Polarized fragmentation functions from Belle
description
Transcript of Polarized fragmentation functions from Belle
8th Circum Pan Pacific Symposium on High Energy Spin PhysicsCairns, June 21, 2011
Ralf Seidl (RIKEN)
for the Belle Collaboration
Transverse quark polarization
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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
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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
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
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Towards a global transversity analysis: Chiral –odd Fragmentation functions
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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
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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 detectorKEKBMain 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%
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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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Collins fragmentation in e+e- : Angles and Cross section cos(1+2) method
1hP
2hP
2cm
21
111
121T
221
21
41y1yyB
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)]
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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)
Transverse single spin asymmetries in SIDIS
Measure azimuthal asymmetries for (at least) two angular modulations simultaneously
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U: unpolarized beamT: transversely polarized target
Collins amplitudes I
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Large, nonzero asymmetries seen
Transversity and Collins effect nonzero
Large - asymmetries require disfavored Collins function of opposite sign
and HERMES, PRL. 94 (2005) 012002M. Diefenthaler @ DIS07, hep-ex 0707.0222
COMPASS, hep-ex/0802.2160
deuteron
Collins amplitudes II
Compatible with zero due to cancellation
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Asymmetries nonzero, consistent with HERMES
SIDIS: Most recent Collins moments
Not completely used in fit, yet
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final HERMES data-set
h−
h+
h+
h−
Proton
Deuteron
Compass
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 Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 15
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)]
16polarized 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)]
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Asymmetry extractionBuild normalized
yields:
Fit with:
or
17
,)( 21
NN
)sin()(2cos)cos(
21122112
122112
dcba
122112 )cos( ba
Amplitude a12 directly measures ( IFF ) x ( -IFF ) (no double ratios)
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Zero tests: Mixed Events
False
Asymmetr
ies co
nsisten
t with
zero
(Red/blue points: Thrust axis last or current event)Pac Spin, June 21, 2011 18polarized 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
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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
arXiv:1104.2425Submitted to PRL
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Results incl. sys. errors: (z1x z2) Binning
Magnitude increasing with zPac Spin, June 21, 2011 polarized fragmentation functions from Belle
m1x m2 binning
Magnitude increasing with mass, then leveling offPac Spin, June 21, 2011 22polarized fragmentation functions from Belle
(z1x m1) Binning
232 d distributions of one hemisphere
Pac Spin, June 21, 2011 polarized fragmentation functions from Belle
(m1x z1) Binning
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First transversity extraction from HERMES and Belle IFF data
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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
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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
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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
Current knowledge on fragmentation functions – DSS, HKNS,AKK
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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
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
29 polarized fragmentation functions from Belle
=
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Martin Leitgab’s Spin 2010 talk
D* Extractionfinal extraction: large acceptance region covered
K+
K-PLab
CosLab
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Status of FF analysis:PID study finishedSmearing correction
finishedAcceptance
correction + nonQCD contribution removal ongoing
Plan: have results soon
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Event Structure for hadron pairs in e+e- annihilation
<Nh+,-> = 6.4
e+e- CMS frame:
e-
e+
22
21112
2
2
21
21
141
21
3
cos
,
cm
aaa
yyyA
zDzDeyAQdzdzd
Xhheed
Spin averaged cross section:
Jet axis: Thrust
GeV 5210ss
E2z h .,
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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 Matrices
Smearing not yet corrected (but small)
Acceptance not yet corrected
Statistic reasonable out to high z
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Sample MC (udsc): ratio
Yield ratios will be almost directly sensitive to disfavored/favored FF ratio
Acceptance effects cancel
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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
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Belle Fragmentation activity
37
Black: about to startGreen: ongoingGrey: finished
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Backup Slides
polarized fragmentation functions from Belle 39
Pac Spin, June 21,
2011
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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Collins fragmentation in e+e- : Angles and Cross section cos(2) method
1hP
2hP
2
21
11TTTT02
21
21
sin41
pkphkh2I2cosq
cm
T
B
MMHHB
ddzdzdXhheedσ
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]
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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
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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)
Pac Spin, June 21, 2011 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)
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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
44
Ph
),cos(ˆ
nPPnP
h
h
No opening cutOpening cut>0.7Opening cut >0.8
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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
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Sample MC (udsc) distributions -
opposite hemispheresYields very similar Naturally
dominating at higher z
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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
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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
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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:
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MC (uds) Rho Collins example
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Acceptance effect visible in all three mass ranges
Magnitude similar, but need more statistics to confirm method