spin dependent fragmentation function analysis at belle
DESCRIPTION
Spin dependent fragmentation function analysis at Belle. Spin 2006 October 5, 京都 , 日本. M. Grosse Perdekamp (University of Illinois and RBRC) A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC). KEKB: L>1.6x10 34 cm -2 s -1 !!. Belle detector. KEKB. Asymmetric collider - PowerPoint PPT PresentationTRANSCRIPT
Spin dependent fragmentation function analysis at Belle
M. Grosse Perdekamp (University of Illinois and RBRC)
A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC)
Spin 2006
October 5, 京都 , 日本
Measurement of the Collins fragmentation function at BELLE 2 Spin2006, October 6th
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
Measurement of the Collins fragmentation function at BELLE 3 Spin2006, October 6th
Good tracking and particle identification!
Measurement of the Collins fragmentation function at BELLE 4 Spin2006, October 6th
Collins fragmentation in e+e- : Angles and Cross section cos() method
1hP
2hP
2
21
111
121221
21
sin4
1
cosq
cm
T
B
zHzHBddzdzd
Xhheedσ
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)]
First |kT| moments of
Collins Function H1⊥
thrustaxis
Measurement of the Collins fragmentation function at BELLE 5 Spin2006, October 6th
Collins fragmentation in e+e- : Angles and Cross section cos(2) method
1hP
2hP
2
21
11TTTT02
21
21
sin4
1
pkphkh2I2cosq
cm
T
B
MM
HHB
ddzdzd
Xhheedσ
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]
Measurement of the Collins fragmentation function at BELLE 6 Spin2006, October 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 (Ph1ˆ n ) ˆ n 0
Measurement of the Collins fragmentation function at BELLE 7 Spin2006, October 6th
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 )
Measurement of the Collins fragmentation function at BELLE 8 Spin2006, October 6th
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
))(()(),(1)(
)(
: 2,1
,1
0
0T
disfavoredfavored
Like
Like
Unlike
Unlike
QFOzHzHF
NN
NN
R
)(),()()(
: ,1
,1
00
zHzHFN
N
N
NS disfavoredfavored
Like
Like
Unlike
Unlike
Measurement of the Collins fragmentation function at BELLE 9 Spin2006, October 6th
Other Favored/Unfavored Combinations charged pions or
• 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)
• 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 (UC)
UL
UC
Measurement of the Collins fragmentation function at BELLE 10
Spin2006, October 6th
Why is it possible to include on_resonance data?Different Thrust distributions
ii
ii
p
npthrust
ˆ
• small B contribution (<1%) in high thrust sample •>75% of X-section continuum under (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
(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)BB00 BB
e+e-qq, q∈uds
e+e-cc
Measurement of the Collins fragmentation function at BELLE 11
Spin2006, October 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)Beam polarization studiesconsistent with zero
A0 (cos(2)) moments
A12 (cos()) moments
Measurement of the Collins fragmentation function at BELLE 12
Spin2006, October 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
Measurement of the Collins fragmentation function at BELLE 13
Spin2006, October 6th
Collins asymmetries II: 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
Measurement of the Collins fragmentation function at BELLE 14
Spin2006, October 6th
• 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
Measurement of the Collins fragmentation function at BELLE 15
Spin2006, October 6th
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?
• How about 2 hadron analysis favored,disfavored FF 1.4 fb-1, 4.5·106 events
2.5 % of off_resonance data
Measurement of the Collins fragmentation function at BELLE 16
Spin2006, October 6th
Summary and outlook
• Double ratios:double ratios from datamost systematic errors cancel
• Analysis procedure passes all null tests
• Systematic uncertainties understood
• Statistics increased from 29 547 fb-1
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 with 29 fb-1 U/L double ratios published (PRL96:232002,2006)
• Analysis almost finalized,smalller additions planned (kt dependence of Collins effect, parameterizations)
• Interference fragmentation function analysis started
• Many more QCD/Spin related studies possible (unpol FFs, timelike DVCS, Polarimetry)
Measurement of the Collins fragmentation function at BELLE 17
Spin2006, October 6th
Backup Slides
Measurement of the Collins fragmentation function at BELLE 18
Spin2006, October 6th
Why correction factors of 1.2 and 0.55?
• Charged pion pairs are the sum of U and L
Errors are correlated when building double ratios UC or LC
• Division of histograms takes correlation not into account
• Proper error calculation confirms correction factors found in correlation studies and distributions
Measurement of the Collins fragmentation function at BELLE 19
Spin2006, October 6th
Collins asymmetries IIa: sin2 /(1+cos2 ) binning (UC)
• Nozeron 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)
• Similar behavior, smaller magnitude as UL asymmetries
thrustz
PRELIMINARY
Measurement of the Collins fragmentation function at BELLE 20
Spin2006, October 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>0.8
Thrust<0.8 (not corrected for heavy quark contributions)
PRELIMINARY
Measurement of the Collins fragmentation function at BELLE 21
Spin2006, October 6th
Collins asymmetries IIIa: QT binning (UC)
• Reduced asymmetries in low thrust sample
• At low thrust significant heavy quark contribution
• High QT (>3.5 GeV) asymmetries from beam related BG
• similar behavior, but smaller magnitude as UL asymmetries
Thrust>0.8
Thrust<0.8 (not corrected for heavy quark contributions)
PRELIMINARY
Measurement of the Collins fragmentation function at BELLE 22
Spin2006, October 6th
Final charm corrected results for e+ e- X (29fb-1 of continuum
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 publishedIntegrated results:
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)%
Final results
Preliminary results
Measurement of the Collins fragmentation function at BELLE 23
Spin2006, October 6th
Final charm corrected results for e+ e- X (547 fb-1)
• 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)%
Measurement of the Collins fragmentation function at BELLE 24
Spin2006, October 6th
B, charm and uds contributions in the data
uds quarkscharm quarksCharged B-mesonsNetral B-mesons
Open symbols: charm enhanced data sample used for charm correctionFull symbols: main data sample
thrust>0.8 thrust<0.8
Measurement of the Collins fragmentation function at BELLE 25
Spin2006, October 6th
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