INT Workshop on orbital angular momentum,
Seattle, February 10
Ralf Seidl (RIKEN)
Transverse quark polarization
q(x),G(x)
Unpolarized distribution function q(x)
Sum of quarks with parallel and antiparallel
polarization relative to proton spin
(well known from Collider DIS
experiments)
Difference of quarks with parallel and
antiparallel polarization relative to
longitudinally polarized proton
(known from fixed target (SI)DIS
experiments)
Dq(x), DG(x)
Helicity distribution function Dq(x)
Difference of quarks with parallel and
antiparallel polarization relative to
transversely polarized proton
(first results from HERMES and
COMPASS – with the help of Belle)
dq(x)
Transversity distribution function dq(x)
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
2
Transversity properties
 Helicity flip amplitude
 Chiral odd
 Since all interactions conserve
chirality one needs another chiral
odd object
 Does not couple to gluons
adifferent QCD evolution than
Dq(x)
 Valence dominateda
Comparable to Lattice
calculations, especially tensor
charge
Positivity bound:
δqx   qx 
 No sumrule, but somehow
more intuitive quantity: PDFs
evolve into OAM, not other
contributions
INT OAM, Feb 10, 2012
Soffer bound:
δqx   12 qx   Dqx 
polarized fragmentation functions from Belle
3
How to access Transversity: another chiral-odd
function
Drell Yan:
 Combine two Transversity
distributions with each
other
SIDIS/pp:
 Combine Transversity
distributions with chiralodd fragmentation function
(FF)
 Total process is chiral-even:
OK
 Possible Partners:
 Collins FF
 Interference FF
 Transverse L FF
 Most require single spin
asymmetries in the
fragmentation
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
4
Towards a global transversity analysis:
Chiral –odd Fragmentation functions
RHIC and SIDIS experiments measure:
Transversity dq(x) X
Collins Fragmentation function H 1  z 
2 Unknown
Functions measured
together
or Interference Fragmentation function (IFF)
•Universality
understood
•Evolution ?
Transversity
Belle measures:
Collins X Collins - finished for charged pion
pairs
or IFF X IFF – charged pions about to be
published
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
5
KEKB:





34
-2
-1
L>2.1x10 cm s
Asymmetric collider
Main
8GeV e- + 3.5GeV e+
√s = 10.58GeV (U(4S))
e+e-U(4S)BB
Continuum production:
10.52 GeV
 e+e-qq (u,d,s,c)
 Integrated Luminosity: >1000 fb-1
 >70fb-1 => continuum
INT OAM, Feb 10, 2012
!!
research at Belle:
Belle detector
KEKB
CP violation and
determination of Cabibbo
Kobayashi Maskawa
(CKM) matrix
polarized fragmentation functions from Belle
6
Belle Detector
Aerogel Cherenkov cnt.
SC solenoid
n=1.015~1.030
1.5T
3.5 GeV e
CsI(Tl)
16X0
TOF counter
8 GeV e-
Central Drift Chamber
small cell +He/C2H6
Good tracking and
particle identification!
e(K)~85%,
e(pK)<10%
Si
INT OAM, Feb 10, 2012
vtx. det.
3/4 lyr. DSSD
polarized fragmentation functions from Belle
m / KL detection
14/15 lyr. RPC+Fe
7
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
8
Fragmentation functions in
e+e- annihilation
2E
z
e-
h
s
,
s  10.52 GeV
 Process:
h
e+
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
e+ e-hX
 At leading order
sum of unpolarized
fragmentation
functions from
quark and antiquark side
9
Collins fragmentation in e+e- :
Angles and Cross section cos(f1+f2) method
2Eh
z
,
s
e+e- CMS frame:
j2-p
e-
s  10.52 GeV


Ph 2

Ph1
j1
j1
j2
[D.Boer: PhD thesis(1998)]
e+
2-hadron inclusive transverse momentum dependent cross section:
dσ e e -  h1h 2 X 
  By cos j1  j 2 H11 z1 H11 z 2 
2
ddz1dz 2d qT
cm
By   y1 - y  
INT OAM, Feb 10, 2012
1
sin 2 
4
polarized fragmentation functions from Belle
Net (anti-)alignment of
transverse quark spins
10
Final Collins results
 First direct measurement of the




Collins effect:
(PRL96: 232002)
Red points : cos(f1 + f2) moment
of Unlike sign pion pairs over like
sign pion pair ratio : AUL
Green points : cos(f1 + f2)
moment of Unlike sign pion pairs
over any charged pion pair ratio :
AUC
Nonzero asymmetries seen
Factor 19 increase in statistics in
second, long paper: 547 fb-1 data
set (PRD78:032011)
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
11
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
12
The Collins effect in the Artru fragmentation model
A simple model to illustrate that
spin-orbital angular momentum
coupling can lead to left right
asymmetries in spin-dependent
fragmentation:
π+ picks up L=1 to
compensate for the
pair S=1 and is emitted
to the right.
String breaks and
a dd-pair with spin
-1 is inserted.
In Artru Model: favored (ie up) and disfavored (ie up-) Collins
function naturally of opposite sign
polarized fragmentation
INT OAM,
functions from Belle
13
Feb 10, 2012
First global analysis from Collins
Hermes, Compass d and Belle data
 First results available, still open questions from
Phys.Rev.D75:054032,2007,
update in Nucl.Phys.Proc.Suppl.1
91:98-107,2009
evolution of Collins FF and transverse momentum
dependence
 More data available now
 Cross check using interference fragmentation functions
needed
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
14
Interference Fragmentation –
thrust method
 e+e- (p+p-)jet1(pp-)jet2X
 Look in the mass region around r




mass (largest interference expected)
Find pion pairs in opposite
hemispheres
Observe angles j1+j2 between the
event-plane (beam, jet-axis) and the
two two-pion planes.
Transverse momentum is integrated
(universal function, evolution
known 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)]
j2-p

Ph1

Ph 2
p-j1
Model predictions by:
•Jaffe et al. [PRL 80,(1998)]
•Radici et al. [PRD 65,(2002)]
A  H1 z1, m1 H1 z 2 , m2 cos j1  j2 
INT OAM, Feb 10, 2012


Ph1  Ph 2
polarized fragmentation functions from Belle
15
Asymmetry extraction
 Build normalized yields:
N (f1  f2 )
,
N
 Fit with:
a12 cos(f1  f2 ) b12
or
a12 cos(f1  f2 ) b12 
c12 cos 2(f1  f2 ) d12 sin( f1  f2 )
Amplitude a12 directly
measures ( IFF ) x ( -IFF )
(no double ratios)
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
16 16
Zero tests: Mixed Events
polarized fragmentation functions from Belle
(Red/blue points: Thrust
axis last or current event)
INT OAM, Feb 10, 2012
17
Weighted MC asymmetries
 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
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
Smearing
In azimuthal
Angle of
thrust
Axis in CMS
Black: injected
Purple
reconstructed
18
Systematic Errors
 Dominant:
 MC asymmetry + its statistical error (up to % level)
 Smaller contributions:
 PID: per mille level
 higher moments: sub per mille level
 Uncertainty on axis smearing correction
 mixed asymmetries: per mille level
 Tau asymmetries
 Note: asymmetries contain events from u,d,s and c
events
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
19
Published results: (z1x z2) Binning
PRL107:072004(2011)
Magnitude increasing with z
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
20
m1x m2 binning
Magnitude increasing with mass, then leveling off
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
21
(z1x m1) Binning
2 d distributions of one hemisphere
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
22
(m1x z1) Binning
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
23
First transversity extraction from
HERMES and Belle IFF data
Alessandro Bacchetta at RHIC DY workshop May 2011:
 Early studies
indicate little
effect of
evolution in
Collins
function, both
results
comparable
 Prelimnary
data by
Compass and
PHENIX not
used
Bacchetta, Radici, Courtoy, arXiv:1104.3855
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
24
Unpolarized Fragmentation
functions
2E
z
e-
h
s
,
s  10.52 GeV
 Process:
h
e+
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
e+ e-hX
 At leading order
sum of unpolarized
fragmentation
functions from
quark and antiquark side
25
Current knowledge on fragmentation
functions – DSS, HKNS,AKK
DeFlorian, Sassot, Stratmann,
Phys.Rev.D75:114010,2007.
Differences between different global fits
still large for high-z gluon contributions,
kaons and disfavored fragmentation
INT OAM, Feb 10, 2012
Hirai, Kumano,
Nagai, Sudoh,
Phys.Rev.D75:
094009,2007
polarized fragmentation functions from Belle
26
Martin Leitgab
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
27
Martin Leitgab
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
28
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
29
Expected uncertinties
 Measurement will give precision data set for low Q2 and high z:
Projected relative
statistical and systematic
uncertainties
e+e- -> h+- X data
In the future: include k_t dependence and measure di-hadron FFs
needed for transversity extraction from di-hadron correlations
30
Event Structure for hadron pairs in
e+e- annihilation
e+e- CMS frame:
2Eh
z
,
s
e-
s  10.52 GeV
<Nh+,-> = 6.4

e+
Spin averaged cross section:
d e  e -  h1h2 X  3 2
 2 A y  ea2 D1 z1 D1 z2 
ddz1dz2
Q
a ,a
Jet axis: Thrust
 cm  1
1
A y    - y  y 2   1  cos 2 
4
2

INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
31
Unpolarized 2-hadron
fragmentation Favored
= up,dp-,cc.
Unfavored
= dp,up-,cc.
 Detect two hadrons
simultaneously:
e+e-hhX
 If two hadrons in opposite
hemispheres one obtains
sensitivity to favored/
disfavored fragmentation:
 Unlike-sign pion pairs (U):

(favored x favored + unfavored x unfavored)
 Like-sign pion pairs (L):
(favored x unfavored + unfavored x favored)
 any charge hadron pairs (C):
(favored + unfavored) x (favored + unfavored)
INT OAM, Feb 10, 2012
 Difficulty: contribution
from one quark
fragmentation qhhX
measure all three:
 (hh)jet1 X
 (h) jet1(h) jet2X
 hhX,
( ) requires
thrust cut
polarized fragmentation functions from Belle
32
Sample MC (udsc) distributions
- pp
 45 fb-1 sampled (~50%
of off resonance data)
 PID corrected using
Martin’s Matrices
 Smearing not yet
corrected (but small)
 Acceptance not yet
corrected
Statistic reasonable
out to high z
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
33
Sample MC (udsc): pp/ppratio
 Yield ratios will be
almost directly
sensitive to
disfavored/favored FF
ratio
 Acceptance effects
cancel
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
34
Summary and outlook
 First direct measurement of the
interference fragmentation function
 Large asymmetries seen, rising with z
and invariant mass
 No sign change at r mass
 No double ratios make interpretation
simple
 Submitted to PRL
 Significant, nonzero Collins
asymmetries, Data used already in
Global analysis
 Measure precise unpolarized
fragmentation functions of many
final states
 Important input for general QCD
physics and helicity structure
measurements
 Analysis progressing:
PID studies finished
• smearing correction finished
• Acceptance correction ongoing
•
INT OAM, Feb 10, 2012
 New di-hadron fragmentation
function analysis started
•
•
Information of favored/disfavored
FF
Vector meson FFs
 VM Collins analysis started

Artru Model test
 Continue to measure precise spin
dependent fragmentation functions
at Belle



kT dependence of Collins function,
p0 ,h, K Collins,
pK, KK IFF
 Measure other interesting QCD-
related quantities at Belle:


Chiral-odd L-fragmentation function
L single spin asymmetry
polarized fragmentation functions from Belle
35
Belle Fragmentation activity
Unpol FFs
e+e-hX:
e+e-(hh)X,
(h)(h)X,hhX:
RIKEN/RBRC Illinois
Indiana
Neutral hadrons:
(p0 ,h0)
John Koster
Charged dihadrons: Ralf
Seidl
p0 ,h0:
Hairong Li
Unpol kT
dependence:
Collins FFs
e+e-(h)(h)X:
kT dependence:
Charged hadrons
(p,K,P):
Martin Leitgab
Martin Leitgab
pp0 : John Koster
pr0: Ralf Seidl
pp: Ralf Seidl
pp0 : John Koster
pK,KK: Francesca
Giordano
Francesca
Giordano
Bilbao
Titech
Black: about
to start
Green:ongoing
Grey: finished
Charlotte Hulse
pr±: ?
Charlotte Hulse
Interference FF: Charged pp : Ralf
e+e-(hh)(hh)X Seidl
Charged pp:
Anselm Vossen
pp0 : Anselm
Vossen
Local P :
L(polFF,SSA) :
Jet-jet asy:
Anselm Vossen
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
Charged pK,
KK:
Nori-aki
Kobayashi
36
Backup Slides
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
37
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
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
38
Collins fragmentation in e+e- :
Angles and Cross section cos(2f0) method
e+e- CMS frame:
•Independent of thrust-axis

Ph 2
2
e-
•Convolution integral I
over transverse momenta
involved

Ph1
j0
[Boer,Jakob,Mulders:
NPB504(1997)345]
e+
2-hadron inclusive transverse momentum dependent cross section:





dσ e  e -  h1h2 X
H1 H1 
  B  cos2j0  I  2ĥ  k T ĥ  p T - k T  p T

2
ddz1dz2 d qT
M
M
1
2 

1
B   sin 2 
4
cm
INT OAM, Feb 10, 2012
Net (anti-)alignment of
transverse quark spins
polarized fragmentation functions from Belle
39
Interference Fragmentation –
“ f0 “ method
 Similar to previous method
 Observe angles j1Rj2R
between the event-plane (beam, twopion-axis) and the two two-pion
planes.
 Theoretical guidance by
Boer,Jakob,Radici
jR2



Ph 3
Ph 3  Ph 4

Ph 4

Ph 2

Ph1 

Ph1  Ph 2
p-jR1
A  H1 z1, m1 H1 z 2 , m2 cos j1R  j2 R 
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
40
Subprocess contributions (MC)
8x8 m1 m2 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)
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
41
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)
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
42
Zero tests: MC
No opening cut
Opening cut>0.7
Opening cut >0.8
 A small asymmetry seen due to acceptance effect
Ph
 Mostly appearing at boundary of acceptance
 Opening cut in CMS of 0.8 (~37 degrees) reduces
acceptance effect to the sub-per-mille level
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
Ph  nˆ
 cos( P, n)
Ph
43
43
Heavy flavor fragmentation
Rolf Seuster:
Phys.Rev.D73:032002
,2006, 103 fb-1
 Charmed hadron
fragmentation much
harder than light
hadron
fragmentation
 heavy quark more
likely to stay in heavy
hadron
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
44
Sample MC (udsc) distributions
- pp
 opposite hemispheres
 Yields very similar
Naturally dominating
at higher z
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
45
Sample MC (udsc) distributions
- pp
 same hemisphere:
 Distributions falling
off rapidly
 Naturally as z1+z2<1
 For same hemisphere
also interesting:
 zPair ,mPair distribution
 Corresponding
resonances’ FF (r ,
K*, F)
 Also unpol
Baseline for IFF
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
46
Higher statistics available at
high z
 B decays almost at rest
 no hadrons above 0.5
 Instead of about 90 pb-1
almost 1000 fb-1 available
 Useful at high z, where
statistics is low
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
47
Rho Collins – similar plans for p0,h
 Measure Collins effect for
e+e-p±r0 X
 According to Artru model
sign change expected wrt.
pion Collins:
sgn a12(p±r0) = - sgn
a12(p±p± )
 Instead of double ratios to
eliminate
acceptance/radiative
effects use combinatoric
BG
INT OAM, Feb 10, 2012
 Normally:
polarized fragmentation functions from Belle
48
MC (uds) Rho Collins example
 Acceptance effect
visible in all three
mass ranges
 Magnitude similar, but
need more statistics to
confirm method
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
49
Collins amplitudes I
 Large, nonzero
asymmetries seen
 Transversity and Collins
effect nonzero
 Large p- asymmetries
require disfavored
Collins function of
opposite sign
M. Diefenthaler @ DIS07, hep-ex 0707.0222
and HERMES, PRL. 94 (2005) 012002
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
50
Systematic studies: Particle
identification
 Particle identification:
create PID efficiency
matrix for K,p,p,e,m
 PID responses from MC
not reliable, use well
identified decays from
data:
 Use D*pslow
D0p
slowpfastK
51 OAM, Feb 10, 2012
INT
p
Reconstructed
particles
Unfolding
REAL Particles
for K,p
identification
 Use L pp for p,p
identification
 J/y m+ m-, e+ e- for
leptons
(if needed also U(1S))

=
p
K
p
m
e
polarized fragmentation functions from Belle
K
p
m
e
Martin Leitgab’s Spin 2010 talk
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
52
D* Extraction
final extraction: large acceptance region covered
CosqLab
Status of FF analysis:
PLab
 PID study finished
 Smearing correction
finished
 Acceptance correction +
nonQCD contribution
removal ongoing
 Plan: have results soon
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
K
K+
53
Collins amplitudes II
COMPASS, hep-ex/0802.2160
deuteron
 Asymmetries nonzero,
 Compatible with zero
consistent with HERMES
due to cancellation
polarized fragmentation functions from Belle
INT OAM, Feb 10, 2012
54
SIDIS: Most recent Collins moments
final HERMES data-set
Compass
Proton
h−
h+
−
Deuteron h
h+
 Not completely used in fit, yet
INT OAM, Feb 10, 2012
polarized fragmentation functions from Belle
55