Polarized fragmentation functions from ｅ + e -

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


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


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 - finished for charged pion pairs

or IFF X IFF – charged pions about to be published

Transversity


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%




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


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)]


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)


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


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)


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


First transversity extraction from HERMES and Belle IFF data


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


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


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


Martin Leitgab


Martin Leitgab


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


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 .,


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


Sample MC (udsc): ratio

Yield ratios will be almost directly sensitive to disfavored/favored FF ratio

Acceptance effects cancel


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


Belle Fragmentation activity

36

Black: about to startGreen:ongoingGrey: finished



Backup Slides


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


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]


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)


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)


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


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



opposite hemispheresYields very similar Naturally

dominating at higher z



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


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


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:


MC (uds) Rho Collins example


Acceptance effect visible in all three mass ranges

Magnitude similar, but need more statistics to confirm method

Collins amplitudes I


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


Martin Leitgab’s Spin 2010 talk

D* Extractionfinal extraction: large acceptance region covered

K+

K-PLab

CosLab


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


Asymmetries nonzero, consistent with HERMES

SIDIS: Most recent Collins moments

Not completely used in fit, yet


final HERMES data-set

h−

h+

h+

h−

Proton

Deuteron

Compass

Documents

Polarized fragmentation functions from ｅ + e -