study of branching ratio of · 1) cross-sections at 14 energy points between 3.73 and 3.80 gev from...
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Study of Branching ratio of Y(3770)DDbar
Hai-bo Li Xiaoshuai Qin Mao-zhi Yang
1
Phys. Rev. D81,011501(2010)
2010/04/16 -04/19, Nanchang city
Outline
1. Theoretical estimation of branching ratio
of Y(3770)non-DDbar
2. Experimental results about
Y(3770)non-DDbar
3. Combining BESII and Belle data to fit
branching fraction of Y(3770) to DDbar.
2
Theoretical estimation of branching ratio of
Y(3770)non-DDbar
The can be viewed as a 13D1
dominated state with a small admixture of
23S1 and expressed as:
3
3 3
1 1
3 3
1 1
(3770) cos 1 sin 2
(3686) sin 1 cos 2
D S
D S
Y.B.Ding, D.H.Qin, and K.T.Chao,
Phys.Rev.D44,3562(1991)
J.L.Rosner, Phys.Rev.D64,094002(2001)
187
338
0.80
1.50
( (3770) ) 467 ( 50%)
( (3770) ) (2.0 )%( 50%)
LH keV
Br LH
Z.G.He, Y.Fan, and K.T.Chao,
Phys.Rev.Lett. 101, 112001(2008)
(3770)
Together with the observed hadronic transitions and E1 transitions,
the non-DDbar decay branching ratio of could reach about 5%.(3770)
~ 12 。
Experimental results about
Y(3770)non-DDbar
Both BESII and CLEO-c found only a few channels
with total branching fraction < 3% .4
PLB641,145(2006)
PRL96,092002(2006)
BESII: ( (3770) ) 7.179 0.195 0.630DD nb
Cleo-c:0.41
0.30( (3770) ) 6.38 0.08DD nb
0.41
0.30( (3770) ) 0.01 0.08non DD nb
( (3770) ) 9%BF non DD
6.6
4.8( (3770) ) 3.3 1.4 %BF non DD
arXiv:1004,1358
at 90% confidence level
( (3770) ) 14.5 1.7 5.8%BF non DD
( (3770) ) 6.57 0.04 0.10DD nb 0.41
0.30( (3770) ) 0.21 0.09non DD nb
Cleo-c:
What we have already known
5
Part of branching ratio
results from PDG
About non-DDbar decays
6
So, are there abundance non-DDbar decay channels not found yet ?
Or , we might misunderstand the branching ratio of non-DDbar decay .
Combining BESII and Belle data to fit
branching fraction of Y(3770) to DDbar.
Motivation:
Both BESII and CLEO-c found only a few channels with total
branching fraction less than 3% .
Consider the continuum distribution
from
Interference of charmonium states need to be
considered.7
*e e DD
( (3770) ) 14.5 1.7 5.8%BF non DD PLB641,145(2006)
BESII:
Cleo-c:
( (3770) ) 7.179 0.195 0.630DD nb
( (3770) ) 9%BF non DD
6.6
4.8( (3770) ) 3.3 1.4 %BF non DD
at 90% confidence level
arXiv:1004,1358
Continuum term
8
To well describe
the data
M.Z.Yang, Mod.Phys.Lett. A 23,3113(2008)
2
0 (3770)( )
DD
F mF s
s a
0
2
(2 ) (2 ) (2 )
( )DD
S S S
cF s
s m im
Data Set
1) Cross-sections at 14 energy points between 3.73 and 3.80 GeV from BESII data with total luminosity of about 15 pb-1
M. Ablikim, et al., BES Collaboration, PLB 668(2008) 263-267.
Introduce ISR correction from reference: M. Ablikim, et al., BES Collaboration, PLB 603(2004) 130-137.
2) Cross-sections at 27 energy points between 3.81 and 4.33GeV from Belle data with integrated luminosity of 673 fb-1 (ISR).
Pakhlova et al. PR D77(2008)011103 (Belle)
9
Data Set
Total data set: 41 data points.
14 data points from BESII, 27 data points from Belle
10
About G(3900)
First put forward in Couple-
channel modelE. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and
T. M. Yan, Phys. Rev. D 21, 203 (1980).
Observed by BABAR and Belle
Collaboration named G(3900)
11
PRD76,111105(R)(2007) BABAR
PRD77,011103 (R)(2008) Belle
Formula for cross section
2 2 24
3
i
i
c
e e i
Q f
m
32 2 2 2
0 0
2
( 4 )( , )
48
ii
i
DDD
i
i
g m mBR D D D D
m
0
2 3 2 2 3 2
2
5 2
2
2
( 4 ) ( 4 )( )
3
( )i ii
i i
D D
cDD i
DDi i
s m s me e DD
s
g Q f mF s e
s m im
0
0
2 3 2 2 3 2
2
5 2
25/2
22 2 3 2 2 2 3 2
( 4 ) ( 4 )( )
3
61 1( )
( 4 ) ( 4 )
i i i
i i ii i
D D
eei i
DDi
D D
s m s me e DD
s
Br mF s e
s m imm m m m
2
0 (3770)( )
DD
F mF s
s a
0
2
(2 ) (2 ) (2 )
( )DD
S S S
cF s
s m im
0
'' '''' 0 ''
2(3900)
2(3900) 1
2 3 2 2 3 2
2
5 2
0
2
(3686) (3686) (3686)
5/2
22 2 3 2 2 2 3 2
( )
1
(3900)
(4040)
( 4 ) ( 4 )( )
3
61 1
( 4 ) ( 4 )
1
2
1 1
(
G
G
D D
ee i
D D
s M
i
G
s m s me e DD
s
c
s m im
Br me
s m imm m m m
c e e
m
2
0
2
0
2
5/2
2 (4040) (4040)
22 2 3 2 2 2 3 2(4040) (4040) (4040)(4040)
5/2
3 (4160) (4160)
22 2 3 2 2 2 3 2(4160) (4160) (4160)(4160) (4160)
6
4 ) ( 4 )
61 1
( 4 ) ( 4 )
ee i
D D
ee i
D D
Br me
s m imm m m
Br me
s m imm m m m
Formula for cross section
13
Fit method
Least 2 fitting method
Fix Y(2S) ‘s width, mass to PDG value
Fix Y(4040)’s width, mass to PDG value
Fix Y(4160)’s width, mass to PDG value
Fix G(3900)’s width, mass to 3.9GeV and 52MeV suggested by BABAR’s fitting result. B.Aubert , et al. PRD76,111105(BABAR)
E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M. Yan, Phys. Rev. D 21, 203 (1980).
For Y(3770)’s total width, 2 methods:
1) constant width
2) s-dependent width
14
s-dependent total width of Y(3770)
0 0
00 0
0 0
3 0 2
0 000 3 2
3 0 2
0 0 3 2
0 00
( ) 1 ( )( ) ( 2 )
( ) 1 ( )
( ) 1 ( )( ) ( 2 )
( ) 1 ( )
( ) (1 )
D Dcm DD D
D D
D DcmD D D
D D
non DD
p rps E M B
p rp
p rps E M B
p rp
s B B
15
0 0( ) ( ) ( ) ( )T non DDD DD Ds s s s
Fix B00/B+- ratio to be 0.481/0.361 ~ 1.33
according to PDG value
M. Ablikim, et al.,
BES Collaboration, PLB 641,145(2006)
Best fit result
2/dof = 1.06
16
Best fit results
17
Statistical error Only!
( (3770) )Br DD
The interference between structures and continuum term
tends to be destructive
( (4040) )Br DD ( (4160) )Br DD
Why large contribution from Y(2S)
The coupling of resonance with virtual photon:
Leptonic decay width decay constant
The coupling of resonance with DDbar
Conclusion: the large coupling of Y(2S) with the virtual photon.
18
0 (2 ) (2 )(2 ) c S SS DDc g Q f m
(3770)12.8
DDg
(2 ) 297Sf MeV (3770) 100f MeV
( (3770) )Br DD
(2 )12.0
S DDg
(2 )2.36 0.04
e e SkeV
(3770)
0.265 0.018e e
keV
About multiple solutions
As the interference has been introduced,
multiple solutions should exist.
At least 8 solutions have been found, but
many with Br(Y(3770) DDbar) less than
70%. So they are abandoned as unphysical
solutions.
19
Conclusion
Our result concludes that taking into account
the interference between Y(3770), Y(2S)
and some higher structures is
a good suggestion to study the DDbar
branching fraction and the puzzle about
non-DDbar branching fraction.
More data sample is suggested for BESIII.
20
Conclusion
Our result concludes that taking into account
the interference between Y(3770), Y(2S)
and some higher structures is
a good suggestion to study the DDbar
branching fraction and the puzzle about
non-DDbar branching fraction.
More data sample is suggested for BESIII.
21
Backup
22
Most recently updated result from
Cleo-c
0.41
0.30( (3770) ) 6.36 0.08e e hadrons nb
( (3770) ) 6.57 0.04 0.10DD nb
( (3770) ) 9%BF non DD
0.41
0.30( (3770) ) 0.21 0.09non DD nb
arXiv:1004,1358
at 90% confidence level
6.6
4.8( (3770) ) 3.3 1.4 %BF non DD
Anomalous line shape of Y(3770)
24
PRL101,102004(2008)
Best fit: One resonance interfering
With DDbar continuum
J.Brodzicka@Lepton Photon 2009
BES Data (33 pb—1) KEDR Data 2.1 pb-1
Fit with two coherent states
favored over single resonance (7σ)
Red: 2 resonance
Green:1 resonance
Part of References
M. Ablikim, et al., BES Collaboration, PLB 668(2008) 263-
267.
M. Ablikim, et al., BES Collaboration, PLB 603(2004) 130-
137.
Pakhlova et al. PR D77(2008)011103 (Belle)
M.Z.Yang, Mod.Phys.Lett. A 23,3113(2008)
Z.G.He, Y.Fan, and K.T.Chao, Phys.Rev.Lett. 101,
112001(2008)
B.Aubert, et al. PRD76,111105(BABAR)
E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M.
Yan, Phys. Rev. D 21, 203 (1980).
25