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Measurements of chiral-odd fragmentation functions at Belle

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Measurements of chiral-odd fragmentation functions at Belle

(see hep-ex/0507063 for details)

Panic 05

October27, Santa Fe, USA

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

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

There are always 2 unknown functions involved which cannot be measured independently

RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x)

Universality appears to be proven

in LO by Collins and Metz:

[PRL93:(2004)252001 ]

The Spin dependent Fragmentation function analysis yields information on

the Collins and the Interference Fragmentation function !

measurements of chiral-odd fragmentation functions at Belle

Belle detector

KEKB

- Average Trigger rates:
- U(4S)BB11.5Hz
- qq28 Hz
- mm + tt16 Hz
- Bhabha 4.4 Hz
- 2g35 Hz

- KEKB
- Asymmetric collider
- 8GeV e- + 3.5GeV e+
- Ös = 10.58GeV (U(4S))
e+e-U(4S)BB

- Off-resonance: 10.52 GeV
e+e-qq (u,d,s,c)

- Integrated Luminosity: ~ 460 fb-1
~ 30fb-1 => off-resonance

measurements of chiral-odd fragmentation functions at Belle

Good tracking and particle identification!

measurements of chiral-odd fragmentation functions at Belle

e+e- CMS frame:

j2-p

e-

Q

j1

j2

j1

e+

2-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment of

transverse quark spins

measurements of chiral-odd fragmentation functions at Belle

e+e- CMS frame:

- Independent of thrust-axis
- Convolution integralI over transverse momenta involved

e-

Q

j0

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

e+

2-hadron inclusive transverse momentum dependent cross section:

Net (anti-)alignment of

transverse quark spins

measurements of chiral-odd fragmentation functions at Belle

Off-resonance data

(in the future also on-resonance)

Track selection:

pT > 0.1GeV

vertex cut:dr<2cm, |dz|<4cm

Acceptance cut

-0.6 < cosqi< 0.9

Event selection:

Ntrack 3

Thrust > 0.8

Z1, Z2>0.2

z2

1.0

3

6

8

9

0.7

2

5

7

8

0.5

1

5

4

6

0.3

0

1

2

3

0.2

z1

0.2

0.3

0.5

0.7

1.0

- Light quark selection
- Hemisphere cut
- Opening angle y cuts:
- - cos(2f0) method: yh1-h2>120
- - cos(f1+f2) method:
- yh1-thrust<60 , yh2-thrust>120

= Diagonal bins

measurements of chiral-odd fragmentation functions at Belle

Cosine modulations

clearly visible

N(f)/N0

No change in cosine moments when

including sine and higher harmonics

(even though double ratios will contain

them)

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

measurements of chiral-odd fragmentation functions at Belle

Q

j0

- QT describes transverse momentum of virtual photon in pp CMS system
- Significant nonzero Asymmetries visible in MC (w/o Collins)
- Acceptance, radiative and momentum correlation effects similar for like and unlike sign pairs

j2

Q

- uds MC (pp) Unlike sign pairs
- uds MC (pp) Like sign pairs

j1

measurements of chiral-odd fragmentation functions at Belle

Double ratio 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

Subtraction method:

2 method gives very small difference in the result

measurements of chiral-odd fragmentation functions at Belle

- Asymmetries do cancel out for MC
- Double ratios of p+p+/p-p- compatible to zero
- Mixed events also show zero result
- Asymmetry reconstruction works well for t MC
(weak decays)

- Single hemisphere analysis yields zero
Double ratios are safe to use

- uds MC (pp-pairs)
- charm MC (pp-pairs)
- Data (p+p+/p-p-)

measurements of chiral-odd fragmentation functions at Belle

- Significant non-zero asymmetries
- Rising behavior vs. z
- cos(f1+f2) double ratios only marginally larger
- First direct measurement of the Collins function

Systematic error

Possible charm contribution

z1

z2

measurements of chiral-odd fragmentation functions at Belle

Systematic errors

Preliminary

Systematic errors

Other errors: smearing,

pid, charm content

MC double ratio

Charge sign ratio

Higher moments

Double ratio method

measurements of chiral-odd fragmentation functions at Belle

- Take unpolarized parameterizations (Kretzer at Q2=2.5GeV2)
- Assume
(PDF-like behavior)

- Assume
- Sensitivity studies in progress

measurements of chiral-odd fragmentation functions at Belle

Outlook:

Summary:

- Double ratios:
double ratios from data

most systematic errors cancel

- Analysis procedure passes all zero tests
- Main systematic uncertainties understood
- Significant nonzero asymmetry with double ratios is observed
- Naive LO analysis shows significant Collins effect
- Data can be used for more sophisticatedanalysis

- Finalize paper (based on hep-ex/0507063)
- On resonance 10 x statistics
- Include p0into analysis:
- Better distinction between favored and disfavored Collins function

- Include Vector Mesons into analysis:
Possibility to test string fragmentation models used to describe Collins effect

- Expansion of analysis to Interference fragmentation function straightforward

measurements of chiral-odd fragmentation functions at Belle

measurements of chiral-odd fragmentation functions at Belle

- Motivation
- Study transverse spin effects in fragmentation
- Global transversity analysis
- Feasibility LEP analysis
[hep-ph/9901216]

- The BELLE detector
- Collins analysis
- Angular definitions and cross sections
- Double Ratios to eliminate radiative/momentum correlation effects
- An experimentalist’s interpretation

- Summary

measurements of chiral-odd fragmentation functions at Belle

Collins Effect in Quark Fragmentation

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

q

Collins Effect:

Fragmentation of a

transversely polarized

quark q into spin-less

hadron h carries an

azimuthal dependence:

measurements of chiral-odd fragmentation functions at Belle

measurements of chiral-odd fragmentation functions at Belle

measurements of chiral-odd fragmentation functions at Belle

- 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)

measurements of chiral-odd fragmentation functions at Belle

Event Structure at Belle

e+e- CMS frame:

Near-side Hemisphere:

hi , i=1,Nn with zi

e-

<Nh+,-> = 6.4

Q

e+

Jet axis: Thrust

Spin averaged cross section:

Far-side:

hj , j=1,Nf with zj

measurements of chiral-odd fragmentation functions at Belle

Ph1

Lepton-CMS

- In the lepton CMS frame
e-=-e+ and the virtual photon is only time-like:

qm=(e-m+p+m)=(Q,0,0,0)

- Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame where
Ph1+Ph2=0

qm’=(q’0,q’)

- Inclusive Cross section for radiative events (acc. to D.Boer):

Ph2

e-

e+

q’

Hadron-CMS

e+’

e-’

P’h1

P’h2

qT

measurements of chiral-odd fragmentation functions at Belle

- Cos2f moments have two contributions:
- CollinsCan be isolated either by subtraction or double ratio method
- Radiative effectsCancels exactly in subtraction method, and in LO of double ratios

- Beam Polarization
zero?Cos(2fLab) asymmetries for jets or gg

- False asymmetries
from weak decays Study effect in t decays, constrain through D tagging

- False asymmetries
from misidentified

hemispheres QT or polar angle cut

- False asymmetries
from acceptanceCancels in double ratios, can be estimated in charge ratios,

fiducial cuts

- Decaying particleslower z cut

measurements of chiral-odd fragmentation functions at Belle

Double Ratio vs Subtraction Method:

Preliminary

Systematic errors

R – S < 0.002

- The difference was
assigned as a systematic

error.

measurements of chiral-odd fragmentation functions at Belle

Preliminary

- Low thrust contains radiative effects
- Collins effect vanishes
Strong experimental indication that double ratio method works

measurements of chiral-odd fragmentation functions at Belle

- Weak (parity violating) decays could also create asymmetries
(seen in ttppnn,

overall t 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 fraction N(charm)/N(all)

measurements of chiral-odd fragmentation functions at Belle

Take simple parameterization to test sensitivity on favored to disfavored Ratio

c

b

measurements of chiral-odd fragmentation functions at Belle

Favored= up+,dp-,cc.

Unfavored= dp+,up+,cc.

- Unlike sign pairs contain either only favored or only unfavored fragmentation functions on quark and antiquark side:
- Like sign pairs contain one
favored and one unfavored fragmentation function each:

measurements of chiral-odd fragmentation functions at Belle

NL- NR

AT=

= 0!

NL+ NR

π

sq

sq

q

q

π

Example: Left-Right Asymmetry in Pion Rates

Collins

Effect

NL : pions to the left

NR : pions to the right

measurements of chiral-odd fragmentation functions at Belle

A simple model to illustrate that

spin-orbital angular momentum

coupling can lead to left right

asymmetries in spin-dependent

fragmentation:

π+ picks up L=1 to

compensate for the

pair S=1 and is emitted

to the right.

String breaks and

a dd-pair with spin

-1 is inserted.

measurements of chiral-odd fragmentation functions at Belle

General Fragmentation Functions

Number density for finding

a spin-less hadron h from a

transversely polarized quark, q:

unpolarized FF

Collins FF

measurements of chiral-odd fragmentation functions at Belle

Unlike sign

pairs

Like sign

pairs

- Already MC contains large asymmetries
- Strong dependence against transverse photon Momentum QT
- Expected to be due to radiative effects
- Difference of DATA and MC is signal
- not so easy to determine

- DATA (pp) fiducial cut
- DATA (KK) fiducial cut
- UDS-MC fiducial cut
- CHARM-MC fiducial cut

j2

Q

Q

j1

j0

measurements of chiral-odd fragmentation functions at Belle