Transverse Spin DependentDi-Hadron Fragmentation Functions at

Anselm Vossen (University of Illinois)Matthias Grosse Perdekamp

(University of Illinois)Martin Leitgab (University of Illinois)

Akio Ogawa (BNL/RBRC) Ralf Seidl (RBRC)

Kieran Boyle (RBRC)

Outline

• Motivation– Analysis of Transverse Spin Effects

in SIDIS, proton-proton– Recent experimental results– Transversity extraction

• Measuring Fragmentation Functions at Belle– Experimental techniques– Interference Fragmentation Function Measurement– Comparison with theory

• Summary & Outlook

Transverse Spin Asymmetries

• Experimental results in SIDIS and pp

Transverse Spin Asymmetries- Single Hadrons

• Large transverse single spin effects persist at large scale

• Convolution of different effects

RL

RLN P

A

1

4

Transversity

PHENIX, forward at s = 62 GeV, nucl-ex/0701031

21

222xx

s

px L

F

Transverse Spin Asymmetries

• Experimental results in SIDIS and pp• Access to fundamental aspects of QCD and nucleon

structure:– TMDs, orbital angular momentum– Initial, final state interactions– Gauge invariance of correlators

• Prominent effects:– Transversity * Collins– Sivers Effect

• Separation of different effects requires measurements at multiple experiments, channels -> pp, SIDIS, e+e-

Measuring Transversity in SIDIS

_

+1h

_

+↑

↑ ↑

↑ ↓

↑ ↑

↓

• Transversity base:

_

Difference in densities for ↑, ↓ quarks in ↑ nucleon •Helicity base:

Need chiral odd partner => Fragmentation function

Chiral odd FFs

+

_

+

1h

_

+

_1H

Collins effect

q

N

: Collins FF

Collins Fragmentation at Belle

• First extraction of transversity quark distribution

Together with HERMES, COMPASSFirst, still model dependent transversity Extraction :

Alexei Prokudin, DIS2008, update of Anselmino et al: hep-ex 0701006

Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)

Collins Extraction of Transversity: model dependence from Transverse

Momentum Dependences!

),(

)(),(

)sin()sin(),()(

),(

22

,122

pzDdy

dkxqkddde

pzHdy

dkxqkddde

AhqhS

qq

hShqSqhS

qq

CollinsUT

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007

k┴ transverse quark momentum in nucleonp┴ transverse hadron momentum in fragmentation

transv

ersity

Collin

s FF

hadron FFquark pdf

The transverse momentum dependencies are unknown anddifficult to obtain experimentally!

Chiral odd FFs

+

_

+ _

+ q

N

_

Lz-1Lz

1H

Interference Fragmentation Function

( )

1h

Advantages of IFF

• Independent Measurement• Favourable in pp: no Sivers• Transverse momentum is integrated

– Collinear factorization

– No assumption about kt in evolution– Universal function– evolution known, collinear scheme can be used – directly applicable to semi-inclusive DIS and pp

• First experimental results from HERMES, COMPASS, PHENIX

Interference FF in Quark Fragmentation

q

1 2

pair

:quark momentum

:quark spin

: momentum difference -

: transverse hadron momentum difference

z

q

h h

T

pair

k

s

R p p

R

E E

2 : relative hadron pair momentum

q

pairE s

qs

k

R

Interference Fragmentation Function:Fragmentation of a transversely polarizedquark q into two spin-less hadron h1, h2 carries anazimuthal dependence:

R

sin

T qk R s

1h

2h

Di-Hadron SSA in SIDIS

(both on proton target, sign convention different)

Added statistics from 2008 running As expected:

No significant asymmetries seen at central-rapidity.

SSA from di-hadron productionExtended kinematic regime compared with SIDISHard scale

15

General Form of Fragmentation Functions

,

1 1

ˆ ( , ) ( , )

T qpair q pairpair pair pair pair pairq

pair

k R sD z M D z M H z ,M

zM

Number density for finding Hadron pair with invariant mass MPair from a transversely polarized quark, q:

unpolarized FF Interference FF

o Quark spin direction unknown: measurement of Interference Fragmentation function in one hemisphere is not possible

sin φ modulation will average out.

o Correlation between two hemispheres with sin φRi single spin asymmetries results in cos(φR1+φR2) modulation of the observed di-hadron yield.

Measurement of azimuthal correlations for di-pion pairs around the jet axis in two-jet events!

Spin Dependent FF in e+e- : NeedCorrelation between Hemispheres !

17

q1

quark-1 spin

Interference effect in e+e-

quark fragmentation will lead to azimuthalasymmetries in di-hadron correlation measurements!

Experimental requirements:

Small asymmetries very large data sample!

Good particle ID to high momenta.

Hermetic detector

Measuring di-Hadron CorrelationsIn e+e- Annihilation into Quarks

electron

positron

q2

quark-2 spin

( )

z2 z1

z1,2 relative pion pair momenta

( )

KEKB: L>2.11 x 1034cm-2s-1 !!• Asymmetric collider• 8GeV e- + 3.5GeV e+

• √s = 10.58GeV ((4S))• e+e-(4S)BB• Continuum production:

10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: ~ 950 fb-1

• >70 fb-1 => continuum

18

Belle detectorKEKB

Collins Asymmetries in Belle 19 May 28th Large acceptance, good tracking and particle identification!

He/C2H6

Interference Fragmentation–thrust method

• e+e- (+-)jet1()jet2X• Find pion pairs in opposite

hemispheres• Measure azimuthal correlations

of• Theoretical guidance by papers

of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]

• Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)]

20

1 2 1 1 1 1 2 2 1 2cosN H z ,m H z ,m

2

1

1hP

2hP

2h1h PP

Model predictions by:

•Jaffe et al. [PRL 80,(1998)]

•Radici et al. [PRD 65,(2002)]

R

h1 h2R =P -P

(Here: z1, (z2)relative momenta of first (second) pair)

Amplitude of modulation directly measures IFF! (squared)

21

Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance

ii

ii

p

npTThrust

ˆ

:

• small B contribution (<1%) in high thrust sample • >75% of X-section continuum under ϒ(4S) resonance• 73 fb-1 662 fb-1

9.44 9.46

e+e- Center-of-Mass Energy (GeV)

0

5

10

15

20

25

(e+

e-

had

ron

s)(n

b)

(1S)10.0010.02

0

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

(3S)10.54 10.58 10.62

0

5

10

15

20

25

(4S)9.44 9.46

e+e- Center-of-Mass Energy (GeV)

0

5

10

15

20

25

(e+

e-

had

ron

s)(n

b)

(1S)10.0010.02

0

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

5

10

15

20

25

(2S)10.34 10.37

0

5

10

15

20

25

(3S)10.54 10.58 10.62

0

5

10

15

20

(3S)10.54 10.58 10.62

0

5

10

15

20

25

(4S)BB00 BB

e+e-qq̅, q uds∈

e+e-cc̅

0.5 0.8 1.0

4s“off”

Asymmetry extraction

• Build normalized yields:

• Fit with:

or

22

,)( 21

N

N N

N RR )( 21

)sin()(2cos

)cos(

21122112

122112

dc

ba

122112 )cos( ba

Amplitude a12 directly measures IFF! (squared)

Zero tests: MC

• A small asymmetry seen due to acceptance effect• Mostly appearing at boundary of acceptance• Opening cut in CMS of 0.8 (~37 degrees) reduces

acceptance effect to the sub-per-mille level•

23

Ph

),cos(ˆ

nPP

nP

h

h

No opening cutOpening cut>0.7Opening cut >0.8

2 2sin /(1 cos ) 0.5

Zero tests: Mixed Events

False A

symmetrie

s consis

tent with

zero

(Red/blue points: Thrust axis last or current event)

• Inject asymmetries in Monte Carlo

• Reconstruction smears thrust axis,

• ~94% of input asymmetry is reconstructed

• (Integrated over thrust axis: 98%)

• Effect is understood, can be reproduced in Toy MC

• Asymmetries corrected

25

SmearingIn azimuthalAngle of thrustAxis in CMS

Black: injectedPurple reconstructed

1 2( )R R

Weighted MC asymmetries

Cuts and Binning• Similar to Collins analysis, full off-resonance and on-resonance data

(7-55): ~73 fb-1 + 588 fb-1

• Visible energy >7GeV • PID: Purities in Pion/Pion Sample > 90% • Same Hemisphere cut within pair (), opposite hemisphere

between pairs• All 4 hadrons in barrel region: -0.6 < cos () <0.9• Thrust axis in central area: abs(thrustz)<0.75• Thrust > 0.8

• zhad1,had2>0.1

• z1 = zhad1+zhad2 and z2 in 9x9 bins

• m and m in 8x8 bins: [0.25 - 2.0] GeV

26

First observation of IFF asymmetries in in e+e- coming up…

Results including systematic errors

8x8 m1 m2 binning 28

PreliminaryPreliminary

Preliminary

Preliminary

PreliminaryPreliminary

PreliminaryPreliminary

9x9 z1 z2 binning

PreliminaryPreliminary Preliminary

Preliminary

PreliminaryPreliminaryPreliminary

PreliminaryPreliminary

Comparison with Collins FF extraction

• a12 Asymmetries directly measure IFF squared

• IFF asymmetries can be integrated over kt

– No double ratios necessary to cancel gluon radiation effects

Subprocess contributions (MC)

9x9 z1 z2 binning

tau contribution (only significant at high z)charged B(<5%, mostly at higher mass)Neutral B (<2%)charm( 20-60%, mostly at lower z)uds (main contribution)

Subprocess contributions (MC)

32

8x8 m1 m2 binning

charged B(<5%, mostly at higher mass)Neutral B (<2%)charm( 20-60%, mostly at highest masses)uds (main contribution)

Charm Asymmetries in simulated data consistent with zero!To be checked with charm enhanced sample

Data not corrected for Charm contributions

Systematic Errors

• Dominant:– MC asymmetry + its statistical error (up to % level)

• Smaller contributions: – mixed asymmetries: per mille level– higher moments: sub per mille level– axis smearing, – tau contribution – Charm contributions

• Possible Gluon radiation not accounted for

Model predictions for e+e-

Invariant mass1 dependence for increasing z1

z1 dependence for increasing z2

34

Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009.

Comparison to theory predictions

35

Leading order, experimental results might contain effects from gluon radiation not contained in the model

Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm )

Z dependence : Rising behavior steeper

However: Theory contains parameters based on HERMES data which already fail to explain COMPASS well

Projections for () () for 580 fb-1

a 12

Minv<0.4 GeV 0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV

0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeVa 12

a 12a 12

a 12

Projections for () (K) for 580 fb-1

Minv<0.7 GeV 0.7 GeV<Minv<0.85 GeV

0.85 GeV<Minv<1.0 GeV1.0 GeV<Minv

Aa 12

a 12

a 12

a 12

Combined Analysis: Extract Transversity Distributions

Transversity, δq(x)Tensor Charge

Lattice QCD: Tensor Charge

Factorization + Evolution

Theo

rySIDIS

~ δq(x) x CFF(z)~ δq(x) x IFF(z)

e+e-

~ CFF(z1) x CFF(z2)~ IFF(z1) x IFF(z2)

pp jets

~ G(x1) x δq(x2) x CFF(z)

pp h+ + h- + X~ G(x1) x δq(x2) x IFF(z)

pp l+ + l- + X~ δq(x1) x δq(x2)

39

Measurements of quark transversity

p+p

SIDIS

e++e-

E704, 1991Large forward SSA

STAR, PHENIX, BRAHMS, 2004~2005Inclusive AN

HERMES 2005, COMPASS 2006AUT

BELLE 2006Collins FF

BELLEIFF

RHICIFF asym.

RHICCollins asym.

JParc, RHIC, FAIRDrell-Yan

COMPASSp target

JLab 3He and 12 GeV

Underway Future1991 2005

BELLE kT dep. Pol. & upol FF, pol. Lambda FF

Summary

• First measurement of Interference Fragmentation Function!

• Asymmetry significant

• Combined Analysis of Di-hadron and single hadron measurements possible

• Systematic effects to be finalized• Future goal: Combined analysis of SIDIS, pp, e+e- data

– Extract transversity– Disentangle contributions to AN

Backup

Charm asymmetries

Charm meeting, June 4th 42Interference fragmentation functions

Charm Studies

• Look at Events with D0 decay in Pi,K pair• Asymmetries with and without Pi from D0 decay

• Way to separate between QCD effects and weak decays?

c /c

D0

/u

u

RL

RLN P

A

1

Transverse Spin Asymmetries at RHIC

• QCD: : very small

• Single transverse spin asymmetries pick up:– Sivers Effect: kT in quark

distribution– Quark transverse

polarization x Collins fragmentation function: kT in fragmentation function

δq x CFF44

Transversity

PHENIX, forward at s = 62 GeV, nucl-ex/0701031

21

222xx

s

px L

F

smA qN /

Transversity Quark Distributions δq(x) fromTransverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS)

Collins- and IFF- asymmetriesin semi-inclusive deep inelastic scattering (SIDIS) and pp measure

~ δq(x) x CFF(z)

combined analysis with CFF from e+e- annihilation

Example: New COMPASS results for Collins Asymmetries on proton target (consistent with previous HERMES results)

46

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

)(

)(

)(

)(

)(cos1

)(sin)2cos(:

2

2

2

2

2

2

0 FavUnfUnfFav

q

FavUnfUnfFav

qUnfUnfFavFav

q

UnfUnfFavFav

q

DDDDe

HHHHe

DDDDe

HHHHeFA

2 methods give very small difference in the result

Final Collins results

Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)

47

48

Collins Fragmentation: Angles and CrossSection: cos() Method (e+e- CMS frame)

1hP

2hP

2

21

111

121221

21

sin4

11

cosq

cm

T

yyyB

zHzHyBddzdzd

Xhheedσ

2-hadron inclusive transverse momentum dependent cross section:

Net anti-alignment oftransverse quark spins

e-

e+

Observable: yield, N12 ( φ1+φ2 ) of π+π- pairs

49

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007

k┴ transverse quark momentum in nucleonp┴ transverse hadron momentum in fragmentation

hadron FF

quark pdf

The transverse momentum dependencies are unknown and veryDifficult to obtain experimentally!

),(

)(),(

)sin()sin(),()(

),(

22

,122

pzDdy

dkxqkddde

pzHdy

dkxqkddde

AhqhS

qq

hShqSqhS

qq

CollinsUT

tra

nsversity

Collins F

F

Collins Extraction of Transversity:unknown Transverse Momentum Dependences!

50

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, Turkand Melis at Transversity 2008,Ferrara. Previously:Phys. Rev. D75:05032,2007

HERMES SIDIS (p)

+ COMPASS SIDIS (d)

+ Belle e+e-

transversity dist.

+ Collins FF

Fit includes:

Extraction of Quark Transversity Distributionsand Collins Fragmentation Functions SIDIS + e+e-

Soffer Bound

Old fit New fit

Examples of fits to azimuthal asymmetries

51

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

N()/N0

2 )

• Cosine modulations

• clearly visible

• P1 contains information on IFF

52

Definition of Vectors and Angles

1 2

1 2

1 2

p+p c.m.s. = lab frame

, : momenta of protons

, : momenta of hadrons

( ) / 2

: proton spin orientation

A B

h h

C h h

C h h

B

P P

P P

P P P

R P P

S

3333333333333333333333333333

3333333333333333333333333333

333333333333333333333333333333333333333333

333333333333333333333333333333333333333333

33333333333333

1hP33333333333333

2hP33333333333333

100 GeVAP33333333333333

100 GeVBP33333333333333

CP33333333333333

BS33333333333333

pp hhX

1 2hadron plane: ,

scattering plane: ,

h h

C B

P P

P P

3333333333333333333333333333

3333333333333333333333333333 : from scattering plane

to hadron planeR : from polarization vector

to scattering plane S

Bacchetta and Radici, PRD70, 094032 (2004)

2 CR33333333333333

SSA from di-hadron production

See Talk R. Yang

IFF in SIDISIFF in SIDIS

R defined by:

R = (z1p

2 – z

2p

1)/(z

1+z

2)

(X. Artru, hep-ph/0207309)

R

Summary & Outlook

• Collins FF at Belle final ->global analysis• 2H Interference FF Analysis underway

• Plans for kT dependent Pol. & Upol. FFs

– Necessary for global analysis w/o model assumptions

• Polarized Lambda FF• 2H Interference FF Measurements at Phenix, HERMES and

COMPASS– Non vanishing effect at HERMES and COMPASS– Together with Belle results -> Independent extraction of

transversity

Proposed Transverse Spin Sum rule

Bakker, Leader, TruemanPhys.Rev.D70:114001,2004

xx L+δΣ=S=2

1

2

1

Gluon contribution is Small (Phenix, Compass results)

Models

• Main contribution: interference of hadron pairs produced in relative s and p wave

• P wave from Vector meson decay

• S wave from non-resonant background

• Signal around vector meson mass

Jaffe, Jin and Tang, PRL 80 (1998) 1166Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006)

• Two different theoretical models gave different prediction of mass dependence

• Sign change is not observed in HERMES/COMPASS results

Interference fragmentation functions

Motivation: Measure quark transverse spin distribution in the nucleon

• Successful global analysis of our Collins results together with HERMES and COMPASS data revealed first glimpse at quark transversity distribution:

• Open questions: evolution of Collins functions

• Independent access via interference fragmentation:

nonzero HERMES results

nonzero COMPASS results

zero PHENIX results (so far)

Alexei Prokudin, DIS2008, update of Anselmino et al: hep-ex 0701006

57

Models• Main contribution: interference of hadron

pairs produced in relative s and p wave

• P wave from Vector meson decay

• S wave from non-resonant background

• Look around -mass

Jaffe, Jin and Tang, PRL 80 (1998) 1166Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006)

• Two different theoretical models gave different prediction of mass dependence

• Sign change is not observed in HERMES/COMPASS results

Charm meeting, June 4th 58Interference fragmentation functions

Combining experiments and on/off resonance

Charm meeting, June 4th Interference fragmentation functions 59

•Treat all experimets separately,•Extract average value in each kinematic bin over all experiments •Separate fit of on- resonance and continuum data•Extract average of continuum and onresonance values

5x5 x 2x2 m1,m2,z1,z2 binning

Red. Chi2 distribution,NDF onresonance 21, NDF continuum 19

Red. Chi2 distribution,NDF: 1 (onres, continuum)

60

Applied Cuts, Binning• Two data sets: off-resonance data ( 29.1 fb-1 ) on-resonance data ( 547 fb-1 )• Track selection:

– pT > 0.1GeV– vertex cut:

dr < 2cm, |dz| <4cm• Acceptance cut

– -0.6 < cosi < 0.9 • Event selection:

– Ntrack 3– Thrust > 0.8 – z1, z2 > 0.2

• Hemisphere cut

• QT < 3.5 GeV• Pion PID selection

0ˆ)ˆ(ˆ)ˆ( 12 nnPnnP hh

z2

0 1 2 3

4 5 6

7 8

9

0.20.3

0.5

0.7

1.0

0.2 0.3 0.5 0.7 1.0

5

86

1

2

3

z1

(z1, z2)-binning

MC asymmetries (no asymmetry expected)

• A small asymmetry seen due to acceptance effect

• Mostly appearing at boundary of acceptance

• Opening cut in CMS of 0.8 (~37 degrees) reduces acceptance effect to the sub-per-mille level

61

Ph

),cos(ˆ

nPP

nP

h

h

No opening cutOpening cut>0.7Opening cut >0.8

in %

Interference Fragmentation – thrust method

• e+e- (+-)jet1()jet2X• Stay in the mass region around -

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)]

62 Interference fragmentation functions

21221111 m,zHm,zHA cos

2

1

1hP

2hP

2h1h PP

Model predictions by:

•Jaffe et al. [PRL 80,(1998)]

•Radici et al. [PRD 65,(2002)]

Charm meeting, June 4th

Central values in binning

Charm meeting, June 4th Interference fragmentation functions 63

9x9 z1 z2 binning

8x8 m1 m2 binning

<z1> <m1> <sin(decay1)>

<z2> <m2> <sin(decay2)>

<cos(decay1)> <cos(decay2)>Polarization factor:<sin2 ()/1+cos2()>

• Hemispheres are independent of each other•In same hemisphere: higher m also corresponds to higher z and higher sin(decay1) •cos(decay1) marginal (important for possible other Legende contributions)

Decay angle moments • sin mostly very

large (85%-98%)• cos very symmetric mostly <1%

• Bin to bin values will be given in results table

• Need to take sin moments into account for theory comparison

64

Chiral odd FFs

+

_

+

qT

?

_

+

_hqT D

Collins effect

Hadronic Tensor

Helicity base: independent amplitudes:

q

’

Nqq ,~

_

Lz-1Lz

1H

Systematic Studies• Mc asymmetries• Reweighted asymmetries

– Constant, linear weights• Mixed events• Single hemispheres• Higher harmonics• Binning• Inverse thrust• Relative process contributions• Correlation studies• Combining data from diff exp• Kinematics correlations & center values• Pid systematics• Cross checks• Asymmetries as polar angles• Decay angle dependent asymmetries• Mixed binning asymmetries

Interference Fragmentation–thrust method

• e+e- (+-)jet1()jet2X• 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)collinear factorization

• Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]

• Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)]

• Independent Measurement• Favourable in pp: no Sivers

67

21221111 m,zHm,zHA cos

2

1

1hP

2hP

2h1h PP

Model predictions by:

•Jaffe et al. [PRL 80,(1998)]

•Radici et al. [PRD 65,(2002)]

Expected sensitivities for ~580 fb-1 () ()

Minv<0.4 GeV 0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV

0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeV

A A A

A A

Cuts and Binning• Similar to Collins analysis, full

off-resonance and on-resonance data(7-55): ~73 fb-1 + 588 fb-1

• Visible energy >7GeV • PID• Same Hemisphere cut within

pair (), opposite hemisphere between pairs

• All 4 hadrons in barrel region:-0.6 < cos () <0.9

• Thrust axis in central area:abs(thrustz)<0.75

• Thrust > 0.8• zhad1,had2>0.1

z1 = zhad1+zhad2 and z2 in 9x9 bins:

[0.2, 0.275, 0.35, 0.425, 0.5, 0.575, 0.65, 0.725, 0.825, 1.0]

m and m in 8x8 bins:[0.25, 0.4, 0.5, 0.62, 0.77, 0.9, 1.1, 1.5, 2.0]

• Mixed single hemisphere binning 8x8 z1 x m1

• Scattering angular binning and sin decay angle binnings for consistency checks

• Orientation of first hadron is positive, second negative, angle and plane defined by R=(P1-P2)/2

69

Pi+ Pi- Purities