precision fragmentation function measurements at belle

Precision fragmentation function measurements at Belle

Trento, June 14 2007

M. Grosse Perdekamp (University of Illinois and RBRC)

A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC)

Outline:•The Collins function measurements

•Access to transversity over Collins fragmentation function•Collins function measurements at Belle

•The Belle detector•Improved statistics with on_resonance data

•Interference fragmentation function measurements•unpolarized fragmentation function measurements

R.Seidl: Fragmentation function measurements at Belle 2 Trento, June 14th

SIDIS experiments (HERMES and COMPASS, eRHIC) measure q(x) together with either Collins Fragmentation function or Interference Fragmentation function

Towards a global transversity analysis

zH1

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 !

Comlpex universality?


KEKB: L>1.6x1034cm-2s-1 !!

• Asymmetric collider• 8GeV e- + 3.5GeV e+

• s = 10.58GeV ((4S))• e+e-S• Off-resonance: 10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: >700 fb-1

• >60fb-1 => off-resonance

Belle detectorKEKB


Good tracking and particle identification!


e-

e+ Jet axis: Thrust

<Nh+,-> = 6.4

GeV 5210ss

E2z h .,

Near-side Hemisphere: hi , i=1,Nn with zi

Far-side: hj , j=1,Nf with zj

Event Structure at Belle

22

21112

2

2

21

21

14

1

2

1

3

cos

,

cm

aaa

yyyA

zDzDeyAQdzdzd

Xhheed

e+e- CMS frame:

Spin averaged cross section:


Collins fragmentation in e+e- : Angles and Cross section cos() method

1hP

2hP

2cm

21

111

121T

221

21

4

1y1yyB

zHzHyBddzdzd

Xhheedσ

sin

cos q

2-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment oftransverse quark spins

e+e- CMS frame:

e-

e+

GeV 5210ss

E2z h .,

[D.Boer: PhD thesis(1998)]


Collins fragmentation in e+e- : Angles and Cross section cos(2) method

1hP

2hP

2

21

11TTTT02

21

21

sin4

1

pkphkh2I2cosq

cm

T

B

MM

HHB

ddzdzd

Xhheedσ

2-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment oftransverse quark spins

•Independent of thrust-axis

•Convolution integral I over transverse momenta involved

e+e- CMS frame:

e-

e+

[Boer,Jakob,Mulders: NPB504(1997)345]


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 < cosi < 0.9 • Event selection:

– Ntrack 3– Thrust > 0.8 – Z1, Z2>0.2

• Hemisphere cut

• QT < 3.5 GeV

(Ph 2 ˆ n ) ˆ n (Ph1 ˆ n ) ˆ n 0

z1

z2

0 1 2 3

4 5 6

7 8

9

0.2

0.3

0.5

0.7

1.0

0.2 0.3 0.5 0.7 1.0

5

86

1

2

3

= Diagonal bins z1

z2


Examples of fits to azimuthal asymmetries

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

N()/N0

No change in cosine moments when including sine and higher harmonics

Cosine modulationsclearly visible

2 )


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:

2

2

2

2

2

2

FavUnfUnfFav

q

FavUnfUnfFav

q

UnfUnfFavFav

q

UnfUnfFavFav

q

DDDDe

HHHHe

DDDDe

HHHHeFA

2 methods give very small difference in the result


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 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 ()


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/0603054]): 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


What about the data under the resonance?

• More than 540 fb-1 of on_resonance data

• (4S) is just small resonance

• More than 75% of hadronic cross sectionfrom open quark-antiquark production

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)


Why is it possible to include on_resonance data?Different Thrust distributions

ii

ii

p

npthrust

ˆ

• e+ e- q q (u d s) MC

• (4S) B+ B- MC

• (4S) B0 B0 MC

• Largest systematic errors reduce with more statistics • Charm-tagged Data sample also increases with statistics

BB00 BB

e+e-qq, q∈uds

e+e-cc


Improved systematic errors (UC)• Tau contribution• PID error• MC double ratios• Charged ratios (• higher moments in Fit• difference double ratio-

subtraction method

•reweighted MC-asymmetries: cos asymmetries underestimated rescaled with 1.21•Correlation studies: statistical error rescaled by1.02 (UL) and 0.55 (UC) – after rigorous error calculation correct•Beam polarization studies consistent with zero•Correction of charm events

A0 (cos(2)) moments

A12 (cos()) moments


Final charm corrected results for e+ e- X (29fb-1 of continuum

data)• Significant non-zero

asymmetries • Rising behavior vs. z

• cos(+) double ratios only marginally larger

• UC asymmetries about 40-50% of UL asymmetries

• First direct measurements of the Collins function

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)%

Final results

Preliminary results


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

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)%

PRELIMINARY


Collins asymmetries II: sin2 /(1+cos2 ) binning (UL)

• Nonzero quark polarization ~ sin2

• Unpolarized de-nominator ~ 1+cos2

• 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

thrustz

PRELIMINARY


• e+e- (+-)jet1(-+)jet2X• Stay in the mass region around -mass• Find pion pairs in opposite

hemispheres• Observe angles 12

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)]

Interference Fragmentation – thrust method

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)]


• Similar to previous method• Observe angles 1R2R

between the event-plane (beam, two-pion-axis) and the two two-pion planes.

• Theoretical guidance by Boer,Jakob,Radici

Interference Fragmentation – “ “ method

R2R1221111 m,zHm,zHA cos

R2

R1

1hP

2hP

3hP

4hP

2h1h PP

4h3h PP


Different model predictions for IFF

•Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of -phaseshift analysissign 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

f1, h1 from spectator model

f1, h1=g1 from GRV98 & GRSV96


Unpolarized FF as important input for all precise QCD measurements

MC simulation, ~1.4 fb-1

2.

• No low-Q2 data available important for evolution

• No high-z data available Huge amount of B-factory

data can help• Favored/Disfavored

disentangling by detecting hadron pairs (as in Collins analysis)?


Summary and outlook

• A first successful global analysis of transversitydata 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

• Continue to measure precise spin dependent fragmentation functions at Belle– kT dependence of Collins function– Favored/disfavored disentanglement– Initerference 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


Backup Slides


B, charm and uds contributions in the data

uds quarkscharm quarksCharged B-mesonsNeutral B-mesons

Open symbols: charm enhanced data sample used for charm correctionFull symbols: main data sample


Collins asymmetries IIa: sin2 /(1+cos2 ) binning (UC)

• Nozeron quark polarization ~ sin2

• Unpolarized de-nominator ~ 1+cos2

• Clear linear behavior seen when using either thrustz or 2nd hadron as polar angle

• Better agreement for thrust axis (~approximate quark axis)

• Similar behavior, smaller magnitude as UL asymmetries

thrustz

PRELIMINARY


Collins asymmetries III: QT binning (UL)

• Reduced asymmetries in low thrust sample

• At low thrust significant B contribution(for t<0.8 ~20 % B for t>0.8 < 1 % B)

• A12 thrust axis dependent

• High QT (>3.5 GeV) asymmetries from beam related BG

• UC plots similarThrust>0.8

Thrust<0.8 (not corrected for heavy quark contributions)

PRELIMINARY


Collins asymmetries IIIa: QT binning (UC)

• Reduced asymmetries in low thrust sample

• At low thrust significant heavy quark contribution

• High QT (>3.5 GeV) asymmetries from beam related BG

• similar behavior, but smaller magnitude as UL asymmetries

Thrust>0.8

Thrust<0.8 (not corrected for heavy quark contributions)

PRELIMINARY


What would we see in e+e-?

Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning

m1

m1

m2

m2

“Jaffe” “Radici”

precision fragmentation function measurements at belle

Documents

e e d

e e boer

e e annihilation

e e jet axis

gev e s

asymmetric collider8gev

bellee e cms frame

mcdouble ratios of p