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