Measurements of chiral-odd fragmentation functions at Belle

Measurements of chiral-odd fragmentation functions at Belle

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)

V. Siegle (RBRC)for the Belle Collaboration

DIS 2006

April 20th, Tsukuba

(see hep-ex/0507063 for details, submitted to PRL)

Spin dependent fragmentation functions at BELLE 2 DIS2006, April 20th

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

hp

sin

qh spk

Collins effect in quark fragmentation


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:


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

Motivation: Global Transversity Analysis q(x)

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 ]


KEKB: L>1.5x1034cm-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: >500 fb-1

• >45fb-1 => off-resonance

Belle detectorKEKB


Good tracking and particle identification!

/ KL detection 14/15 lyr. RPC+Fe

Central Drift Chamber small cell +He/C2H6

CsI(Tl) 16X0

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


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

2cm

21

110

T2

21

21

4

1y1yyB

MM

HH22yB

ddzdzd

Xhheedσ

sin

ˆˆcos TTTT pkphkhq

I

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

• Pions selected by PID cut• Track selection:

– pT > 0.1GeV– vertex cut:

dr<2cm, |dz|<4cm• Acceptance cut

– -0.6 < cosh < 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 binsz1

Spin dependent fragmentation functions at BELLE 10

DIS2006, April 20th

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 )


DIS2006, April 20th

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

F sin2()

1 cos2()

e2

q (H Fav H

Fav HUnf H

Unf)

e2

q (DFav D

Fav DUnf D

Unf)

e2

q (H Fav H

Unf HUnf H

Fav)

e2

q (DFav D

Unf DUnf D

Fav)

2 methods give very small difference in the result


DIS2006, April 20th

Other Favored/Unfavored Combinations charged pairs

• 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)

Improvement: 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


DIS2006, April 20th

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 ()


DIS2006, April 20th

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 errors rescaled by 14%Beam polarization studiesconsistent with zero


DIS2006, April 20th

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)%

Submitted to PRL

Preliminary


DIS2006, April 20th

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


DIS2006, April 20th

• 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 [Phys.Rev.D67:094003,2003] and Artru, Collins [Z.Phys.C69:277-286,1996 ]

Interference Fragmentation – thrust method

21221111 m,zHm,zHA cos

2

1

1hP

2hP

2h1h PP


DIS2006, April 20th

Summary and outlook

• Double ratios:double ratios from datamost systematic errors cancel

• Analysis procedure passes all null tests

• Systematic uncertainties understood

Significant nonzero asymmetry with double ratios are observed

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

• Data can be used for more sophisticated analysis

• Paper with UL/L double ratios (hep-ex/0507063) is submitted

• Leading order fits ongoing• On resonance 10 x

statisticsdetailed final analysis on Collins results

• Interference fragmentation function analysis started

• Include Vector Mesons into Collins analysis:Possibility to test string

fragmentation models used to describe Collins effect

• Many more QCD/Spin related studies possible (unpol FFs, timelike DVCS, Polarimetry)

Summary: Outlook:


DIS2006, April 20th


DIS2006, April 20th

Small double ratios in low thrust data sample

• Low thrust contains radiative effects

• Collins effect vanishes

Strong experimental indication that double ratio method works

A0

A12


DIS2006, April 20th

Typical hadronic events at Belle

ii

ii

p

npthrust

ˆ


DIS2006, April 20th

• 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

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)

Belle is well suited for FF measurements:


DIS2006, April 20th

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:


DIS2006, April 20th

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


DIS2006, April 20th

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


DIS2006, April 20th

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


DIS2006, April 20th

Systematics: charm contribution?

• Weak (parity violating) decays could also create asymmetries(seen in overall dilution 5%)

• Especially low dilution in combined z-bins with large pion asymmetry

• Double ratios from charm MC compatible to zero

Charm decays cannot explain large double ratios seen in the data

Charm enhanced D* Data sample used to calculate and correct the charm contribution to the double ratios (see hep-ex/0507063 for details)

Charm

fra

ctio

n

N(c

harm

)/N

(all)


DIS2006, April 20th

Take simple parameterization to test sensitivity on favored to disfavored Ratio

Favored/Disfavored contribution Sensitivity

2

cb


DIS2006, April 20th

• 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


DIS2006, April 20th

Different model predictions for IFF

•Jaffe at 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


DIS2006, April 20th

PRELIMINARYf1, h1 from spectator modelf1, h1=g1 from GRV98 & GRSV96

Different model predictions for IFF

• 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)


DIS2006, April 20th

What would we see?

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

m1

m1

m

2

m

2

“Jaffe” “Radici”


DIS2006, April 20th

What do we see? I: events

• Animation of an event

• lepton tracks, thrust axis and all particle momenta in the CMS frame

• Ph1=P1+P2

• Ph2=P3+P4

• Plane defined by leptons and thrust

• Planes defined by hadron pairs

Measurements of chiral-odd fragmentation functions at Belle

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