Measurements of chiral-odd fragmentation functions at Belle D. Gabbert (University of Illinois and RBRC) M. Grosse Perdekamp (University of Illinois and RBRC) K. Hasuko (RIKEN/RBRC) S. Lange (Frankfurt University) A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC) V. Siegle (RBRC) for the Belle Collaboration HERMES Transversity Working Week November 09, 東東東東東東 東東東 、 (see hep-ex/0507063 for details)
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Measurements of chiral-odd fragmentation functions at Belle D. Gabbert (University of Illinois and RBRC) M. Grosse Perdekamp (University of Illinois and.
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Measurements of chiral-odd fragmentation functions at Belle
D. Gabbert (University of Illinois and RBRC)M. Grosse Perdekamp (University of Illinois and RBRC)
K. Hasuko (RIKEN/RBRC) S. Lange (Frankfurt University)
A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC)
V. Siegle (RBRC)for the Belle Collaboration
HERMES Transversity Working Week
November 09, 東京工業大学、大岡山
(see hep-ex/0507063 for details)
measurements of chiral-odd fragmentation functions at Belle 2 Transversity Week Nov 09, 2005
SIDIS experiments (HERMES and COMPASS) measure q(x) together with either Collins Fragmentation function or Interference Fragmentation function
Motivation: 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
The Spin dependent Fragmentation function analysis yields information on the Collins and the Interference Fragmentation function !
Universality appears to be provenin LO by Collins and Metz:[PRL93:(2004)252001 ]
measurements of chiral-odd fragmentation functions at Belle 3 Transversity Week Nov 09, 2005
Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:
hp
sin
qh spk
measurements of chiral-odd fragmentation functions at Belle 24
Transversity Week Nov 09, 2005
• Good detector performance (acceptance, momentum resolution, pid)
• Jet production from light quarks off-resonance (60 MeV below resonance)
(~10% of all data)• Intermediate Energy
Sufficiently high scale (Q2 ~ 110 GeV2)- can apply pQCD
Not too high energy (Q2 << MZ2)
-avoids additional complication from Z interference• Sensitivity = A2sqrt(N) ~ x19 (60) compared to LEP
ABelle / ALEP ~ x2 (A scales as ln Q2)
LBelle / LLEP ~ x23 (230)
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)
Belle is well suited for FF measurements:
measurements of chiral-odd fragmentation functions at Belle 25
Transversity Week Nov 09, 2005
What is the transverse momentum QT of the virtual photon?
• In the lepton CMS frame e-=-e+ and the virtual photon is only time-like:q=(e-+p+)=(Q,0,0,0)
• Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame wherePh1+Ph2=0
q’=(q’0,q’)• Inclusive Cross section for
radiative events (acc. to D.Boer):
Ph1
e+e-
Ph2
e-’
e+’
q’
P’h1 P’h2
qT
Lepton-CMS
Hadron-CMS
measurements of chiral-odd fragmentation functions at Belle 26
Transversity Week Nov 09, 2005
Experimental issues
• Cos2 moments have two contributions:– Collins Can be isolated either by subtraction or double ratio method– Radiative effects Cancels exactly in subtraction method, and in LO of
double ratios• Beam Polarization
zero? Cos(2Lab) asymmetries for jets or • False asymmetries
from weak decays Study effect in decays, constrain through D tagging
• False asymmetries from misidentified hemispheres QT or polar angle cut
• False asymmetries from acceptance Cancels in double ratios, can be estimated in charge ratios,
fiducial cuts• Decaying particles lower z cut
measurements of chiral-odd fragmentation functions at Belle 27
Transversity Week Nov 09, 2005
Preliminary Systematic errors
Double Ratio vs Subtraction Method:
R – S < 0.002
The difference was assigned as a systematic error.
measurements of chiral-odd fragmentation functions at Belle 28
Transversity Week Nov 09, 2005
Systematics: charm contribution?
• Weak (parity violating) decays could also create asymmetries(seen in overall dilution 5%)
• Especially low dilution in combined z-bins with large pion asymmetry
• Double ratios from charm MC compatible to zero
Charm decays cannot explain large double ratios seen in the data
Charm enhanced D* Data sample used to calculate and correct the charm contribution to the double ratios (see hep-ex/0507063 for details)
Charm
fra
ctio
n
N(c
harm
)/N
(all)
measurements of chiral-odd fragmentation functions at Belle 29
Transversity Week Nov 09, 2005
Different charge combinations additional information
• Unlike sign pairs contain either only favored or only unfavored fragmentation functions on quark and antiquark side:
• Like sign pairs contain one favored and one unfavored fragmentation function each:
Favored = u,d,cc.
Unfavored = d,u,cc.
measurements of chiral-odd fragmentation functions at Belle 30
Transversity Week Nov 09, 2005
Example: Left-Right Asymmetry in Pion Rates
sq
π
qq
π sqp
p
= 0 !AT =
NL - NR
NL + NR
Collins Effect
NL : pions to the left
NR : pions to the right
measurements of chiral-odd fragmentation functions at Belle 31
Transversity Week Nov 09, 2005
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:
measurements of chiral-odd fragmentation functions at Belle 32
Transversity Week Nov 09, 2005
General Fragmentation Functions
h
qhh
hqhqh
h
q zM
spkpzHzDpzD
ˆ),()(),( 2,
1,
1
Number density for finding a spin-less hadron h from a transversely polarized quark, q:
unpolarized FF Collins FF
measurements of chiral-odd fragmentation functions at Belle 33
Transversity Week Nov 09, 2005
Raw asymmetries vs transverse photon momentum QT
1hP
2hP
1hP
2hP
•Already MC contains large asymmetries
•Strong dependence against transverse photon Momentum QT