fragmentation functions at belle
DESCRIPTION
Fragmentation Functions at Belle. Anselm Vossen (University of Illinois) Matthias Grosse Perdekamp (University of Illinois) Martin Leitgab (University of Illinois) Akio Ogawa (BNL/RBRC) Ralf Seidl (RBRC) Kieran Boyle (RBRC) for the Belle collaboration. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/1.jpg)
Fragmentation Functions at Belle
Anselm Vossen (University of Illinois)Matthias Grosse Perdekamp
(University of Illinois)Martin Leitgab (University of Illinois)
Akio Ogawa (BNL/RBRC) Ralf Seidl (RBRC)
Kieran Boyle (RBRC)
for the Belle collaboration
SPIN2008, University of Virginia
![Page 2: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/2.jpg)
Outline
• Motivation– Collins FF for transversity extraction in global QCD Analysis
of single transverse spin asymmetries in pp and SIDIS• Measuring Fragmentation Functions at Belle
– Experimental techniques– Collins FF results
• Interference Fragmentation Functions– Planned measurements of IFF at Belle– Recent results from PHENIX
• Summary & Outlook
![Page 3: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/3.jpg)
Motivation: Transversity Quark Distributions δq(x) fromTransverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering
Collins- and IFF- asymmetriesin semi-inclusive deep inelastic scattering (SIDIS) and pp measure
~ δq(x) x CFF(z) combined analysis with CFF from e+e- annihilation
Example: COMPASS results for Collins Asymmetries on proton target (see talk by H. Wollny)
![Page 4: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/4.jpg)
Collins Effect in Quark FragmentationJ.C. Collins, Nucl. Phys. B396, 161(1993)
q
momentum hadron relative : 2
zmomentum hadron e transvers:
momentum hadron :
spinquark : momentumquark :
h
sE
EEpp
sk
h
qh
h
h
q
qs
k
hph ,
Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:
hp
sin
qh spk
![Page 5: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/5.jpg)
5
General Form of Fragmentation Functions
h
qhh
hqhqh
hq zM
spkpzHzDpzD
ˆ ),()(),( 2,
1,
1
Number density for finding hadron h from a transversely polarized quark, q:
unpolarized FF Collins FF
![Page 6: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/6.jpg)
o Quark spin direction unknown: measurement of Collins function in one hemisphere is not possible sin φ modulation will average out.
o Correlation between two hemispheres with sin φi Collins single spin asymmetries results in cos(φ1+φ2) modulation of the observed di-hadron yield.
Measurement of azimuthal correlations for pion pairs around the jet axis in two-jet events!
Collins FF in e+e- : NeedCorrelation between Hemispheres !
![Page 7: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/7.jpg)
7
q1
quark-1 spin
Collins effect in e+e-
quark fragmentation will lead to azimuthalasymmetries in di-hadron correlation measurements!
Experimental requirements: Small asymmetries very large data sample! Good particle ID to high momenta. Hermetic detector
Collins Effect in di-Hadron CorrelationsIn e+e- Annihilation into Quarks!
electron
positron
q2
quark-2 spin
z2 z1
z1,2 relative pion momenta
![Page 8: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/8.jpg)
KEKB: L>1.7x1034cm-2s-1 !!• Asymmetric collider• 8GeV e- + 3.5GeV e+
• √s = 10.58GeV (U(4S))• e+e-U(4S)BB• Continuum production:
10.52 GeV• e+e-qq (u,d,s,c)• Integrated Luminosity: >700 fb-1
• >60fb-1 => continuum
8
Belle detectorKEKB
![Page 9: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/9.jpg)
Collins Asymmetries in Belle 9 May 28th Large acceptance, good tracking and particle identification!
![Page 10: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/10.jpg)
10
Collins Fragmentation: Angles and CrossSection: cos(12) Method (e+e- CMS frame)
j1
1hP
2hPj2
j1j
2
2
21
111
121221
21
sin411
cosq
cm
T
yyyB
zHzHyBddzdzd
Xhheedσ jj
2-hadron inclusive transverse momentum dependent cross section:
Net anti-alignment oftransverse quark spins
e-
e+
Observable: yield, N12 ( φ1+φ2 ) of π+π- pairs
![Page 11: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/11.jpg)
11
Collins Fragmentation: Angles and Cross Section cos(20) Method (CMS Frame)
j0
1hP2hP
2
21
11TTTT02
21
21
sin411
pkphkh22cosq
cm
T
yyyB
MMHHyB
ddzdzdXhheedσ Ij
2-hadron inclusive transverse momentum dependent cross section:
Net anti-alignment oftransverse quark spins
Independent of thrust-axis
Convolution integral I over transverse momenta
[Boer,Jakob,Mulders: NPB504(1997)345]
e-
e+
Observable: yield,N0 ( 2φ0 ) of π+π- pairs
![Page 12: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/12.jpg)
Examples of fits to azimuthal asymmetries
12
D1 : spin averaged fragmentation function,
H1: Collins fragmentation function
N()/N0
No change in cosine moments when including sine and higher harmonics
20 12)
• Cosine modulations
• clearly visible
• P1 contains information on Collins function
![Page 13: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/13.jpg)
13
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)2cos(:
2
2
2
2
2
2
0 FavUnfUnfFavq
FavUnfUnfFavq
UnfUnfFavFavq
UnfUnfFavFavq
DDDDe
HHHHe
DDDDe
HHHHeFA
j
2 methods give very small difference in the result
![Page 14: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/14.jpg)
14
Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance
ii
ii
p
npTThrust
ˆ :
• small B contribution (<1%) in high thrust sample • >75% of X-section continuum under ϒ (4S) resonance• 29 fb-1 547 fb-1 • several systematic errors reduce with more statistics • Charm-tagged Data sample also increases
9.44 9.46
e+e- Center-of-Mass Energy (GeV)
0
5
10
15
20
25
(e+ e
- ha
dron
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
- ha
dron
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)BB00 BB
e+e-qq, q uds∈
e+e-cc
0.5 0.8 1.0
4s“off”
![Page 15: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/15.jpg)
15
Applied Cuts, Binning• Two data sets: off-resonance data ( 29.1 fb-1 ) 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• Pion PID selection
0ˆ)ˆ(ˆ)ˆ( 12 nnPnnP hh
z2
0 1 2 3
4 5 6
7 8
9
0.20.3
0.5
0.7
1.0
0.2 0.3 0.5 0.7 1.0
5
86
1
2
3
z1
(z1, z2)-binning
![Page 16: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/16.jpg)
16
Final Collins results
Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)
![Page 17: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/17.jpg)
Combined Analysis: Extract Transversity Distributions
Transversity, δq(x)Tensor Charge
Lattice QCD: Tensor Charge
Factorization + Universality ?!
Theo
rySIDIS
~ δq(x) x CFF(z)~ δq(x) x IFF(z)
e+e-
~ CFF(z1) x CFF(z2)~ IFF(z1) x IFF(z2)
pp jets
~ G(x1) x δq(x2) x CFF(z)
pp h+ + h- + X~ G(x1) x δq(x2) x IFF(z)
pp l+ + l- + X~ δq(x1) x δq(x2)
![Page 18: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/18.jpg)
18
Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, Turkand Melis at Transversity 2008,Ferrara. Previously:Phys. Rev. D75:05032,2007
HERMES SIDIS
+ COMPASS SIDIS
+ Belle e+e-
transversity dist.
+ Collins FF
Fit includes:
Extraction of Quark Transversity Distributionsand Collins Fragmentation Functions SIDIS + e+e-
Soffer Bound
Old fit New fit
New fit
Old fit
![Page 19: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/19.jpg)
19
Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007
k┴ transverse quark momentum in nucleonp┴ transverse hadron momentum in fragmentation
hadron FF
quark pdf
The transverse momentum dependencies are unknown and veryDifficult to obtain experimentally!
),()(),(
)sin()sin(),()(),(
22
,122
pzDdy
dkxqkddde
pzHdy
dkxqkdddeA
hqhS
hShqSqhS
CollinsUT
transversit
y
Collins F
F
Collins Extraction of Transversity:unknown Transverse Momentum Dependences!
![Page 20: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/20.jpg)
20
Why di-hadron SSA in SIDIS & p+p
• Di-hadron vs single hadron– Collinear factorization– No model uncertainties due to kT dependence of FF and PDF– Doesn’t need quark momentum– No need to separate effects like Sivers/Collins effects in single
hadron measurement– Completely independent measurement
• Di-hadron measurement in fixed target vs collider– At higher scale
• sub-leading twist effects suppressed• factorization assumption better justified
![Page 21: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/21.jpg)
Interference Fragmentation–thrust method
• e+e- (+-)jet1()jet2X• Stay in the mass region around r-mass• Find pion pairs in opposite hemispheres• Observe angles j1+j2 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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)]
• Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)]
21 21221111 m,zHm,zHA jj cos
j2
j1
1hP
2hP
2h1h PP
Model predictions by:•Jaffe et al. [PRL 80,(1998)]•Radici et al. [PRD 65,(2002)]
![Page 22: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/22.jpg)
Expected sensitivities for 60 fb-1
• () () pairs as a function of the invariant mass m,1 x m,2
• Similar distributions to be shown as a function of z,1 x z,2
• Other hadron combinations
22
![Page 23: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/23.jpg)
23
Measurements of quark transversity
p+p
SIDIS
e++e-
E704, 1991Large forward SSA
STAR, PHENIX, BRAHMS, 2004~2005Inclusive AN
HERMES 2005, COMPASS 2006AUT
BELLE 2006Collins FF
BELLEIFF
RHICIFF asym.
RHICCollins asym.
JParc, RHIC, FAIRDrell-Yan
COMPASSp target
JLab 3He and 12 GeV
Underway Future1991 2005
CourtesyRuizhe Yang
![Page 24: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/24.jpg)
24
Definition of Vectors and Angles
1 2
1 2
1 2
p+p c.m.s. = lab frame
, : momenta of protons
, : momenta of hadrons
( ) / 2
: proton spin orientation
A B
h h
C h h
C h h
B
P P
P P
P P P
R P P
S
1hP
2hP
100 GeVAP
100 GeVBP
CP
BS
pp hhX
1 2hadron plane: ,
scattering plane: ,
h h
C B
P P
P P
: from scattering plane to hadron plane
R : from polarization vector to scattering plane
S
Bacchetta and Radici, PRD70, 094032 (2004)
2 CR
![Page 25: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/25.jpg)
25
vs invariant mass of the pairsinUTA
Consistent with 0, despite the second bin of 0h- pairs and the last bin of h+h- pairs are 2 from 0.
Systematic errors
Polarization 5%
Relative lumi. 5x10-4
No systematic effects detected from bunch shuffling
Ruizhe Yang, U of I,PKU RBRC Workshop2008
![Page 26: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/26.jpg)
26
Future• Prospects from future large transverse spin
data sample from PHENIX• Sub-percent sensitivity possible
![Page 27: Fragmentation Functions at Belle](https://reader036.vdocument.in/reader036/viewer/2022062501/56816621550346895dd97736/html5/thumbnails/27.jpg)
Summary & Outlook
• Collins FF at Belle final ->global analysis• 2H Interference FF Analysis underway• Plans for k_T dependent Upol FFs
– Necessary for global analysis w/o model assumptions
• 2H Interference FF at Phenix– First measurement of IFF at p-p collider– Analysis of 2008 data underway