Precision fragmentation function measurements at Belle
Trento, June 14 2007
M. Grosse Perdekamp (University of Illinois and RBRC)
A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC)
Outline:•The Collins function measurements
•Access to transversity over Collins fragmentation function•Collins function measurements at Belle
•The Belle detector•Improved statistics with on_resonance data
•Interference fragmentation function measurements•unpolarized fragmentation function measurements
R.Seidl: Fragmentation function measurements at Belle 2 Trento, June 14th
SIDIS experiments (HERMES and COMPASS, eRHIC) measure q(x) together with either Collins Fragmentation function or Interference Fragmentation function
Towards a 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
Spin dependent Fragmentation function analysis in e+e- Annihilation yields
information on the Collins and the Interference Fragmentation function !
Comlpex universality?
R.Seidl: Fragmentation function measurements at Belle 3 Trento, June 14th
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: >700 fb-1
• >60fb-1 => off-resonance
Belle detectorKEKB
R.Seidl: Fragmentation function measurements at Belle 4 Trento, June 14th
Good tracking and particle identification!
R.Seidl: Fragmentation function measurements at Belle 5 Trento, June 14th
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:
R.Seidl: Fragmentation function measurements at Belle 6 Trento, June 14th
Collins fragmentation in e+e- : 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 .,
[D.Boer: PhD thesis(1998)]
R.Seidl: Fragmentation function measurements at Belle 7 Trento, June 14th
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]
R.Seidl: Fragmentation function measurements at Belle 8 Trento, June 14th
Applied cuts, binning
• Off-resonance data – 60 MeV below (4S)
resonance– 29.1 fb-1
Later also on-resonance data: 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
(Ph 2 ˆ n ) ˆ n (Ph1 ˆ n ) ˆ n 0
z1
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
= Diagonal bins z1
z2
R.Seidl: Fragmentation function measurements at Belle 9 Trento, June 14th
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 )
R.Seidl: Fragmentation function measurements at Belle 10 Trento, June 14th
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
R.Seidl: Fragmentation function measurements at Belle 11 Trento, June 14th
Testing the double ratios with MC• Asymmetries do cancel out for MC• Double ratios of
compatible with zero• Mixed event pion pairs also show
zero result• Asymmetry reconstruction works
well for MC (weak decays)• Single hemisphere analysis yields
zeroDouble ratios are safe to use
•uds MC (UL/L double ratios)
•uds MC (UL/C double ratios) •Data ()
R.Seidl: Fragmentation function measurements at Belle 12 Trento, June 14th
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
R.Seidl: Fragmentation function measurements at Belle 13 Trento, June 14th
What about the data under the resonance?
• More than 540 fb-1 of on_resonance data
• (4S) is just small resonance
• More than 75% of hadronic cross sectionfrom open quark-antiquark production
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)
R.Seidl: Fragmentation function measurements at Belle 14 Trento, June 14th
Why is it possible to include on_resonance data?Different Thrust distributions
ii
ii
p
npthrust
ˆ
• e+ e- q q (u d s) MC
• (4S) B+ B- MC
• (4S) B0 B0 MC
• Largest systematic errors reduce with more statistics • Charm-tagged Data sample also increases with statistics
BB00 BB
e+e-qq, q∈uds
e+e-cc
R.Seidl: Fragmentation function measurements at Belle 15 Trento, June 14th
Improved systematic errors (UC)• Tau contribution• PID error• MC double ratios• Charged ratios (• higher moments in Fit• difference double ratio-
subtraction method
•reweighted MC-asymmetries: cos asymmetries underestimated rescaled with 1.21•Correlation studies: statistical error rescaled by1.02 (UL) and 0.55 (UC) – after rigorous error calculation correct•Beam polarization studies consistent with zero•Correction of charm events
A0 (cos(2)) moments
A12 (cos()) moments
R.Seidl: Fragmentation function measurements at Belle 16 Trento, June 14th
Final charm corrected results for e+ e- X (29fb-1 of continuum
data)• Significant non-zero
asymmetries • Rising behavior vs. z
• cos(+) double ratios only marginally larger
• UC asymmetries about 40-50% of UL asymmetries
• First direct measurements of the Collins function
Integrated results:
A0(UL) (3.06 ± 0.57 ± 0.55)%
A12(UL) (4.26 ± 0.68 ± 0.68)%
A0(UC) (1.270 ± 0.489 ± 0.350)%
A12(UC) (1.752 ± 0.592 ± 0.413)%
Final results
Preliminary results
R.Seidl: Fragmentation function measurements at Belle 17 Trento, June 14th
Charm corrected results for e+ e- X (547 fb-1)
• Significance largely increased
• Behavior unchanged• Reduced systematic
errors due to statistics• Precise measurements of
the Collins function
Integrated results:
A0(UL) (2.67 ± 0.10 ± 0.26)%
A12(UL) (3.55 ± 0.08 ± 0.15)%
A0(UC) (1.11 ± 0.11 ± 0.22)%
A12(UC) (1.46 ± 0.09 ± 0.13)%
PRELIMINARY
R.Seidl: Fragmentation function measurements at Belle 18 Trento, June 14th
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
R.Seidl: Fragmentation function measurements at Belle 19 Trento, June 14th
• 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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]
• Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)]
Interference Fragmentation – thrust method
21221111 m,zHm,zHA cos
2
1
1hP
2hP
2h1h PP
Model predictions by:
•Jaffe et al. [PRL 80,(1998)]
•Radici et al. [PRD 65,(2002)]
R.Seidl: Fragmentation function measurements at Belle 20 Trento, June 14th
• Similar to previous method• Observe angles 1R2R
between the event-plane (beam, two-pion-axis) and the two two-pion planes.
• Theoretical guidance by Boer,Jakob,Radici
Interference Fragmentation – “ “ method
R2R1221111 m,zHm,zHA cos
R2
R1
1hP
2hP
3hP
4hP
2h1h PP
4h3h PP
R.Seidl: Fragmentation function measurements at Belle 21 Trento, June 14th
Different model predictions for IFF
•Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of -phaseshift analysissign change at mass
-originally no predictions on actual magnitudes
-Tang included some for RHIC-Spin
• Radici et al. [Phys. Rev. D65 (2002)] : Spectator model in the s-p channel no sign change observed (updated model has Breit-Wigner like asymmetry)
PRELIMINARY
f1, h1 from spectator model
f1, h1=g1 from GRV98 & GRSV96
R.Seidl: Fragmentation function measurements at Belle 22 Trento, June 14th
Unpolarized FF as important input for all precise QCD measurements
MC simulation, ~1.4 fb-1
2.
• No low-Q2 data available important for evolution
• No high-z data available Huge amount of B-factory
data can help• Favored/Disfavored
disentangling by detecting hadron pairs (as in Collins analysis)?
R.Seidl: Fragmentation function measurements at Belle 23 Trento, June 14th
Summary and outlook
• A first successful global analysis of transversitydata using the HERMES,COMPASS and published Belle data
• Belle Collins data largely improved from 29 547 fb -1
• Significant, nonzero asymmetries Collins function is large
• Long Collins paper is nearly finished
• Continue to measure precise spin dependent fragmentation functions at Belle– kT dependence of Collins function– Favored/disfavored disentanglement– Initerference Fragmentation function
measurements (started) • Measure precise unpolarized fragmentation
functions of many final states Important input for general QCD physics and
helicity structure measurements• Measure other interesting QCD-related
quantities at Belle:– Chiral-odd -fragmentation function– Event shapes– R-ratio with ISR
R.Seidl: Fragmentation function measurements at Belle 24 Trento, June 14th
Backup Slides
R.Seidl: Fragmentation function measurements at Belle 25 Trento, June 14th
B, charm and uds contributions in the data
uds quarkscharm quarksCharged B-mesonsNeutral B-mesons
Open symbols: charm enhanced data sample used for charm correctionFull symbols: main data sample
R.Seidl: Fragmentation function measurements at Belle 26 Trento, June 14th
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
R.Seidl: Fragmentation function measurements at Belle 27 Trento, June 14th
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
R.Seidl: Fragmentation function measurements at Belle 28 Trento, June 14th
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
R.Seidl: Fragmentation function measurements at Belle 29 Trento, June 14th
What would we see in e+e-?
Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning
m1
m1
m2
m2
“Jaffe” “Radici”