collins asymmetries in belle measurement of collins asymmetries in e + e - annihilation at the kek...
DESCRIPTION
Collins Asymmetries in Belle3 September 6 th o Very basic QCD process: Fundamental test case for any approach to solve QCD at soft scales. o Tests of universality and factorization between e + 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 spin critical input for transverse proton spin program at DESY, CERN, JLab and RHIC Why is the Collins Fragmentation Function Interesting?TRANSCRIPT
Collins Asymmetries in Belle
Measurement of Collins Asymmetries in e+e- Annihilation at the KEK B-Factory
XII Workshop on High Energy Spin 2007Joint Institute for Nuclear Research, Dubna, September 6th
M. Grosse Perdekamp. Illinois
D. Gabbert Illinois and RBRCM. Grosse 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
Collins Asymmetries in Belle 2 September 6th
----------- Outline ------------
o Motivation Collins FF for global QCD analysis of single transverse asymmetries in pp and SIDIS
o Collins Asymmetries from e+e- LEP first work on Delphi data in the 90s: Bonivento, Matteuzzi, Kotzinian, (DELPHI note,1995), Efremov, Smirnova, Tkachev (Nucl. Phys. Proc. Suppl. 74,
1999) Experimental technique Results
o Future Plans• Spin dependent observables• Precision measurement of spin averaged
hadron fragmentation functions
Collins Asymmetries in Belle 3 September 6th
o Very basic QCD process: Fundamental test case for any approach to solve QCD at soft scales.
o Tests of universality and factorization between e+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 spin critical input for transverse proton spin program at DESY, CERN, JLab and RHIC
Why is the Collins Fragmentation Function Interesting?
Collins Asymmetries in Belle 4 September 6th
Motivation Transversity Quark Distributions δq(x) fromCollins- (CFF) and Interference-Fragmentation (IFF)
Collins- and IFF- asymmetriesin semi-inclusive deep inelastic scattering (SIDIS) and pp measure ~ δq(x) x CFF(z) ~ δq(x) x IFF(z)
Collins- and IFF- asymmetriesin e+e- annihilation are of the form ~ CFF(z1) x CFF(z2)
~ IFF(z1) x IFF(z2)
global QCD analysis
Latest HERMES results for Collins Asym-Metries, M. Diefenthaler, DIS 2007, Munich
Collins Asymmetries in Belle 5 September 6th
Global Analysis: Extract Transversity Distributions
Transversity, δq(x)Tensor Charge
Lattice QCD: Tensor Charge
Factorization + Universality ?!
Theo
ry
RBRC Transversity Workshop 2000
SIDIS~ δq(x) x CFF(z)~ δq(x) x IFF(z)
e+e-
~ CFF(z1) x CFF(z2)~ IFF(z1) x IFF(z2)
pp jets~ G(x1)xδq(x2) x CFF(z)
pp h+ + h- + X~ G(x1)xδq(x2) x IFF(z)
pp l+ + l- + X~ δq(x1) x δq(x2)
Collins Asymmetries in Belle 6 September 6th
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:
Collins Asymmetries in Belle 7 September 6th
The Preliminary DELPHI Collins Result
1
1
6.2 1.7 (stat. error)H ppmD
Efremov, Smirnova, Tkachev (Nucl. Phys. Proc. Suppl. 74, 1999)
1
1
12.9 1.4 (stat. error)H ppmD
Sample: 3.5 x 106 events at √s=MZ0Analysis: di-hadron correlation for leading hadrons
35<θ2<135
15< θ2 <175
endc
aps
endc
aps
First result on Collins Asymmetries in e+e- Monte Carlo for acceptance corrections Un-estimated (large) systematic errors DELPHI result e+e- compatible with HERMES+ BELLE (Efremov, Goeke, Schweitzer)
Measurement of Collins Asymmetries
In e+e- at KEK B with the Belle Phys.Rev.Lett.96:232002,2006
and update at Spin 2006 in Kyoto
Collins Asymmetries in Belle 9 September 6th
Collins Effect in Quark FragmentationJ.C. Collins, Nucl. Phys. B396, 161(1993)
q
momentum hadron relative : 2
zmomentum hadron e transvers:
momentum hadron :
spinquark : momentumquark :
h
sE
EEpp
sk
h
qh
h
h
q
qs
k
hph ,
Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:
hp
sin
qh spk
Collins Asymmetries in Belle 10
September 6th
General Form of Fragmentation Functions
h
qhh
hqhqh
hq zM
spkpzHzDpzD
ˆ ),()(),( 2,
1,
1
Number density for finding hadron h from a transversely polarized quark, q:
unpolarized FF Collins FF
Collins Asymmetries in Belle 11
September 6th
o Quark spin direction unknown: measurement of Collins function in one hemisphere is not possible sin φ modulation will average out.
o Correlation between two hemispheres with sin φi Collins single spin asymmetries results in cos(φ1+φ2) modulation of the observed di-hadron yield.
Measurement of azimuthal correlations for pion pairs around the jet axis in two-jet events!
Collins FF in e+e- : NeedCorrelation between Hemispheres !
Collins Asymmetries in Belle 12
September 6th
q1
quark-1 spin
Collins effect in e+e-
quark fragmentation will lead to azimuthalasymmetries in di-hadron correlation measurements!
Experimental requirements: Small asymmetries very large data sample! Good particle ID to high moments. Hermetic detector
Collins Effect in di-Hadron CorrelationsIn e+e- Annihilation into Quarks!
electron
positron
q2
quark-2 spin
z2 z1
z1,2 relative pion momenta
Collins Asymmetries in Belle 13
September 6th
KEKB– Asymmetric collider– 8 GeV e- + 3.5 GeV e+
– s = 10.58 GeV , e+e- ϒS– Off-resonance: 10.52 GeV e+e- qq (u,d,s,c)– Integrated Luminosity: 547 fb-1 (on resonance) 60 fb-1 (off-resonance)
Belle detectorKEKB
KEKB: L>1.6 x 1034cm-2s-1 !!
Average Trigger rates:(4S)BB 11.5Hzqq 28 Hz 16 HzBhabha 4.4 Hz2 35 Hz
1.5 x 109 hadronic events in analysis ~ 430 x DELPHI …
Collins Asymmetries in Belle 14
September 6th
Luminosity vs time for 24 hours at KEKB Continuous Injection Constant Collision
Rate
24 hours
high energy ring - beam current
low energy ring - beam current
HER lifetime
LER lifetime
∫Ldt vs day time
∫Ldt =1fb-1/day
Collins Asymmetries in Belle 15
September 6th Large acceptance, good tracking and particle identification!
Collins Asymmetries in Belle 16
September 6th
Hadronic Events observed with Belle
ii
ii
p
npthrust
particles
ˆThrust ~ 1 ~ 0.5
1.5 x 109 hadronic events in analysis
Off resonance: 29fb-1 , √s=10.52 GeV (published)
On resonance: 547fb-1 , √s=10.58 GeV (preliminary)
Collins Asymmetries in Belle 17
September 6th
Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance
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 • several 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
(e+ e
- ha
dron
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
- ha
dron
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)BB00 BB
e+e-qq̅, q∈uds
e+e-cc̅
0.5 0.8 1.0
Collins Asymmetries in Belle 18
September 6th
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 < cosi < 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
Collins Asymmetries in Belle 19
September 6th
e-
e+ Jet axis: Thrust
<Nh+,-> = 6.4
GeV 5210ss
E2z h ., Near-side Hemisphere: hi , i=1,Nn with zi
far-side hemisphere: hj , j=1,Nf with zj
Event Structure at Belle
22
21112
2
2
21
21
141
21
3
cos
,
cm
aaa
yyyA
zDzDeyAQdzdzd
Xhheed
e+e- CMS frame:
Spin averaged cross section:
Collins Asymmetries in Belle 20
September 6th
Collins Fragmentation: Angles and CrossSection: cos() Method (e+e- CMS
frame)
1hP
2hP
2cm
21
111
121T
221
21
41y1yyB
zHzHyBddzdzd
Xhheedσ
sin
cos q
2-hadron inclusive transverse momentum dependent cross section:
Net anti-alignment oftransverse quark spins
e-
e+
Observable: yield, N12(φ1+φ2) of π+π- pairs
Collins Asymmetries in Belle 21
September 6th
Collins Fragmentation: Angles and Cross Section cos(2) Method (CMS
Frame)
1hP2hP
2cm
21
110
T2
21
21
41y1yyB
MMHH22yB
ddzdzdXhheedσ
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
[Boer,Jakob,Mulders: NPB504(1997)345]
e-
e+
Observable: yield,N0(2φ0) of π+π- pairs
Collins Asymmetries in Belle 22
September 6th
z2
QTe- e+
21110
222
2
21
)2cos(sin ... before as... zDzDQQ
qdQdzdzd
dN
T
T
T
z1 21 pp Frame:
Complication: Radiative Contribution to the Di-Hadron Cross Section
same cos(2Φ0)dependence asCollins effect …
Collins Asymmetries in Belle 23
September 6th
Examples of Fits to Azimuthal Asymmetries
D1 : spin averaged fragmentation function, H1: Collins fragmentation function
N0()/<N0>
2 )
2a0R0 R1
2
2a12
N12(Φ1+Φ2)/<N12>
)2cos()2cos()2(
00011
1111011
0
000 ab
DaDDcDHbHDaD
NNR
a0 and a12 contain Collins + radiative effects+ acceptance effects
Collins Asymmetries in Belle 24
September 6th
Large Radiative and Acceptance Effects !
Example:a0 for unlike-sign pion pairs: a0
U
generated uds-MCvs reconstructed uds-MCvs data (Difference MC-data: charm contribution)
a0 for like-sign pion pairs: a0L
generated uds-MCvs reconstructed uds-MCvs data (Difference MC-data: charm contribution)
generated uds-MC
reconstructed uds-MCdata
data
reconstructed uds-MC
generated uds-MC
Collins Asymmetries in Belle 25
September 6th
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
(I) radiative effects are charge independent and cancel.
(II) Acceptance effects cancel.
(III) RUL and RL depend depend on Hfav and Hdis differently.
A12 retains sensitivity for the Collins effect!
Cross checked againstsubtraction RUL-RL withidentical results.
Form double ratios for unlike and like-sign pion pairs:
Collins Asymmetries in Belle 26
September 6th
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)
• ± pairs(favored + unfavored) x (favored + unfavored)
• A. Efremov et al. ([hep-ph/0603054]): charged 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.
Collins Asymmetries in Belle 27
September 6th
Consistency Checks for Double Ratio
(0) Check that Monte Carlo Double asymmetries are 0.(1) Calibrate with “known” physics asymmetry: Weak decays produce azimuthal asymmetries. Showed that double ratio method give correct asymmetry for tau-sample.(2) Comparison of Double Ratio with Subtraction Method leads to identical results.(3) Observe polar angle dependence
(4) Smaller asymmetry for lower thrust sample
(5) Null tests:
(a) mixed events give 0 asymmetry (b) single side asymmetries average to 0
)cos1(sin~ 2
2
0
A
Collins Asymmetries in Belle 28
September 6th
Double Ratios From Monte Carlo
Monte Carlo knowsRadiative and accep-tance effects!
Do they cancel in the final double ratio?
Assign largest observedaverage MC double ratio + statistical error as systematic error
<A0UL>=0.0013∓0.0009
0.0022
Collins Asymmetries in Belle 29
September 6th
Collins Asymmetries: 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
Collins Asymmetries in Belle 30
September 6th
Other Experimental Issues
• Beam Polarization zero? cos(2) asymmetries for jets or • False asymmetries from weak decays estimate charm contribution 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 from data, fiducial cuts• Correlations from decays
lower z cut
Collins Asymmetries in Belle 31
September 6th
Final Charm Corrected Results for e+ e- 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
Collins Asymmetries in Belle 32
September 6th
Preliminary Charm Corrected Results for
e+ e- 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
Collins Asymmetries in Belle 33
September 6th
Improved Systematic Errors (UC)• Tau contributions• PID systematics
• MC double ratios• Charged ratios (• Higher order terms• Double ratio-subtraction
method
Reweighting asymmetries: underestimation of cos asymmetries rescaled by 1.21Correlation studies:statistical errrors rescaled by 1.02 (UL) and 0.55 (UC)
A0 (cos(2)) moments
A12 (cos()) moments
Collins Asymmetries in Belle 34
September 6th
Collins Asymmetries I: 4x4 z1, z2 binning
• 547 fb-1 charm corrected data sample, • UL and UC double ratios
PRELIMINARY PRELIMINARY
A0 (cos(2)) moments A12 (cos()) moments
Collins Asymmetries in Belle 35
September 6th
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:
Collins Asymmetries in Belle 36
September 6th
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 for QCD at soft scales!
Future spin dependent FFs: update Collins FF measure pT dependence interference
fragmentation Collins FF for VMs Lambdas Precision measurement of spin averaged fragmentation func-
tions as input to RHIC program with inclusive hadrons and
future precision measurements in
SIDIS.
Collins Asymmetries in Belle 37
September 6th
Motivation ∆G from QCD Analysis of ALL for inclusive hadrons: π0,+,-, η, K+,-
PHENIX π0 cross section a |η|<0.35 Phys.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)
Collins Asymmetries in Belle 38
September 6th
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
Collins Asymmetries in Belle 39
September 6th
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+,- pions kaons protons
Input also for precision measurements of quark helicity distributions in SIDIS, in particular at a possible future electron- polarized proton collider.
Collins Asymmetries in Belle 40
September 6th
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>0.8Thrust<0.8 (not corrected for heavy quark contributions)
PRELIMINARY