark spinsQe+e- CMS frame:e- e+ [D.Boer: PhD thesis(1998)]

Collins fragmentation in e+e- : Angles and Cross section cos(2f0) methodj02-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment oftransverse quark spinsQ2Independent of thrust-axisConvolution integral I over transverse momenta involved e+e- CMS frame:e- e+ [Boer,Jakob,Mulders: NPB504(1997)345]

Applied cuts, binningOff-resonance data 60 MeV below U(4S) resonance29.1 fb-1 Later also on-resonance data: 547 fb-1Track selection:pT > 0.1GeVvertex cut: dr0.2

Hemisphere cutQT < 3.5 GeV

z1

Examples of fits to azimuthal asymmetriesCosine modulationsclearly visibleD1 : spin averaged fragmentation function, H1: Collins fragmentation functionN(f)/N0No change in cosine moments when including sine and higher harmonics

2f0(f1+f2)

Methods to eliminate gluon contributions: Double ratios and subtractionsDouble ratio method:Subtraction method:Pros: Acceptance cancels outCons: Works only if effects are small (both gluon radiation and signal)Pros: Gluon radiation cancels out exactlyCons: Acceptance effects remain2 methods give very small difference in the result

Testing the double ratios with MCAsymmetries do cancel out for MCDouble ratios of p+p+/p-p- compatible with zeroMixed event pion pairs also show zero resultAsymmetry reconstruction works well for t MC (weak decays)Single hemisphere analysis yields zeroDouble ratios are safe to use

uds MC (UL/L double ratios)uds MC (UL/C double ratios) Data (p+p+/p-p-)

Other Favored/Unfavored Combinations charged pions or p0Unlike-sign pion pairs (U):(favored x favored + unfavored x unfavored)Like-sign pion pairs (L):(favored x unfavored + unfavored x favored) pp0 pairs(favored + unfavored) x (favored + unfavored)P.Schweitzer([hep-ph/0603054]): charged pp 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= up+,dp-,cc.Unfavored= dp+,up-,cc.Build new double ratios:Unlike-sign/ charged pp pairs (UC)ULUC

What about the data under the resonance?More than 540 fb-1 of on_resonance data U(4S) is just small resonance More than 75% of hadronic cross sectionfrom open quark-antiquark production

Why is it possible to include on_resonance data?Different Thrust distributions e+ e- q q (u d s) MC U(4S) B+ B- MC U(4S) B0 B0 MC Largest systematic errors reduce with more statistics Charm-tagged Data sample also increases with statistics

Improved systematic errors (UC)Tau contributionPID errorMC double ratiosCharged ratios (p+p+ /p-p- )higher moments in Fitdifference double ratio-subtraction methodreweighted MC-asymmetries: cos(f1+f2) asymmetries underestimated rescalied with 1.21Correlation studies: statististical error rescaled by1.02 (UL) and 0.55 (UC) after rigorous errorcalculation correctBeampolarization studies consistent with zeroCorrection ofcharm events

A0 (cos(2f0)) momentsA12 (cos(f1 + f2)) moments

Final charm corrected results for e+ e- p p X (29fb-1 of continuum data)Significant non-zero asymmetries Rising behavior vs. zcos(f1+f2) double ratios only marginally largerUC asymmetries about 40-50% of UL asymmetriesFirst direct measurements of the Collins functionFinal resultsPreliminary results

Sheet1

Integrated results:

A0(UL)(3.06 0.57 0.55)%

A12(UL)(4.26 0.68 0.68)%

A0(UC)(1.270 0.489 0.350)%

A12(UC)(1.752 0.592 0.413)%

Charm corrected results for e+ e- p p X (547 fb-1)Significance largely increasedBehavior unchangedReduced systematic errors due to statisticsPrecise measurements of the Collins functionPRELIMINARY

Sheet1

Integrated results:

A0(UL)(2.67 0.10 0.26)%

A12(UL)(3.55 0.08 0.15)%

A0(UC)(1.11 0.11 0.22)%

A12(UC)(1.46 0.09 0.13)%

Global Analysis - SIDIS measurements I: HERMES (proton)Nonzero AsymmetriesCollins function and Transversity nonzeroSame magnitude, opposite sign for p+ and p- AsymmetriesHint for a large and negative disfavored Collins function

PRL 94, 012002 (2005) and hep-ex/0612010 Taken at cQSM value of dr = -0.30 of Schweitzer and WakamatsuhH

Global Analysis - SIDIS measurements II: COMPASS (deuteron)Smaller asymmetries than in proton case Hint of cancellation of transversity in isoscalar targetPRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007 -ACollFirst fits to HERMES and COMPASS data using assumptions on Transversity show results consistent with each otherKaon asymmetries shown last year (both experiments)

Global Analysis- Belle Collins function: asymmetries for double ratios of ppunlikesign / pplikesign for 29 fb-1Direct measurement of the Collins effectCollins function largeConsistent with large, negative disfavored Collins functionRS et al., PRL 96, 232002 (2006) +inclusion of U(4S) data:>500 fb-1 (not yet included in global fit by Anselmino et al: hep-ex 0701006)

PRELIMINARY

First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins dataHERMES AUT p dataCOMPASS AUT d dataBelle e+ e- Collins dataKretzer FF

First extraction of transversity (up to a sign)

Anselmino et al: hep-ex 0701006

Interference fragmentation functione+e- (p+p-)jet1(p-p+)jet2XStay in the mass region around r-massFind pion pairs in opposite hemispheresObserve angles j1+j2 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 and Artru,CollinsEarly work by Collins, Heppelman, Ladinski

j2-pp-j1Model predictions by:Jaffe et al. [PRL 80,(1998)]Radici et al. [PRD 65,(2002)]

Different model predictions for IFFJaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of pp-phaseshift analysisasign change at r-massoriginally no predictions on actual magnitudesTang included some for RHIC-Spin Radici et al. [Phys. Rev. D65 (2002)] : Spectator model in the s-p channel ano sign change observed (updated model has Breit-Wigner like asymmetry)

Unpolarized FF as important input for all precise QCD measurements No low-Q2 data available important for evolutionNo high-z data availableHuge amount of B-factory data can helpFavored/Disfavored disentangling by detecting hadron pairs (as in Collins analysis)?MC simulation, ~1.4 fb-12.

Future measurements I: EIC, transverse spinTransversity at higher x already measured by HERMES, COMPASS and JLAB12,first DY transversity from JPARC or FAIR?Lower x will be interesting for tensor charge

Summary and outlookContinue to measure precise spin dependent fragmentation functions at BellekT dependence of Collins functionFavored/disfavored disentanglementIniterference Fragmentation function measurements (started) Measure precise unpolarized fragmentation functions of many final statesImportant input for general QCD physics and helicity structure measurementsMeasure other interesting QCD-related quantities at Belle:Chiral-odd L-fragmentation functionEvent shapesR-ratio with ISR A first successful global analysis of transversitydata using the HERMES,COMPASS and published Belle dataBelle Collins data largely improved from 29 547 fb -1Significant, nonzero asymmetries Collins function is largeLong Collins paper is nearly finished

Backup SlidesBelle

Interference Fragmentation f0 methodSimilar to previous methodObserve angles j1R+j2R between the event-plane (beam, two-pion-axis) and the two two-pion planes.Theoretical guidance by Boer,Jakob,Radici

jR2p-jR1

What would we see in e+e-?Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m1pp

m1pp

m2pp m2pp JaffeRadici

Sivers interpretationTaken from H. Tanaka in Trento04Attractive rescattering of hit quark by gluon creates transverse momentumM.Burkardt [hep-ph0309269] impact parameter formalismOrbital angular momentum at finite impact parameterobserved and true x differObservable left/right asymmetry>

Hohe energien spin ist erhaltungsgroesse (fuer kleine Quarkmassen)Auch als test einsetzbar

Artru sieht fuer VM entgegengesetzes Vorzeichen*Jet achse aus allen Teilchen mit Pt>0.1 GeV

*Spin averaged dihadron cross sectionConvolution integral erklaeren!

Radiativen Term schon einfuehren, proportional zu 1