measurements of chiral-odd fragmentation functions at belle d. gabbert (university of illinois and...
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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
HERMES Transversity Working Week
November 09, 東京工業大学、大岡山
(see hep-ex/0507063 for details)
measurements of chiral-odd fragmentation functions at Belle 2 Transversity Week Nov 09, 2005
SIDIS experiments (HERMES and COMPASS) measure q(x) together with either Collins Fragmentation function or Interference Fragmentation function
Motivation: Global Transversity Analysis
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 ]
measurements of chiral-odd fragmentation functions at Belle 3 Transversity Week Nov 09, 2005
KEKB: L>1.5x1034cm-2s-1 !!
• KEKB– 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: ~ 460 fb-1
~ 45fb-1 => off-resonance
Belle detectorKEKB
•Average Trigger rates:(4S)BB 11.5Hzqq 28 Hz 16 HzBhabha 4.4 Hz2 35 Hz
measurements of chiral-odd fragmentation functions at Belle 4 Transversity Week Nov 09, 2005
measurements of chiral-odd fragmentation functions at Belle 5 Transversity Week Nov 09, 2005
Good tracking and particle identification!
measurements of chiral-odd fragmentation functions at Belle 6 Transversity Week Nov 09, 2005
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:
measurements of chiral-odd fragmentation functions at Belle 7 Transversity Week Nov 09, 2005
Collins fragmentation: 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 .,
measurements of chiral-odd fragmentation functions at Belle 8 Transversity Week Nov 09, 2005
Collins fragmentation: 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]
measurements of chiral-odd fragmentation functions at Belle 9 Transversity Week Nov 09, 2005
Typical hadronic events at Belle
ii
ii
p
npthrust
ˆ
measurements of chiral-odd fragmentation functions at Belle 10
Transversity Week Nov 09, 2005
Applied cuts, binning
• Off-resonance data (in the future also on-resonance)
• 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
• Light quark selection• Hemisphere cut
• Opening angle cuts:- cos(2) method: h1-h2- cos() method:
h1-thrusth2-
thrustz2
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
(Ph 2 ˆ n ) ˆ n (Ph1 ˆ n ) ˆ n 0
= Diagonal bins
measurements of chiral-odd fragmentation functions at Belle 11
Transversity Week Nov 09, 2005
Examples of fitting the azimuthal asymmetries
D1 : spin averaged fragmentation function,
H1: Collins fragmentation function
N()/N0
No change in cosine moments when including sine and higher harmonics(even though double ratios will containthem)
Cosine modulationsclearly visible
measurements of chiral-odd fragmentation functions at Belle 12
Transversity Week Nov 09, 2005
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
measurements of chiral-odd fragmentation functions at Belle 13
Transversity Week Nov 09, 2005
Methods to eliminate gluon contributions: Double ratios and
subtractionsDouble 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 method gives very small difference in the result
measurements of chiral-odd fragmentation functions at Belle 14
Transversity Week Nov 09, 2005
Testing the double ratios with MC
• Asymmetries do cancel out for MC
• Double ratios of compatible to zero
• Mixed events also show zero result
• Asymmetry reconstruction works well for MC (weak decays)
• Single hemisphere analysis yields zero
Double ratios are safe to use
uds charm mixed kk mixedconstant 0.26%±0.19% -0.45%±0.33% 0.06%±0.09% 0.01%±0.16%
reduced c
1.17 1.35 1.14 1.2
•uds MC (pairs)
•charm MC pairs
•Data ()
measurements of chiral-odd fragmentation functions at Belle 15
Transversity Week Nov 09, 2005
Small double ratios in low thrust data sample
• Low thrust contains radiative effects
• Collins effect vanishes Strong experimental
indication that double ratio method works
• Nonzero asymmetries at high QT also seen in MC, due to acceptance and background effect
Preliminary
measurements of chiral-odd fragmentation functions at Belle 16
Transversity Week Nov 09, 2005
Results for -pairs for 30fb-1
• Significant non-zero asymmetries
• Rising behavior vs. z
• cosdouble ratios only marginally larger
• First direct measurement of the Collins function
z1
z2
Systematic errorPossible charm contribution
measurements of chiral-odd fragmentation functions at Belle 17
Transversity Week Nov 09, 2005
PreliminarySystematic errors
Systematic errors
Double ratio method
Higher momentsCharge sign ratio
MC double ratio
Other errors: smearing,pid, charm content
measurements of chiral-odd fragmentation functions at Belle 18
Transversity Week Nov 09, 2005
• Take unpolarized parameterizations (Kretzer at Q2=2.5GeV2)
• Assume
(PDF-like behavior)• Assume • Sensitivity studies
in progress
An experimentalist’s interpretation: fitting parameterizations of the Collins
function(s)
measurements of chiral-odd fragmentation functions at Belle 19
Transversity Week Nov 09, 2005
Take simple parameterization to test sensitivity on favored to disfavored Ratio
Favored/Disfavored contribution Sensitivity
2c
cb
measurements of chiral-odd fragmentation functions at Belle 20
Transversity Week Nov 09, 2005
Summary and outlook
• Double ratios:double ratios from datamost 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 sophisticated analysis
• Finalize paper (based on hep-ex/0507063)
• On resonance 10 x statistics
• Include into 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
Summary: Outlook:
measurements of chiral-odd fragmentation functions at Belle 21
Transversity Week Nov 09, 2005
measurements of chiral-odd fragmentation functions at Belle 22
Transversity Week Nov 09, 2005
Outline
• 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 23
Transversity Week Nov 09, 2005
Collins Effect in Quark Fragmentation 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 transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:
hp
sin
qh spk
measurements of chiral-odd fragmentation functions at Belle 24
Transversity Week Nov 09, 2005
• 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:
measurements of chiral-odd fragmentation functions at Belle 25
Transversity Week Nov 09, 2005
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
measurements of chiral-odd fragmentation functions at Belle 26
Transversity Week Nov 09, 2005
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
measurements of chiral-odd fragmentation functions at Belle 27
Transversity Week Nov 09, 2005
Preliminary Systematic errors
Double Ratio vs Subtraction Method:
R – S < 0.002
The difference was assigned as a systematic error.
measurements of chiral-odd fragmentation functions at Belle 28
Transversity Week Nov 09, 2005
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)
measurements of chiral-odd fragmentation functions at Belle 29
Transversity Week Nov 09, 2005
Different charge combinations additional information
• 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:
Favored = u,d,cc.
Unfavored = d,u,cc.
measurements of chiral-odd fragmentation functions at Belle 30
Transversity Week Nov 09, 2005
Example: Left-Right Asymmetry in Pion Rates
sq
π
π sqp
p
= 0 !AT =
NL - NR
NL + NR
Collins Effect
NL : pions to the left
NR : pions to the right
measurements of chiral-odd fragmentation functions at Belle 31
Transversity Week Nov 09, 2005
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:
measurements of chiral-odd fragmentation functions at Belle 32
Transversity Week Nov 09, 2005
General Fragmentation Functions
h
qhh
hqhqh
h
q zM
spkpzHzDpzD
ˆ),()(),( 2,
1,
1
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 33
Transversity Week Nov 09, 2005
Raw asymmetries vs transverse photon momentum QT
1hP
2hP
1hP
2hP
•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 () fiducial cut
•DATA (KK) fiducial cut
•UDS-MC fiducial cut
•CHARM-MC fiducial cut
Unlike signpairs
Like signpairs