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Measurement of Collins Asymmetries at Belle
Measurement of Collins Asymmetries in e+e-
Annihilation at Belle
D. Gabbert
Illinois and RBRCM. G.Perdekamp
Illinois and RBRCK. Hasuko
RIKEN and RBRCS. Lange
Frankfurt M. Leitgab
IllinoisD. Mertens
Illinois A. Ogawa
BNL and RBRCR. Seidl
Illinois and RBRC V. Siegle
RBRC
for the Belle Collaboration
AGS&RHIC Users’
MeetingJune 19th , Brookhaven National Laboratory
Measurement of Collins Asymmetries at Belle 2June 19th
----------- Outline ------------
o
MotivationCollins FF for global QCD analysis of singletransverse asymmetries in pp and SIDIS
o
Collins Asymmetries from e+e-
LEP first work on Delphi data in the 90s: Efremov, Smirnova, Tkatchev andBonivento, Matteuzzi, Kotzinian
Experimental techniqueResults
Measurement of Collins Asymmetries at Belle 3June 19th
o Very basic QCD process: Fundamental test case for any approach to solve QCD at soft scales.
o Tests of universality and factorization betweene+e-, DIS and p-p collisions
o Symmetry properties
o Evolution is fundamental QCD prediction
o Connection between microscopic and macroscopic observables:
Probe/analyzer for transverse quark spincritical input for transverse proton spin programat DESY, CERN, JLab and RHIC
Why is the Collins Fragmentation Function Interesting?
Measurement of Collins Asymmetries at Belle 4June 19th
Motivation
Transversity
Quark Distributionsfrom Collins-
and Interference-Fragmentation
Collins-
and IFF-
asymmetriesin SIDIS and pp are of the form
~ Transversity (x) x CFF(z)
~ Transversity (x) x IFF(z)
Collins-
and IFF-
asymmetriesin e+e-
are of the form
~ CFF(z1
) x CFF(z2
)
~ IFF(z1
) x IFF(z2
)
global QCD analysis
New HERMES results for Collins AsymmetriesM. Diefenthaler, DIS 2007, Munich
Measurement of Collins Asymmetries at Belle 5June 19th
Global Analysis: Extract Transversity
Distributions
EIC JLAB, COMPASS, HERMES,
IFF versity transCollins versity trans
SIDIS
××
⇒
ity transversersity transv :Yan Drell A
GSI IFF ersity transv
Collins sity transver:Jetsin A Jets hadrons, inclusivefor A
pp
TT
T
N
×
××
⇒TransversityTensor Charge
FF ceInterferen x FF ceInterferen
Collins x Collins ee - ⇒+
Lattice QCD: Tensor Charge
Factorization +
Universality ?!
Belle
RHIC / GSI
Theo
ry
RBRC Transversity
Workshop 2000
Measurement of Collins Asymmetries at Belle 6June 19th
First QCD Analysis of SIDIS + e+e-
!
Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007
HERMES SIDIS+ COMPASS SIDIS
+ Belle e+e-
transversity dist.
+ Collins FF
Fit includes:
Measurement of Collins AsymmetriesIn e+e-
at KEK B with the Belle Phys.Rev.Lett.96:232002,2006
and update at Spin 2006 in Kyoto
Measurement of Collins Asymmetries at Belle 8June 19th
Collins Effect in Quark FragmentationJ.C. Collins, Nucl. Phys. B396, 161(1993)
φ
q
momentum hadron relative : 2
zmomentum hadron e transvers:
momentum hadron : spinquark : momentumquark :
h
sE
EEppsk
h
qh
h
h
q
=
=⊥
v
v
v
r
qsv
kv
hph v,
Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:
⊥hpv
( )φsin∝
⋅×∝ ⊥ qh spk vvv
Measurement of Collins Asymmetries at Belle 9June 19th
General Form of Fragmentation Functions
( )h
qhh
hqhqh
hq zM
spkpzHzDpzD
vvv ⋅×
+= ⊥⊥
⊥⊥↑
ˆ ),()(),( 2,
1,
1
Number density for finding hadron
h
from a transversely polarized quark, q:
unpolarized FF Collins FF
Measurement of Collins Asymmetries at Belle 10June 19th
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
Θ
Event Structure at Belle
( ) ( ) ( ) ( )
( )( ) ( )Θ+=⎟
⎠⎞⎜
⎝⎛ +−=
=Ω
→ ∑−+
22
21112
2
2
21
21
141
21
3
cos
,
cm
aaa
yyyA
zDzDeyAQdzdzd
Xhheed ασ
e+e- CMS frame:
Spin averaged cross section:
Measurement of Collins Asymmetries at Belle 11June 19th
o Quark spin direction unknown: measurement ofCollins function in one hemisphere is not possiblesin φ
modulation will average out.
o Correlation between two hemispheres withsin φi
Collins single spin asymmetries results incos(φ1
+φ2
)
modulation of the observed di-hadronyield.
Measurement of azimuthal
correlations for pion
pairsaround the jet axis in two-jet events!
Collins FF in e+e-
: NeedCorrelation between Hemispheres !
Measurement of Collins Asymmetries at Belle 12June 19th
Collins Fragmentation: Angles and Cross Section cos(φ1
+φ2
) Method
ϕ1
1hPr
2hPr
ϕ2
−π
ϕ1
ϕ2
( ) ( ) ( ) [ ]( ) [ ]( )
( ) ( ) Θ=−=
+=Ω
→ ⊥⊥−+
2cm
21
111
121T
221
21
41y1yyB
zHzHyBddzdzd
Xhheedσ
sin
cos ϕϕLq
2-hadron inclusive transverse momentum dependent cross section:
Net anti-alignment oftransverse quark spins
Θ
e+e- CMS frame:
e-
e+
Observables: N12
(φ1
+φ2
), A12
(z1
,z2
)
Measurement of Collins Asymmetries at Belle 13June 19th
Collins Fragmentation: Angles and Cross Section cos(2φ0
) Method
ϕ0
1hPr2hP
r
( ) ( ) ( ) ( )
( ) ( ) Θ=−=
⎢⎣
⎡⎥⎦
⎤⋅−⋅⋅=
Ω→ ⊥⊥−+
2cm
21
110
T2
21
21
41y1yyB
MMHH22yB
ddzdzdXhheedσ
sin
ˆˆcos TTTT pkphkhq
IϕL
2-hadron inclusive transverse momentum dependent cross section:
Net anti-alignment oftransverse quark spins
Θ •Independent of thrust-axis
•Convolution integral I over transverse momenta involved
e+e- CMS frame:
e-
e+
[Boer,Jakob,Mulders: NPB504(1997)345]
A0
Observables: N0
(φ0
), A12
(z1
,z2
)
Measurement of Collins Asymmetries at Belle 14June 19th
Hadronic
Events observed with Belle
∑∑
=
⋅=
ii
ii
p
npthrust v
v
particles
ˆ~ 1 ~ 0.5
1.5 x 109 hadronic events in analysis
On resonance: 547fb-1
, √s=10.52 GeV
(published)Off resonance: 29fb-1 , √s=10.58 GeV
(preliminary)
Measurement of Collins Asymmetries at Belle 15June 19th
z2
QTe- e+
( ) ( )∑ ⎥⎦
⎤⎢⎣
⎡+
∝Ω 21110
222
2
21
)2cos(sin zDzDQQ
qdqdzdzd
dN
T
T
T
φθ
z1 21 pp vv −=
Frame:
Gluon Emission
Measurement of Collins Asymmetries at Belle 16June 19th
Examples of Fits to Azimuthal
Asymmetries
D1 : spin averaged fragmentation function,
H1
: Collins fragmentation function
N0
(φ)/<N0
>
2φ0 (φ1
+φ2
)
2a0R0 R12 2a12
N12
(φ)/<N12
>
[ ] )cos()cos()(000
11
1111011
0
000 φφφ ab
DaDDcDHbHDaD
NNR +=
++∝=
Measurement of Collins Asymmetries at Belle 17June 19th
Method to eliminate gluon contributions: Double ratios for unlike-
and like sign pions
),()cos(411
)()(
21/
1221
12
2112
12
2112
12
12
zzA
NN
NN
RR
R
LUL
LUL
signLike
signUnLike
φφ
φφφφ
++≈
++== −
− (I) radiative
effects arecharge independentand cancel.
(II) RUL
and RL
dependdepend on Hfav
andHdis
differently.
A12 retains sensitivityfor the Collins effect!
Form double ratios for unlike and like-sign pion
pairs:
Measurement of Collins Asymmetries at Belle 18June 19th
Two Double Ratios
•
Unlike-sign pion pairs (U):(favored
x favored + unfavored
x unfavored)•
Like-sign pion pairs (L):(favored
x unfavored
+ unfavored
x favored)•
π±π0
pairs(favored + unfavored) x (favored + unfavored)
•
A. Efremov
et al. ([hep-ph/0603054]): charged ππ
pairs are similar (and easier to handle) (C):
(favored + unfavored) x (favored + unfavored)
Double ratios unlike/like-sign not very sensitive in separating favored and disfavored Collins functions look at unlike-sign/charge-sum
UL
UC
Observables:A12
(UL), A12
(UC)A0
(UL) , A0
(UC)published and input tofit by Anselmino
et al.
Measurement of Collins Asymmetries at Belle 19June 19th
Final Charm Corrected Results for e+ e- π π X (29fb-1, off-resonance Data)
•
Significant non-zero asymmetries
•
Rising behavior vs. z• UL/C
asymmetries about 40-
50% of UL/L
asymmetries•
First direct measurements
of the Collins function
• UL/L data published
A0(UL/L) (3.06 ± 0.57 ± 0.55)%
A12(UL/L) (4.26 ± 0.68 ± 0.68)%
A0(UL/C) (1.27 ± 0.49 ± 0.35)%
A12(UL/C) (1.75 ± 0.59 ± 0.41)%
Phys.Rev.Lett.96:232002,2006
Measurement of Collins Asymmetries at Belle 20June 19th
Preliminary Charm Corrected Results for e+ e- π π X (547 fb-1 ,on-resonance)
•
Significance largely increased
•
Behavior unchanged•
Reduced systematics•
Precise measurements
of the Collins function
Integrated results:A0(UL/L) (2.67 ± 0.10 ± 0.26)%
A12(UL/L) (3.55 ± 0.08 ± 0.15)%
A0(UL/C) (1.11 ± 0.11 ± 0.22)%
A12(UL/C) (1.46 ± 0.09 ± 0.13)%
Preliminary
Measurement of Collins Asymmetries at Belle 21June 19th
Summary & Outlook
Observation of large azimuthal asymmetries in light quark frag-mentation. Updated statistics:
∫Ldt =
29 fb-1 547 fb-1
Double ratios reliably cancel contributions from detector acceptance and gluon radiation.
Important input for the transverse spin physics programs at RHIC, HERMES, COMPASS and JLab.
Fundamental test case forQCD at soft scales!
Future spin dependent FFs: update Collins FFmeasure pT dependenceinterference fragmentationCollins FF for VMsLambdas
Precision measurement of spinaveraged fragmentation func-
tions as input to RHIC program with inclusive hadrons and futureprecision measurements in SIDIS.
Measurement of Collins Asymmetries at Belle 22June 19th
Motivation ∆G from QCD Analysis of ALL
for inclusive hadrons: π0,+,-, η, K+,-
PHENIX π0
cross section a |η|<0.35Phys.Rev.Lett.91:241803,2003
Deviation connected to uncertaintiesin FFs gluon FF!
Idea: QCD analysis ofLEP and Belle data willfix uncertainty in know-ledge of FFs
(gluon FF, flavor separation)
Measurement of Collins Asymmetries at Belle 23June 19th
What is Known Experimentally in e+e-
?
Hirai, Kumano,Nagai, Sudohep-ph/0612009(including errors!)
Earlier work:
KretzerBinnewies, Potter, AlbinoKniehl, Kramer, PotterAlbino, Kniehl, Kramer
Most recent work:
De Florian, Sassot,Stratmann
Measurement of Collins Asymmetries at Belle 24June 19th
Belle MC
<1% of data sample work in progress
Belle Impact on the Knowledge of FFs
2/
sEz
h
=2/
sEz
h
=
FF
FF
Compilation of dataavailable for the char-ged
hadron
FF
Belle: Charged h+/-,
pions, kaons, protons
precision at high z!
h+,-pionskaonsprotons
Input also for precision measurements of quarkhelicity
distributions in SIDIS, in particular ata possible future electron-polarized proton collider.
Measurement of Collins Asymmetries at Belle 25June 19th
o Very basic QCD process: Fundamental test case for any approach to solve QCD at soft scales.
o Tests of universality and factorization betweene+e-, DIS and p-p collisions
o Symmetry properties
o Evolution is fundamental QCD prediction
o Connection between microscopic and macroscopic observables:
Probe/analyzer for transverse quark spincritical input for transverse proton spin programat DESY, CERN, JLab and RHIC
Why is the Collins Fragmentation Function Interesting?
Measurement of Collins Asymmetries at Belle 26June 19th
Measurement of Collins Asymmetries at Belle 27June 19th
•
KEKB–
Asymmetric collider–
8GeV e-
+ 3.5GeV e+
–
√s = 10.58GeV (Υ(4S))e+e- Υ(4S) Β⎯Β
–
Off-resonance: 10.52 GeVe+e- q⎯q (u,d,s,c)
–
Integrated Luminosity: > 600 fb-1
> 60fb-1
=> off-resonance
Belle detectorKEKB
KEKB: L>1.6 x 1034cm-2s-1 !!
•Average Trigger rates:Υ(4S) BB 11.5Hzq⎯q
28 Hzμμ + ττ
16 HzBhabha
4.4 Hz2γ
35 Hz
1.5 x 109 hadronic events in analysis
Measurement of Collins Asymmetries at Belle 28June 19th
Good tracking and particle identification!
Measurement of Collins Asymmetries at Belle 29June 19th
•
Good detector performance (acceptance, momentum resolution, pid)
•
Jet production from light quarksoff-resonance (60 MeV below resonance) (~10% of all data)
•
Intermediate EnergySufficiently high scale (Q2 ~ 110 GeV2)
-
can apply pQCDNot too high energy (Q2 << MZ
2)-avoids complication from Z interference
•
Sensitivity = A2sqrt(N) ~ x 25 (100) compared to LEPABelle
/ ALEP ~ x 2
(A scales as
ln Q2)∫LBelle
dt
/ ∫LLEP
dt
~
x 46 (600)
Total number of hadronic
events ~ 1.5 x 109
9.44 9.46
e+e- Center-of-Mass Energy (GeV)
0
5
10
15
20
25
σ(e+ e
- →ha
dron
s)(n
b)
ϒ(1S)10.0010.02
0
5
10
15
20
25
ϒ(2S)10.34 10.37
0
5
10
15
20
25
ϒ(3S)10.54 10.58 10.62
0
5
10
15
20
25
ϒ(4S)9.44 9.46
e+e- Center-of-Mass Energy (GeV)
0
5
10
15
20
25
σ(e+ e
- →ha
dron
s)(n
b)
ϒ(1S)10.0010.02
0
5
10
15
20
25
ϒ(2S)10.34 10.37
0
5
10
15
20
25
5
10
15
20
25
ϒ(2S)10.34 10.37
0
5
10
15
20
25
ϒ(3S)10.54 10.58 10.62
0
5
10
15
20
ϒ(3S)10.54 10.58 10.62
0
5
10
15
20
25
ϒ(4S)
Belle is Well Suited for FF Measurements:
Measurement of Collins Asymmetries at Belle 30June 19th
Applied Cuts, Binning
• Originally off_resonance data, now also on_resonance data (29.1 547 fb-1)
• Track selection:– pT > 0.1GeV– vertex cut:
dr<2cm, |dz|<4cm
• Acceptance cut– -0.6 < cosθi < 0.9
• Event selection:– Ntrack ≥
3– Thrust > 0.8 –
Z1
, Z2
>0.2
• Hemisphere cut
•
QT < 3.5 GeV•
Pion PID selection
(Ph 2 ⋅ ˆ n ) ˆ n ⋅ (Ph1 ⋅ ˆ n ) ˆ n < 0
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
z1
Measurement of Collins Asymmetries at Belle 31June 19th
Experimental Issues
•
Cos2φ
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(2φ) asymmetries for jets or γγ
•
False asymmetriesfrom weak decays Study effect in τ 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
Measurement of Collins Asymmetries at Belle 32June 19th
Why is it Possible to Include Data on Resonance? Different Thrust Distributions
∑∑ ⋅
=
ii
ii
p
npthrust
ˆ
• small B contribution (<1%) in high thrust sample •>75% of X-section continuum under
Υ (4S) resonance•29 fb-1 547 fb-1
•many systematic errors reduce with
more statistics • Charm-tagged Data sample also increases
9.44 9.46
e+e- Center-of-Mass Energy (GeV)
0
5
10
15
20
25
σ(e+ e
- →ha
dron
s)(n
b)
ϒ(1S)10.0010.02
0
5
10
15
20
25
ϒ(2S)10.34 10.37
0
5
10
15
20
25
ϒ(3S)10.54 10.58 10.62
0
5
10
15
20
25
ϒ(4S)9.44 9.46
e+e- Center-of-Mass Energy (GeV)
0
5
10
15
20
25
σ(e+ e
- →ha
dron
s)(n
b)
ϒ(1S)10.0010.02
0
5
10
15
20
25
ϒ(2S)10.34 10.37
0
5
10
15
20
25
5
10
15
20
25
ϒ(2S)10.34 10.37
0
5
10
15
20
25
ϒ(3S)10.54 10.58 10.62
0
5
10
15
20
ϒ(3S)10.54 10.58 10.62
0
5
10
15
20
25
ϒ(4S)−+ BB00 BB
e+e- qq̅, q∈uds
e+e- cc̅
Measurement of Collins Asymmetries at Belle 33June 19th
Collins Asymmetries I: 4x4 z1
, z2 binning
•
547 fb-1
charm corrected data sample, • UL
and UC
double ratios
PRELIMINAR
YPRELIMINAR
Y
A0 (cos(2φ0
)) moments A12 (cos(φ1 + φ2
)) moments
Measurement of Collins Asymmetries at Belle 34June 19th
Collins Asymmetries II: sin2
θ/(1+cos2
θ) Binning (UL)
•
Nonzero quark polarization ~ sin2 θ
•
Unpolarized de-
nominator ~ 1+cos2
θ•
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
θ2
PRELIMINARY
Measurement of Collins Asymmetries at Belle 35June 19th
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 similar
Thrust>0.8
Thrust<0.8 (not corrected for heavy quark contributions)
PRELIMINARY
Measurement of Collins Asymmetries at Belle 36June 19th
Improved Systematic Errors (UC)• Tau contributions• PID systematics∗
• MC double ratios•
Charged ratios (π+π+
/π−π−
)•
Higher order terms•
Double ratio-subtraction method
Reweighting asymmetries: underestimation of cos(φ1+φ2)
asymmetries rescaled by 1.21Correlation studies:
statistical errrors rescaled by 1.02 (UL) and 0.55 (UC)Beam polarization studies
consistent with zero
A0 (cos(2φ0
)) moments
A12 (cos(φ1 + φ2
)) moments