INT Workshop on orbital angular momentum,Seattle, February 10
Ralf Seidl (RIKEN)
Transverse quark polarization
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 2
q(x), G(x)
Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton(known from fixed target (SI)DIS experiments)
q(x),G(x)
q(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)
Unpolarized distribution function q(x)
Helicity distribution function q(x)
Transversity distribution function q(x)
Sum of quarks with parallel and antiparallel polarization relative to proton spin(well known from Collider DIS experiments)
Transversity properties
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 3
Helicity flip amplitude Chiral odd Since all interactions conserve
chirality one needs another chiral odd object
Does not couple to gluons different QCD evolution than q(x)
Valence dominated Comparable to Lattice calculations, especially tensor charge
No sumrule, but somehow more intuitive quantity: PDFs evolve into OAM, not other contributions
Positivity bound:
Soffer bound:
xqxδq
xqxqxδq 21
How to access Transversity: another chiral-odd function
Drell Yan: Combine two
Transversity distributions with each other
SIDIS/pp: Combine Transversity
distributions with chiral-odd 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
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 5
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 - finished for charged pion pairs
or IFF X IFF – charged pions about to be published
Transversity
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 6
KEKB: L>2.1x1034cm-2s-1 !!Asymmetric collider8GeV e- + 3.5GeV e+
√s = 10.58GeV ((4S))e+e-(4S)BBContinuum production:
10.52 GeVe+e-qq (u,d,s,c) Integrated Luminosity: >1000
fb-1
>70fb-1 => continuum
Belle detectorKEKB
Main research at Belle:CP violation and determination of
Cabibbo Kobayashi Maskawa (CKM) matrix
/ KL detection 14/15 lyr. RPC+Fe
Central Drift Chamber small cell +He/C2H6
CsI(Tl) 16X0
Aerogel Cherenkov cnt. n=1.015~1.030
Si vtx. det. 3/4 lyr. DSSD
TOF counter
SC solenoid 1.5T
8 GeV e
3.5 GeV e
Belle Detector
Good tracking and particle identification!
(K)~85%,(K)<10%
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 7
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 8
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 9
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
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 10
Collins fragmentation in e+e- : Angles and Cross section cos(1+2) 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)]
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 11
Final Collins resultsFirst direct measurement of the
Collins effect: (PRL96: 232002)
Red points : cos(1 + 2) moment of Unlike sign pion pairs over like sign pion pair ratio : AUL
Green points : cos(1 + 2) moment of Unlike sign pion pairs over any charged pion pair ratio : AUC
Nonzero asymmetries seenFactor 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 12
polarized fragmentation functions from Belle 13
INT OAM,
Feb 10, 2012
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
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
More data available now Cross check using interference fragmentation
functions needed
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 14
Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.191:98-107,2009
Interference Fragmentation – thrust method
e+e- (+-)jet1()jet2XLook in the mass region around -
mass (largest interference expected)
Find pion pairs in opposite hemispheres
Observe angles 1+2 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)]
15polarized fragmentation functions from Belle
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)]
INT OAM, Feb 10, 2012
Asymmetry extraction
Build normalized yields:
Fit with:
or
16
,)( 21
N
N
)sin()(2cos
)cos(
21122112
122112
dc
ba
122112 )cos( ba
Amplitude a12 directly measures ( IFF ) x ( -IFF ) (no double ratios)
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 16
Zero tests: Mixed Events
False
Asy
mm
etrie
s con
siste
nt with
zero
(Red/blue points: Thrust axis last or current event)INT OAM, Feb 10, 2012 17polarized fragmentation functions from Belle
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
INT OAM, Feb 10, 2012 18polarized fragmentation functions from Belle
19
Systematic Errors Dominant:
MC asymmetry + its statistical error (up to % level)
Smaller contributions: PID: per mille level higher moments: sub per mille levelUncertainty on axis smearing correctionmixed asymmetries: per mille levelTau asymmetries
Note: asymmetries contain events from u,d,s and c events
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle
20
Published results: (z1x z2) Binning
Magnitude increasing with zINT OAM, Feb 10, 2012 polarized fragmentation functions from Belle
PRL107:072004(2011)
m1x m2 binning
Magnitude increasing with mass, then leveling offINT OAM, Feb 10, 2012 21polarized fragmentation functions from Belle
(z1x m1) Binning
22
2 d distributions of one hemisphereINT OAM, Feb 10, 2012 polarized fragmentation functions from Belle
(m1x z1) Binning
INT OAM, Feb 10, 2012 23polarized fragmentation functions from Belle
First transversity extraction from HERMES and Belle IFF data
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 24
Early studies indicate little effect of evolution in Collins function, both results comparable
Prelimnary data by Compass and PHENIX not used
Alessandro Bacchetta at RHIC DY workshop May 2011:
Bacchetta, Radici, Courtoy, arXiv:1104.3855
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 25
Unpolarized Fragmentation functions
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
Current knowledge on fragmentation functions – DSS, HKNS,AKK
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 26
DeFlorian, Sassot, Stratmann, Phys.Rev.D75:114010,2007.
Differences between different global fits still large for high-z gluon contributions, kaons and disfavored fragmentation
Hirai, Kumano, Nagai, Sudoh, Phys.Rev.D75:094009,2007
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 27
Martin Leitgab
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 28
Martin Leitgab
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 29
Expected uncertintiesMeasurement will give precision data set for low Q2 and high z:
e+e- -> h+- X data
Projected relative statistical and systematic uncertainties
In the future: include k_t dependence and measure di-hadron FFs needed for transversity extraction from di-hadron correlations 30
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 31
Event Structure for hadron pairs in e+e- annihilation
<Nh+,-> = 6.4
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 .,
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 32
Unpolarized 2-hadron fragmentation
Detect two hadrons simultaneously:e+e-hhX
If two hadrons in opposite hemispheres one obtains sensitivity to favored/ disfavored fragmentation:
Difficulty: contribution from one quark fragmentation qhhX
measure all three: (hh)jet1 X
(h) jet1(h) jet2X
hhX,
( ) requires thrust cut
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)
Favored = u,d,cc.
Unfavored = d,u,cc.
Sample MC (udsc) distributions -
45 fb-1 sampled (~50%
of off resonance data)PID corrected using
Martin’s MatricesSmearing 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): ratio
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 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
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, , K Collins, pK, KK IFF
Measure other interesting QCD-related quantities at Belle: Chiral-odd -fragmentation
function single spin asymmetry
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 35
Belle Fragmentation activity
36
Black: about to startGreen:ongoingGrey: finished
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 37
Backup Slides
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 38
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 39
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]
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 40
Similar to previous methodObserve 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
41
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
Subprocess contributions (MC)
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 42polarized fragmentation functions from Belle
9x9 z1 z2 binning
Zero tests: MC
A small asymmetry seen due to acceptance effectMostly appearing at boundary of acceptanceOpening 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
INT OAM, Feb 10, 2012 43polarized fragmentation functions from Belle
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 -
opposite hemispheresYields very similar Naturally
dominating at higher z
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 45
Sample MC (udsc) distributions -
same hemisphere:Distributions falling
off rapidly Naturally as z1+z2<1
For same hemisphere also interesting:zPair ,mPair distributionCorresponding
resonances’ FF ( , K*, )
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
Measure Collins effect for e+e-±X
According to Artru model sign change expected wrt. pion Collins:sgn a12(±) = - sgn a12(±± )
Instead of double ratios to eliminate acceptance/radiative effects use combinatoric BG
Rho Collins – similar plans for ,
Normally:
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 48
MC (uds) Rho Collins example
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 49
Acceptance effect visible in all three mass ranges
Magnitude similar, but need more statistics to confirm method
Collins amplitudes I
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 50
Large, nonzero asymmetries seen
Transversity and Collins effect nonzero
Large - asymmetries require disfavored Collins function of opposite sign
and HERMES, PRL. 94 (2005) 012002
M. Diefenthaler @ DIS07, hep-ex 0707.0222
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
51 polarized fragmentation functions from Belle
=
INT OAM, Feb 10, 2012
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 52
Martin Leitgab’s Spin 2010 talk
D* Extractionfinal extraction: large acceptance region covered
K+
K-PLab
CosLab
INT OAM, Feb 10, 2012 53polarized fragmentation functions from Belle
Status of FF analysis:PID study finishedSmearing correction
finishedAcceptance
correction + nonQCD contribution removal ongoing
Plan: have results soon
COMPASS, hep-ex/0802.2160
deuteron
Collins amplitudes II
Compatible with zero due to cancellation
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 54
Asymmetries nonzero, consistent with HERMES
SIDIS: Most recent Collins moments
Not completely used in fit, yet
INT OAM, Feb 10, 2012 polarized fragmentation functions from Belle 55
final HERMES data-set
h−
h+
h+
h−
Proton
Deuteron
Compass