Precision fragmentation function measurements at Belle Freiburg, June 6 2007 R. Seidl (University of...
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Transcript of Precision fragmentation function measurements at Belle Freiburg, June 6 2007 R. Seidl (University of...
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
R.Seidl: Fragmentation function measurements at Belle 3 Freiburg, June 6th
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 ??
R.Seidl: Fragmentation function measurements at Belle 4 Freiburg, June 6th
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)
R.Seidl: Fragmentation function measurements at Belle 5 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 6 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 7 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 8 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 9 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 10 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 11 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 12 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 13 Freiburg, June 6th
Good tracking and particle identification!
R.Seidl: Fragmentation function measurements at Belle 14 Freiburg, June 6th
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:
R.Seidl: Fragmentation function measurements at Belle 15 Freiburg, June 6th
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)]
R.Seidl: Fragmentation function measurements at Belle 16 Freiburg, June 6th
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]
R.Seidl: Fragmentation function measurements at Belle 17 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 18 Freiburg, June 6th
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 )
R.Seidl: Fragmentation function measurements at Belle 19 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 20 Freiburg, June 6th
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 ()
R.Seidl: Fragmentation function measurements at Belle 21 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 22 Freiburg, June 6th
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)
R.Seidl: Fragmentation function measurements at Belle 23 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 24 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 25 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 26 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 27 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 28 Freiburg, June 6th
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)
R.Seidl: Fragmentation function measurements at Belle 29 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 30 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 31 Freiburg, June 6th
• 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)]
R.Seidl: Fragmentation function measurements at Belle 32 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 33 Freiburg, June 6th
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)?
R.Seidl: Fragmentation function measurements at Belle 34 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 35 Freiburg, June 6th
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
R.Seidl: Fragmentation function measurements at Belle 37 Freiburg, June 6th
• 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
R.Seidl: Fragmentation function measurements at Belle 38 Freiburg, June 6th
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
>