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Measurement of Fragmentation Functions at
Anselm Vossen (University of Illinois)Matthias Grosse Perdekamp
(University of Illinois)Martin Leitgab (University of Illinois)
Akio Ogawa (BNL/RBRC) Ralf Seidl (RBRC)
Kieran Boyle (RBRC)
DIS2010, Florence, April 19-23
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Outline
• Motivation– Analysis of Transverse Spin Effects
in SIDIS, proton-proton– Recent experimental results– Transversity extraction
• Measuring Fragmentation Functions at Belle– Experimental techniques– Interference Fragmentation Function Measurement– Comparison with theory
• Summary & Outlook
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Transverse Spin Asymmetries
• Experimental results in SIDIS and pp
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Transverse Spin Asymmetries- Single Hadrons
• Large transverse single spin effects persist at large scale
• Convolution of different effects
RL
RLN P
A
1
4
Transversity
PHENIX, forward at s = 62 GeV, nucl-ex/0701031
21
222xx
s
px L
F
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Transverse Spin Asymmetries
• Experimental results in SIDIS and pp• Access to fundamental aspects of QCD and nucleon
structure:– TMDs, orbital angular momentum– Initial, final state interactions– Gauge invariance of correlators
• Prominent effects:– Transversity * Collins– Sivers Effect
• Separation of different effects requires measurements at multiple experiments, channels -> pp, SIDIS, e+e-
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Chiral odd FFs
+
_
+
1h
_
+
_1H
Collins effect
q
N
: Collins FF
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Collins Fragmentation at Belle
• First extraction of transversity quark distribution
Together with HERMES, COMPASSFirst, still model dependent transversity Extraction :
Alexei Prokudin, DIS2008, update of Anselmino et al: hep-ex 0701006
Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)
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Collins Extraction of Transversity: model dependence from Transverse
Momentum Dependences!
),(
)(),(
)sin()sin(),()(
),(
22
,122
pzDdy
dkxqkddde
pzHdy
dkxqkddde
AhqhS
hShqSqhS
CollinsUT
Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007
k┴ transverse quark momentum in nucleonp┴ transverse hadron momentum in fragmentation
transv
ersity
Collin
s FF
hadron FFquark pdf
The transverse momentum dependencies are unknown anddifficult to obtain experimentally!
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Chiral odd FFs
+
_
+ _
+ q
N
_
Lz-1Lz
1H
Interference Fragmentation Function
( )
1h
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Advantages of IFF
• Independent Measurement• Favourable in pp: no Sivers• Transverse momentum is integrated
– Collinear factorization
– No assumption about kt in evolution– Universal function– evolution known, collinear scheme can be used – directly applicable to semi-inclusive DIS and pp
• First experimental results from HERMES, COMPASS, PHENIX
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Interference FF in Quark Fragmentation
q
1 2
pair
:quark momentum
:quark spin
: momentum difference -
: transverse hadron momentum difference
z
q
h h
T
pair
k
s
R p p
R
E E
2 : relative hadron pair momentum
q
pairE s
qs
k
R
Interference Fragmentation Function:Fragmentation of a transversely polarizedquark q into two spin-less hadron h1, h2 carries anazimuthal dependence:
R
sin
T qk R s
1h
2h
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Di-Hadron SSA in SIDIS
(both on proton target, sign convention different)
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Added statistics from 2008 running As expected:
No significant asymmetries seen at central-rapidity.
SSA from di-hadron productionExtended kinematic regime compared with SIDISHard scale
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o Quark spin direction unknown: measurement of Interference Fragmentation function in one hemisphere is not possible
sin φ modulation will average out.
o Correlation between two hemispheres with sin φRi single spin asymmetries results in cos(φR1+φR2) modulation of the observed di-hadron yield.
Measurement of azimuthal correlations for di-pion pairs around the jet axis in two-jet events!
Spin Dependent FF in e+e- : NeedCorrelation between Hemispheres !
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q1
quark-1 spin
Interference 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 momenta.
Hermetic detector Observable:cos(φR1+φR2)
modulation measures
Measuring di-Hadron CorrelationsIn e+e- Annihilation into Quarks
electron
positron
q2
quark-2 spin
( )
z1,2 relative pion pair momenta
z2 z1
( )
11H H
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KEKB: L>2.11 x 1034cm-2s-1 !!• Asymmetric collider• 8GeV e- + 3.5GeV e+
• √s = 10.58GeV ((4S))• e+e-(4S)BB• Continuum production:
10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: > 1000 fb-1
• >70 fb-1 => continuum
16
Belle detectorKEKB
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17Collins Asymmetries in Belle 17 May 28th Large acceptance, good tracking and particle identification!
He/C2H6
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Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance
ii
ii
p
npTThrust
ˆ
:
• small B contribution (<1%) in high thrust sample • >75% of X-section continuum under ϒ(4S) resonance• 73 fb-1 662 fb-1
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-qq̅, q uds∈
e+e-cc̅
0.5 0.8 1.0
4s“off”
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Cuts and Binning• Similar to Collins analysis, full off-resonance and on-resonance data
(7-55): ~73 fb-1 + 588 fb-1
• Visible energy >7GeV • PID: Purities in Pion/Pion Sample > 90% • Same Hemisphere cut within pair (), opposite hemisphere
between pairs• All 4 hadrons in barrel region: -0.6 < cos () <0.9• Thrust axis in central area: abs(thrustz)<0.75• Thrust > 0.8
• zhad1,had2>0.1
• z1 = zhad1+zhad2 and z2 in 9x9 bins
• m and m in 8x8 bins: [0.25 - 2.0] GeV
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Results including systematic errors
8x8 m1 m2 binning 28
PreliminaryPreliminary
Preliminary
Preliminary
PreliminaryPreliminary
PreliminaryPreliminary
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219x9 z1 z2 binning
PreliminaryPreliminary Preliminary
Preliminary
PreliminaryPreliminaryPreliminary
PreliminaryPreliminary
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Subprocess contributions (MC)
9x9 z1 z2 binning
tau contribution (only significant at high z)charged B(<5%, mostly at higher mass)Neutral B (<2%)charm( 20-60%, mostly at lower z)uds (main contribution)
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Subprocess contributions (MC)
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8x8 m1 m2 binning
charged B(<5%, mostly at higher mass)Neutral B (<2%)charm( 20-60%, mostly at highest masses)uds (main contribution)
Charm Asymmetries in simulated data consistent with zero!To be checked with charm enhanced sample
Data not corrected for Charm contributions
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Comparison to theory predictions
Leading order, experimental results might contain effects from gluon radiation not contained in the model
Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm )
Z dependence : Rising behavior steeper
However: Theory contains parameters based on HERMES data which already fail to explain COMPASS well
Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009.
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Projections for () () for 580 fb-1
a 12
Minv<0.4 GeV 0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV
0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeVa 12
a 12a 12
a 12
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Projections for () (K) for 580 fb-1
Minv<0.7 GeV 0.7 GeV<Minv<0.85 GeV
0.85 GeV<Minv<1.0 GeV1.0 GeV<Minv
Aa 12
a 12
a 12
a 12
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Summary
• First measurement of Interference Fragmentation Function!
• Asymmetry significant
• Combined Analysis of Di-hadron and single hadron measurements possible
• Systematic effects to be finalized• Future goal: Combined analysis of SIDIS, pp, e+e- data
– Extract transversity– Disentangle contributions to AN
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Outlook
• Near future– IFF/Collins for more flavors– A lot of effort on precise measurements of
unpolarized identified fragmentation functions, first results soon!
– Unpolarized two hadron fragmentation functions
• Far future– Continue to measure precise spin dependent fragmentation
functions at Belle• kT dependence of Collins function• Artru model test with Vector meson Collins
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Backup
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Towards a global transversity analysis: Chiral –odd Fragmentation functions
RHIC and SIDIS experiments measure:
Transversity q(x) X
Collins Fragmentation function
or Interference Fragmentation function (IFF)
zH1
2 Unknown Functions measured together
•Universality understood•Evolution ?
Belle measures:
Collins X Collins
or IFF X IFF
Transversity
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Motivation
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Fragmentation functions in e+e- annihilation
• Process:
e+ e-hX
• At leading order sum of unpolarized fragmentation functions from quark and anti-quark side
e-
e+
GeV 5210ss
E2z h .,
h
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World data and motivation for precise FFs
• Most data obtained at LEP energies,
• At lower CMS energies very little data available
• 3-jet fragmentation to access gluon FF theoretically difficult
Gluon fragmentation from evolution not yet well constrained
Higher z FFs (>0.7) hardly available
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Current knowledge on fragmentation functions - DSS
DeFlorian, Sassot, Stratmann, PRD hep-ph/0703242
Differences between different global fits still large for high-z gluon contributions and kaons
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Systematic studies: Particle identification• Particle identification:
create PID efficiency matrix for K,,p,e,
• PID responses from MC not reliable, use well identified decays from data:– Use
D*slowD0slowfastK for K, identification
– Use p for p, identification
– J/ + -, e+ e- for leptons (if needed also (1S))
Unfolding
=
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D* Extractionfinal extraction: large acceptance region covered
K+
K-PLab
CosLab
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Event Structure for hadron pairs in e+e- annihilation
<Nh+,-> = 6.4
Far-side: hj , j=1,Nf with zj
e+e- CMS frame:
e-
e+
22
21112
2
2
21
21
14
1
2
1
3
cos
,
cm
aaa
yyyA
zDzDeyAQdzdzd
Xhheed
Spin averaged cross section:
Jet axis: Thrust
GeV 5210ss
E2z h .,
Near-side Hemisphere: hi , i=1,Nn with zi
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Unpolarized 2-hadron fragmentation
• Detect two hadrons simultaneously
• If two hadrons in opposite hemispheres one obtains sensitivity to favored/disfavored fragmentation:
•
• Problems:–Either need to ensure
two-jet topology (thrust cut)
–Or contribution from one quark fragmentation qhhX
• Unlike-sign pion pairs (U):(favored x favored + unfavored x unfavored)
• Like-sign pion pairs (L):(favored x unfavored + unfavored x favored)
• ± or any charge hadron pairs (C):(favored + unfavored) x (favored + unfavored)
Favored = u,d,cc.
Unfavored = d,u,cc.
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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
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First global analysis from Collins Hermes, Compass d and Belle data
• First results available, still open questions from evolution of Collins FF and transverse momentum dependence
Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.191:98-107,2009
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Asymmetry extraction
• Build normalized yields:
• Fit with:
or
,)( 21
N
N
)sin()(2cos
)cos(
21122112
122112
dc
ba
122112 )cos( ba
Amplitude a12 directly measures IFF! (squared, no double ratios)
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Zero tests: MC
• A small asymmetry seen due to acceptance effect
• Mostly appearing at boundary of acceptance• Opening cut in CMS of 0.8 (~37 degrees)
reduces acceptance effect to the sub-per-mille level
43
Ph
),cos(ˆ
nPP
nP
h
h
No opening cutOpening cut>0.7Opening cut >0.8
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Zero tests: Mixed Events
False
Asy
mm
etrie
s con
siste
nt with
zero
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• Inject asymmetries in Monte Carlo
• Reconstruction smears thrust axis,
• ~94% of input asymmetry is reconstructed
• (Integrated over thrust axis: 98%)
• Effect is understood, can be reproduced in Toy MC
• Asymmetries corrected
SmearingIn azimuthalAngle of thrustAxis in CMS
Black: injectedPurple reconstructed
Weighted MC asymmetries
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Cuts and Binning• Similar to Collins analysis, full off-resonance and on-resonance data
(7-55): ~73 fb-1 + 588 fb-1
• Visible energy >7GeV • PID: Purities in Pion/Pion Sample > 90% • Same Hemisphere cut within pair (), opposite hemisphere
between pairs• All 4 hadrons in barrel region: -0.6 < cos () <0.9• Thrust axis in central area: abs(thrustz)<0.75• Thrust > 0.8
• zhad1,had2>0.1
• z1 = zhad1+zhad2 and z2 in 9x9 bins
• m and m in 8x8 bins: [0.25 - 2.0] GeV
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Results including systematic errors
8x8 m1 m2 binning
PreliminaryPreliminary
Preliminary
Preliminary
PreliminaryPreliminary
PreliminaryPreliminary
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Results for 9x9 z1 z2 binning
PreliminaryPreliminary Preliminary
Preliminary
PreliminaryPreliminaryPreliminary
PreliminaryPreliminary
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Model predictions for e+e-
Invariant mass1 dependence for increasing z1
z1 dependence for increasing z2
Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009.
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Comparison to theory predictions
Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm )
Z dependence : Rising behavior steeper
However: Theory contains parameters based on HERMES data which already fail to explain COMPASS well
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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 (Ph1ˆ 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
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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
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D* analysis
• Measure signal Ni and yield contributions in Fit of
m(D*-m(K,fast)) distribution to obtain real K, yields
• Repeat Fits for particular particle likelihood selection to obtain Nij
• Ratio of signals gives efficiency
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Further FF measurements
• Additional FF measurements planned:– cross check with completely
different systematics)
– (PHENIX ALL measurement available, higher strange content??)
–Other decaying particles
(KS,f0,…?)
–kt dependent FFs
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analysis, leptons• Similarly calculate
efficiencies from
m(P distribution • Most kinematic
regions well covered• So far: lepton efficiencies
from MC,
in the future: extract efficiencies form J/ decays
• Perform inversion of efficiency matrix, keep stable inverse matrices
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Interference Fragmentation – “0 “ method
• Similar to previous method
• Observe angles 1R+2R
between the event-plane (beam, two-pion-axis) and the two two-pion planes.
• Theoretical guidance by Boer, Jakob, Radici R2R1221111 m,zHm,zHA cos
R2
R1
1hP
2hP
3hP
4hP
2h1h PP
4h3h PP
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First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins data
• HERMES AUT p data
• COMPASS AUT d data
• Belle e+ e-
Collins data• Kretzer FF
First extraction of transversity (up to a sign)
Anselmino et al: hep-ex 0701006
Tensor charges obtained from this fit (from Alexei Prokudin) at Q2= 2.4 GeV2:
0.340 +0.398 -
0.346 +0.392 -
189.0195.0
150.0203.0
0.236
0.569
166.0
403.0
du
du
d
u
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Cuts and Binning• Similar to Collins analysis, full off-
resnanance data(7-55): ~60 fb-1
• HadronB(J) skim• visible energy >7GeV • PID:
– e veto:eid>0.8
– veto:mu_like>0.9&&mu_chi2!=0.
– p veto:kpr<0.2
– : kpi<0.3
– K: kpi>0.6
• Hemisphere cut between pairs• z1 = zhad1+zhad2 and z2 in 5 bins:
[0.2 , 0.3 , 0.4 , 0.55 ,0.75, 1]• m and m in 5 bins:
[0.25 , 0.40 , 0.55 , 0.77 ,1.2, 2]
• m and m in 5 bins:
[0.5 , 0.7 , 0.9 , 1.2 ,1.6, 2]
• m and m in 5 bins:
[0.9 , 1.1 ,1.4, 1.8, 2.2, 3] • For pairs with charge sum=0
first hadron is positive, second negative, angle and plane defined by R=(P1-P2)/2
• Same sign pion pairs ordered according to z
• All 4 hadrons in barrel region:-0.6 < cos <0.9
• Trust axis in central area:abs(thrustz)<0.75
• Thrust > 0.8
• z1,2>0.1
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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”
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Improved systematic errors• Tau contribution (not shown)• Quark axis correction• PID systematics• MC uncertainties• Charged ratios (++ /-- )• higher moments in Fit (not shown)• difference double ratio-subtraction
method
•Beam polarization studies consistent with zero•Correction for charm events
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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:
In Artru Model: favored (ie u) and disfavored (ie u) Collins function naturally of opposite sign
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Examples of fits to azimuthal asymmetries
• Cosine modulations
• clearly visible
• P1 contains information on Collins function
D1 : spin averaged fragmentation function,
H1: Collins fragmentation function
N()/N0
No change in cosine moments when including sine and higher harmonics
2 )
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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)2cos(:
2
2
2
2
2
2
0 FavUnfUnfFav
q
FavUnfUnfFav
q
UnfUnfFavFav
q
UnfUnfFavFav
q
DDDDe
HHHHe
DDDDe
HHHHeFA
2 methods give very small difference in the result
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Asymmetry extraction
• Build normalized yields:
• Fit with:
or
64
,)( 21
N
N N
N RR )( 21
)sin()(2cos
)cos(
21122112
122112
dc
ba
122112 )cos( ba
Amplitude a12 directly measures IFF! (squared)
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Zero tests: MC
• A small asymmetry seen due to acceptance effect• Mostly appearing at boundary of acceptance• Opening cut in CMS of 0.8 (~37 degrees) reduces
acceptance effect to the sub-per-mille level•
65
Ph
),cos(ˆ
nPP
nP
h
h
No opening cutOpening cut>0.7Opening cut >0.8
2 2sin /(1 cos ) 0.5
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Zero tests: Mixed Events
False A
symmetrie
s consis
tent with
zero
(Red/blue points: Thrust axis last or current event)
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• Inject asymmetries in Monte Carlo
• Reconstruction smears thrust axis,
• ~94% of input asymmetry is reconstructed
• (Integrated over thrust axis: 98%)
• Effect is understood, can be reproduced in Toy MC
• Asymmetries corrected
67
SmearingIn azimuthalAngle of thrustAxis in CMS
Black: injectedPurple reconstructed
1 2( )R R
Weighted MC asymmetries
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Cuts and Binning• Similar to Collins analysis, full off-resonance and on-resonance data
(7-55): ~73 fb-1 + 588 fb-1
• Visible energy >7GeV • PID: Purities in Pion/Pion Sample > 90% • Same Hemisphere cut within pair (), opposite hemisphere
between pairs• All 4 hadrons in barrel region: -0.6 < cos () <0.9• Thrust axis in central area: abs(thrustz)<0.75• Thrust > 0.8
• zhad1,had2>0.1
• z1 = zhad1+zhad2 and z2 in 9x9 bins
• m and m in 8x8 bins: [0.25 - 2.0] GeV
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Comparison with Collins FF extraction
• a12 Asymmetries directly measure IFF squared
• IFF asymmetries can be integrated over kt
– No double ratios necessary to cancel gluon radiation effects
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Systematic Errors
• Dominant:– MC asymmetry + its statistical error (up to % level)
• Smaller contributions: – mixed asymmetries: per mille level– higher moments: sub per mille level– axis smearing, – tau contribution – Charm contributions
• Possible Gluon radiation not accounted for
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Model predictions for e+e-
Invariant mass1 dependence for increasing z1
z1 dependence for increasing z2
71
Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009.
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Combined Analysis: Extract Transversity Distributions
Transversity, δq(x)Tensor Charge
Lattice QCD: Tensor Charge
Factorization + Evolution
Theo
rySIDIS
~ 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) x δq(x2) x CFF(z)
pp h+ + h- + X~ G(x1) x δq(x2) x IFF(z)
pp l+ + l- + X~ δq(x1) x δq(x2)
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7373
Measurements of quark transversity
p+p
SIDIS
e++e-
E704, 1991Large forward SSA
STAR, PHENIX, BRAHMS, 2004~2005Inclusive AN
HERMES 2005, COMPASS 2006AUT
BELLE 2006Collins FF
BELLEIFF
RHICIFF asym.
RHICCollins asym.
JParc, RHIC, FAIRDrell-Yan
COMPASSp target
JLab 3He and 12 GeV
Underway Future1991 2005
BELLE kT dep. Pol. & upol FF, pol. Lambda FF
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• What contributes most of the visible mass in the universe?
– Not Higgs: The QCD interaction!
• Proton mass is dominated by it
• Proton momentum is half carried by quarks, half by gluons
• SPIN is fundamental quantity:What role does it play in strong interactions?
Spin crisis: EMC - Quarks contribute only ~30% to nucleon spin
Nucleon spin still not understood
Confinement Large transverse single spin
asymmetries Interesting transverse spin
effects help us understand QCD
Motivation for QCD Spin Physics?Motivation for QCD Spin Physics?
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Spin Decomposition of the ProtonSpin Decomposition of the Proton
v v s
1 1Δu Δd Δq
2 2Σ 1 ???
Naïve quark model – 3 valence quark
CERN, SLAC, DESY, JLAB: 0.30
…and orbital angular momentum…
1
2 q gJ J 1
Σ2
G
q
g
L
L
QCD:..additional contributions from gluons and gluon splitting, sea quarks…
GΣ21
21
ΔG = ?
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Kinematics
Central arms
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vs invariant mass of the pairsin
UTA
Added statistics from 2008 running NEWNo significant asymmetries seen at mid-rapidity.
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Di-Hadron SSA in SIDIS
(both on proton target, sign convention different)
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Definition of Vectors and Angles
1 2
1 2
1 2
p+p c.m.s. = lab frame
, : momenta of protons
, : momenta of hadrons
( ) / 2
: proton spin orientation
A B
h h
C h h
C h h
B
P P
P P
P P P
R P P
S
OOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOO
1hPOOOOOOOOOOOOOO
2hPOOOOOOOOOOOOOO
100 GeVAPOOOOOOOOOOOOOO
100 GeVBPOOOOOOOOOOOOOO
CPOOOOOOOOOOOOOO
BSOOOOOOOOOOOOOO
pp hhX
1 2hadron plane: ,
scattering plane: ,
h h
C B
P P
P P
OOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOO : from scattering plane
to hadron planeR : from polarization vector
to scattering plane S
Bacchetta and Radici, PRD70, 094032 (2004)
2 CROOOOOOOOOOOOOO