precision fragmentation function measurements at belle

Precision fragmentation function measurements at Belle

Freiburg, June 6 2007

R. Seidl (University of Illinois and RBRC)

Outline:•Why QCD and spin physics?•Transversity and the Collins function

•Transversity as thirsd leading twist distribution function•Access to transversity over Collins fragmentation function•Collins function measurements at Belle

•The Belle detector•Improved statistics with on_resonance data

•First global analysis from SIDIS and Belle data

•Interference fragmentation function measurements•unpolarized fragmentation function measurements

R.Seidl: Fragmentation function measurements at Belle 2 Freiburg, June 6th

Why QCD and spin physics?

• QCD as the right theory of quarks and gluons,

• Perturbative part well understood

• Nucleon as simplest bound state of QCD poorly understood (though building block of most matter in universe)

• Significant surprises when including spin:

Spin crisis: Quarks contribute only ~30% to nucleon spin

Large transverse single spin asymmetries which are forbidden by perturbative QCD observed

“You think you understand something? Now add spin ...” – R. Jaffe


The (spin) structure of the Nucleon

Longitudinal Spin Sum Rule:

Transverse Spin (BLT) Sum Rule?

zz LG2

1S

2

1

xx L2

1S

2

1

Double Spin Asymmetries (pp,SIDIS)

W-production (pp)

Exclusive processes (DVCS,etc)

Chiral-odd Fragmentation functions (Collins,IFF Sivers

effect??

Color Glass condensate ??


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)

Sum of quarks with parallel and antiparallel polarization relative to proton spin(well known from Collider DIS experiments)

q(x)

Quark distributions

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)


Cross sections in (semi)inclusive pp and DIS, factorization

fq(x1) fq(x2) Dh(z) TdP

d

fq(x1) Dh(z) 2dQ

d•Hard scales PT and Q2

•Convolution integrals over all involved momenta

•Factorization of involved distribution and fragmentation functions

•(kT)-dependent distribution and fragmentation functions

k

k’

Q

2P

1P

1P

PS

lS

1PS

2PS


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

Positivity bound:

Soffer bound:

xqxδq

xqxqxδq 21


Finding another chiral odd object in SIDIS Collins fragmentation function

Cross section factorizes: epehX = qqpq(x)QED Dqh(z)

Transverse momentum dependent Distribution functionsTransverse momentum dependent Fragmentation functions

Both Sivers and Collins Effect create azimuthal asymmetries


Azimuthal asymmetries in SIDIS

•Sivers and Collins effect are not distiguishable with longitudinally polarized target

•Higher Twist effects are kinematically favored in longitudinal case

•With transversely polarized target a 2nd angle allows to distinguish effects

U: unpolarized beamT: transversely polarized target


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


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


SIDIS experiments (HERMES and COMPASS, eRHIC) measure q(x) together with either Collins Fragmentation function or Interference Fragmentation function

Towards a global transversity analysis

zH1

RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x)

There are always 2 unknown functions involved which cannot be measured independently

Spin dependent Fragmentation function analysis in e+e- Annihilation yields

information on the Collins and the Interference Fragmentation function !

Universality appears to be proven in LO by Collins and Metz:

[PRL93:(2004)252001 ]+most recent work from

Amsterdam Group


KEKB: L>1.6x1034cm-2s-1 !!

• Asymmetric collider• 8GeV e- + 3.5GeV e+

• s = 10.58GeV ((4S))• e+e-S• Off-resonance: 10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: >700 fb-1

• >60fb-1 => off-resonance

Belle detectorKEKB


Good tracking and particle identification!


e-

e+ Jet axis: Thrust

<Nh+,-> = 6.4

GeV 5210ss

E2z h .,

Near-side Hemisphere: hi , i=1,Nn with zi

Far-side: hj , j=1,Nf with zj

Event Structure at Belle

22

21112

2

2

21

21

14

1

2

1

3

cos

,

cm

aaa

yyyA

zDzDeyAQdzdzd

Xhheed

e+e- CMS frame:

Spin averaged cross section:


Collins fragmentation in e+e- : Angles and Cross section cos() 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)]


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]


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 (Ph1 ˆ 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


Examples of fits to azimuthal asymmetries

D1 : spin averaged fragmentation function,

H1: Collins fragmentation function

N()/N0

No change in cosine moments when including sine and higher harmonics

Cosine modulationsclearly visible

2 )


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:

2

2

2

2

2

2

FavUnfUnfFav

q

FavUnfUnfFav

q

UnfUnfFavFav

q

UnfUnfFavFav

q

DDDDe

HHHHe

DDDDe

HHHHeFA

2 methods give very small difference in the result


Testing the double ratios with MC• Asymmetries do cancel out for MC• Double ratios of

compatible with zero• Mixed event pion pairs also show

zero result• Asymmetry reconstruction works

well for MC (weak decays)• Single hemisphere analysis yields

zeroDouble ratios are safe to use

•uds MC (UL/L double ratios)

•uds MC (UL/C double ratios) •Data ()


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


What about the data under the resonance?

• More than 540 fb-1 of on_resonance data

• (4S) is just small resonance

• More than 75% of hadronic cross sectionfrom open quark-antiquark production

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)


Why is it possible to include on_resonance data?Different Thrust distributions

ii

ii

p

npthrust

ˆ

• e+ e- q q (u d s) MC

• (4S) B+ B- MC

• (4S) B0 B0 MC

• Largest systematic errors reduce with more statistics • Charm-tagged Data sample also increases with statistics


Improved systematic errors (UC)• Tau contribution• PID error• MC double ratios• Charged ratios (• higher moments in Fit• difference double ratio-

subtraction method

•reweighted MC-asymmetries: cos asymmetries underestimated rescalied with 1.21•Correlation studies: statististical error rescaled by1.02 (UL) and 0.55 (UC) – after rigorous errorcalculation correct•Beampolarization studies consistent with zero•Correction ofcharm events

A0 (cos(2)) moments

A12 (cos()) moments


Final charm corrected results for e+ e- X (29fb-1 of continuum

data)• Significant non-zero

asymmetries • Rising behavior vs. z

• cos(+) double ratios only marginally larger

• UC asymmetries about 40-50% of UL asymmetries

• First direct measurements of the Collins function

Integrated results:

A0(UL) (3.06 ± 0.57 ± 0.55)%

A12(UL) (4.26 ± 0.68 ± 0.68)%

A0(UC) (1.270 ± 0.489 ± 0.350)%

A12(UC) (1.752 ± 0.592 ± 0.413)%

Final results

Preliminary results


Charm corrected results for e+ e- X (547 fb-1)

• Significance largely increased

• Behavior unchanged• Reduced systematic

errors due to statistics• Precise measurements of

the Collins function

Integrated results:

A0(UL) (2.67 ± 0.10 ± 0.26)%

A12(UL) (3.55 ± 0.08 ± 0.15)%

A0(UC) (1.11 ± 0.11 ± 0.22)%

A12(UC) (1.46 ± 0.09 ± 0.13)%

PRELIMINARY


Global Analysis - SIDIS measurements I: HERMES (proton)

• Nonzero Asymmetries Collins function and

Transversity nonzero• Same magnitude, opposite

sign for and Asymmetries

Hint for a large and negative disfavored Collins function

PRL 94, 012002 (2005) and hep-ex/0612010

Taken at QSM value of r = -0.30 of Schweitzer and Wakamatsu

H


Global Analysis - SIDIS measurements II: COMPASS (deuteron)

• Smaller asymmetries than in proton case

Hint of cancellation of transversity in isoscalar target

PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007

-AC

oll

• First fits to HERMES and COMPASS data using assumptions on Transversity show results consistent with each other

• Kaon asymmetries shown last year (both experiments)


Global Analysis- Belle Collins function: asymmetries

for double ratios of unlikesignlikesign for 29 fb-1

• Direct measurement of the Collins effect

• Collins function large• Consistent with large,

negative disfavored Collins function

RS et al., PRL 96, 232002 (2006)

+ inclusion of (4S) data: >500 fb-1 (not yet included in global fit by Anselmino et al: hep-ex 0701006)

PRELIMINARY


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


• e+e- (+-)jet1(-+)jet2X• Stay in the mass region around -mass• Find pion pairs in opposite

hemispheres• Observe angles 12

between the event-plane (beam, jet-axis) and the two two-pion planes.

• Transverse momentum is integrated(universal function, evolution easy directly applicable to semi-inclusive DIS and pp)

• Theoretical guidance by papers of Boer,Jakob,Radici and Artru,Collins

• Early work by Collins, Heppelman, Ladinski

Interference fragmentation function

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)]


Different model predictions for IFF

•Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of -phaseshift analysissign change at mass

-originally no predictions on actual magnitudes

-Tang included some for RHIC-Spin

• Radici et al. [Phys. Rev. D65 (2002)] : Spectator model in the s-p channel no sign change observed (updated model has Breit-Wigner like asymmetry)

PRELIMINARY

f1, h1 from spectator model

f1, h1=g1 from GRV98 & GRSV96


Unpolarized FF as important input for all precise QCD measurements

MC simulation, ~1.4 fb-1

2.

• No low-Q2 data available important for evolution

• No high-z data available Huge amount of B-factory

data can help• Favored/Disfavored

disentangling by detecting hadron pairs (as in Collins analysis)?


Future measurements I: EIC, transverse spin

• Transversity at higher x already measured by HERMES, COMPASS and JLAB12,

• first DY transversity from JPARC or FAIR?

Lower x will be interesting for tensor charge


Summary and outlook

• A first successful global analysis of transversitydata using the HERMES,COMPASS and published Belle data

• Belle Collins data largely improved from 29 547 fb -1

• Significant, nonzero asymmetries Collins function is large

• Long Collins paper is nearly finished

• Continue to measure precise spin dependent fragmentation functions at Belle– kT dependence of Collins function– Favored/disfavored disentanglement– Initerference Fragmentation function

measurements (started) • Measure precise unpolarized fragmentation

functions of many final states Important input for general QCD physics and

helicity structure measurements• Measure other interesting QCD-related

quantities at Belle:– Chiral-odd -fragmentation function– Event shapes– R-ratio with ISR


Backup Slides

Belle


• Similar to previous method• Observe 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


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”

R.Seidl:The W physics program at PHENIX 39 PVSA, BNL April 27th

Sivers interpretation

Taken from H. Tanaka in Trento’04

•Attractive rescattering of hit quark by gluon creates transverse momentum•M.Burkardt [hep-ph0309269] – impact parameter formalism•Orbital angular momentum at finite impact parameter•observed and true x differ•Observable left/right asymmetry

>

precision fragmentation function measurements at belle

Documents

spin physics

spin sq

spin crisis

jaffethe spin structure

collins functiontransversity

double spin asymmetries

transverse spin blt

lsivers effect