measurements of fragmentation functions at belle: results and prospects d. gabbert (university of...

Measurements of fragmentation functions at Belle: results and prospects

D. Gabbert (University of Illinois and RBRC)M. Grosse Perdekamp (University of Illinois and RBRC)

K. Hasuko (RIKEN/RBRC) S. Lange (Frankfurt University)

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

for the Belle Collaboration

(see hep-ex/0607014 and Phys.Rev.Lett.96:232002,2006 for Collins results)

Outline:

• The KEKB rings and the Belle Experiment

• Transverse Spin Physics

•Motivations

•Collins analysis and parameterizations

•Interference Fragmentation functions

• Unpolarized fragmentation functions

R.Seidl:Measurements of fragmentation functions at Belle: results and prospects 2 BNL, July 21th

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: >600 fb-1

• >60fb-1 => off-resonance

Belle detectorKEKB


Good tracking and particle identification!


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

Important input for 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

The Spin dependent Fragmentation function analysis yields information on the Collins and the Interference Fragmentation function !

Universality appears to be provenin LO by Collins and Metz:

[PRL93:(2004)252001 ]+most recent work from

Amsterdam Group


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)]


Applied cuts, binning

• Off-resonance data – 60 MeV below (4S)

resonance– 29.1 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


Testing the double ratios with MC• Asymmetries do cancel out for MC• Double ratios of

compatible with zero• Mixed events 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 (UL):(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 (UL/C)

UL/L

UL/C

R.Seidl:Measurements of fragmentation functions at Belle: results and prospects 10

BNL, July 21th

Systematic errors• Tau contributions• PID systematics

• MC double ratios• Charged ratios (

• Higher order terms• Double ratio-subtraction

methodtaken from UL/L analysisFurther studies:Reweighting asymmetries: underestimation of cos asymmetriesCorrelation studies:statistical errrors rescaled by 14%Beam polarization studiesconsistent with zero


BNL, July 21th

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

• UL/C asymmetries about 40-50% of UL/L asymmetries

• First direct measurements of the Collins function

Integrated results:

A0(UL/L) (3.06 ± 0.57 ± 0.55)%

A12(UL/L) (4.26 ± 0.68 ± 0.68)%

A0(UL/C) (1.270 ± 0.489 ± 0.350)%

A12(UL/C) (1.752 ± 0.592 ± 0.413)%

Final results

Preliminary results


BNL, July 21th

Fits to the HERMES data by the Torino Group

• A. Prokudin fitted the HERMES (Sivers and) Collins Data

• Either Soffer bound for transversity:2q(x) = | q + q |

• Or q(x) = q(x) • GRV1998 for

unpolarized PDFs• Kretzer FF• Gaussian kT

Assumption

HERMES 02-04 Data

COMPASS 02 Data


BNL, July 21th

Fits to our UL/L data:

Efremov, Goeke, Schweitzer: [hep-ph/0603054]:

•Taking reasonable transversity from QSM•Gaussian intrinsic transverse momentum dependenceHERMES, COMPASS and Belle results are consistent with each other

However: Fit errors on Collins function still large

Probably improvement by UL/C data (not yet included)

Can we do better?


BNL, July 21th

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


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

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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)


BNL, July 21th

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


BNL, July 21th

• 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 and Artru,Collins

• Early work by Collins, Heppelman, Ladinski

Interference Fragmentation – thrust method

21221111 m,zHm,zHA cos

2

1

1hP

2hP

2h1h PP


BNL, July 21th

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


BNL, July 21th

Unpolarized FFs

MC simulation, ~1.4 fb-1

2.

• Performed Systematic studies:– Smearing– Tracking efficiency– Acceptance– Energy scale

• Particle ID study not yet finished

• AKK: Try flavor tagged/enhanced analysis?


BNL, July 21th

Summary and outlook

• Collins analysis:– Analysis procedure passes all null

tests – Systematic uncertainties

understood Significant nonzero

asymmetry with double ratios are observed

• UL/C about half as large UL/L double ratios

• Data can be used for more sophisticated analysis

• Paper is published• Important input for

Transversity measurements now and in the future

• Leading order fits ongoing• On resonance >10 x

statisticslong paper on Collins results

• Interference fragmentation function analysis started

• Unpolarized FF analysis almost complete but lacks manpower

• Many more QCD/Spin related studies possible (VM Collins, timelike DVCS, Polarimetry, kT-dependent FFs, “Sivers”FF, Event Shapes )

Results: Prospects:


BNL, July 21th


BNL, July 21th

• Spin composition of the nucleon:– Contribution of quark spin

small– Contribution of gluon spin

also small?– Orbital angular

momentum? Sivers effect?

• Single spin asymmetries small in pQCD– …but large and nonzero!– Understandable by gauge

link contributions

• Sivers effect:– Unpolarized quarks in transversely

polarized nucleon– Non-centered quark distribution in

impact parameter spaceRescattering creates left-right

asymmetry

• Boer-Mulders effect:• Transversely polarized quarks in

unpolarized nucleon• Vacuum polarization effect?

• Collins effect:• Fragmentation of transversly

polarized quark into unpolarized hadron

• Connects microscopic quantitiy (transverse spin) to macroscopic quantity (azimuthal asymmetries)

QCD: the right theory, but many surprisesespecially in spin …


BNL, July 21th

J.C. Collins, Nucl. Phys. B396, 161(1993)

q

momentum hadron relative : 2

z

momentum hadron e transvers:

momentum hadron :

spinquark :

momentumquark :

h

sE

EE

p

p

s

k

h

qh

h

h

q

qs

k

hph

,

Collins Effect:Fragmentation with of a quark q with spin sq into a spinless hadron h carries anazimuthal dependence:

hp

sin

qh spk

Collins effect in quark fragmentation


BNL, July 21th

The Collins Effect in the Artru Fragmentation Model

π+ 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:


BNL, July 21th

Typical hadronic events at Belle

ii

ii

p

npthrust

ˆ


BNL, July 21th

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 )


BNL, July 21th

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


BNL, July 21th

Small double ratios in low thrust data sample

• Low thrust contains radiative effects

• Collins effect at least smeared for low thrust

Strong experimental indication that double ratio method works

A0

A12


BNL, July 21th

Results for e+ e- X for 29fb-1

• Significant non-zero asymmetries

• Rising behavior vs. z• cosdouble ratios

only marginally larger• First direct

measurement of the Collins function

• Integrated results:– cos(2) method

(3.06±0.57±0.55)%– cos(2) method

(4.26±0.68±0.68)%

z1

z2

Systematic error

A0

A12

Final results


BNL, July 21th

• Good detector performance (acceptance, momentum resolution, pid)

• Jet production from light quarks off-resonance (60 MeV below resonance)

(~10% of all data)• Intermediate Energy

Sufficiently high scale (Q2 ~ 110 GeV2)- can apply pQCD

Not too high energy (Q2 << MZ2)

-avoids additional complication from Z interference• Sensitivity = A2sqrt(N) ~ x19 (60) compared to LEP

ABelle / ALEP ~ x2 (A scales as ln Q2)

LBelle / LLEP ~ x23 (230)

9.44 9.46


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


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)

Belle is well suited for FF measurements:


BNL, July 21th

What is the transverse momentum QT of the virtual photon?

• In the lepton CMS frame e-=-e+ and the virtual photon is only time-like:q=(e-+p+)=(Q,0,0,0)

• Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame wherePh1+Ph2=0

q’=(q’0,q’)• Inclusive Cross section for

radiative events (acc. to D.Boer):

Ph1

e+e-

Ph2

e-’

e+’

q’

P’h1 P’h2

qT

Lepton-CMS

Hadron-CMS


BNL, July 21th

Raw asymmetries vs QT

1hP

2hP

1hP

2hP

• QT describes transverse momentum of virtual photon in CMS system

•Significant nonzero Asymmetries visible in MC (w/o Collins)

•Acceptance, radiative and momentum correlation effects similar for like and unlike sign pairs

•uds MC () Unlike sign pairs

•uds MC () Like sign pairs


BNL, July 21th

Experimental issues

• Cos2 moments have two contributions:– Collins Can be isolated either by subtraction or double ratio method– Radiative effects Cancels exactly in subtraction method, and in LO of

double ratios• Beam Polarization

zero? Cos(2Lab) asymmetries for jets or • False asymmetries

from weak decays Study effect in decays, constrain through D tagging

• False asymmetries from misidentified hemispheres QT or polar angle cut

• False asymmetries from acceptance Cancels in double ratios, can be estimated in charge ratios,

fiducial cuts• Decaying particles lower z cut


BNL, July 21th

Take simple parameterization to test sensitivity on favored to disfavored Ratio

Favored/Disfavored contribution Sensitivity

2

cb


BNL, July 21th

• 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


BNL, July 21th

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”


BNL, July 21th

• Spin composition of the nucleon:– Contribution of quark spin

small– Contribution of gluon spin

also small?– Orbital angular

momentum? Sivers effect?

• Single spin asymmetries small in pQCD– …but large and nonzero!– Understandable by gauge

link contributions

• Sivers effect:– Unpolarized quarks in transversely

polarized nucleon– Non-centered quark distribution in

impact parameter spaceRescattering creates left-right

asymmetry

• Boer-Mulders effect:• Transversely polarized quarks in

unpolarized nucleon• Vacuum polarization effect?

• Collins effect:• Fragmentation of transversly

polarized quark into unpolarized hadron

• Connects microscopic quantitiy (transverse spin) to macroscopic quantity (azimuthal asymmetries)

QCD: the right theory, but many surprisesespecially in spin …

measurements of fragmentation functions at belle: results and prospects d. gabbert (university of...

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