The contribution of the continuum amplitudeIn e﹢e﹣Charmonium

Changzheng YUAN Changzheng YUAN

IHEP, BeijingIHEP, Beijing

2nd International Workshop on Heavy Quarkonium

Sept. 20 – 22, 2003, Fermilab

OUTLINE

1. The continuum amplitude

2. The form factors at psi’ mass

3. The universal -90°phase

4. Summary

The overlooked amplitude

In e﹢e﹣ annihilation experimentfor charmonium production,continuum amplitude contributesto all decay channels …

e﹢e﹣ψ(2S) @ BESII

Except for scan experiment,the continuum amplitude has been overlooked in bothexperiment and theory!

exp

exp

expexp expexp expexp

The overlooked amplitude

σexp=σtheo

σ’exp=σexperiment

The overlooked amplitude

At ψ(2S)

Born ISR =1.3MeV

RES (nb) 7887 4046 640

CON (nb) ~14 ~14 ~14Continuum contribution becomes larger after considering ISR and beam spread!

1. |aggg|=02. |aggg|=|aγ|3. |aggg|=3.4|aγ|4. |aggg|=5|aγ|5. |aggg|=10|aγ|

The overlooked amplitude2

3

2

3

2

3 |||||||| 3

i

g

ii

ggB eaaeaeaaa aga 2

3

2

3

2

3 |||||||||||| 3

i

c

i

g

i

c

ii

gcgB eaeaaeaeaeaaaa caaga

exp

expexp

k

ψ(2S)

J/ψ

There is interference…

The overlooked amplitude

The consequences: 1. Results from different experiments not comparable a) beam spread (reduce/shift peak) b) data taking energy (hadron peak) c) selection criteria (s-dependent)

2. Wrong theoretical inferences a) the form factors b) the relative phase between strong and electromagnetic decays

0.5 MeV shift

90-95 % RES

BEPC2

CESRc

hep-ph/0308041

(e﹢e﹣ρπ) atEcm=mψ(3770).

The form factors at ψ(2S) 0 and ﹢

﹣

2222

Re12

)(MMs

st

fes

Born

)(4

)(2

2/3

3

ss

s ffConBorn PF

)()()(214

)(22

2/3

3

ssBsBs

s ffBorn PF

)90,0(,/3

)(2

i

t

e eMiMs

ssB

Proportion RES CON INT

BES

(1.3MeV)

0 40.9 % 60.4% – 1.3%

+– 41.4 % 60.0% – 1.4%

[scan] +– 43.8% 55.1% +1.1%

DORIS

(2.0Mev)

+– 32.7 % 68.5% – 1.2%

Wang, Mo, YuanPLB557, 192(2003)

0 and ﹢﹣

0BrBrRESRES RES

ff

INTCONRES

f F

Branching ratio reportedBES 0

+–

DORIS +–

510)9.06.1( 63.2

7.2 10)5.3(

510)6.16.2(

510)6.02.1( 510)1.11.2(

510)4.11.2(

68.11.2 10)7.2(

63.37.3 10)8.4(

510)1.23.3(

900 90510)1.17.18.3(

66.15.3 10)6.54.8(

510)58(

Real resonance decay branching ratio

(BES)

(DASP)

(BES) Gerard, PLB425,365(1998)

Brodsky, SLAC-pub-3747(1985)

The form factors at ψ(2S)

The universal -90°phase

Phase

Branching ratios

All previous analyses handle only these two diagrams, but we have one more now …

Then what can we get ?

The universal -90°phase

J/ψ Decays: 1. AP: 90 ° M. Suzuki, PRD63, 054021 (2001) 2. VP: (106 ±10) ° J. Jousset et al., PRD41, 1389 (1990) D. Coffman et al., PRD38, 2695 (1988) N. N. Achasov, talk at Hadron2001 3. PP: (90 ±10) ° M. Suzuki, PRD60, 051501 (1999) 4. VV: (138 ±37) ° L. Köpke and N. Wermes, Phys. Rep. 74, 67 (1989) 5. NN: (89 ±15) ° R. Baldini et al., PLB444, 111 (1998)

ψ(2S)VP 1. φ=180 ° (± 90 ° ruled out!) M. Suzuki, PRD63, 054021 (2001)

|φ|Existing analyses without considering the continuum amplitude

The universal -90°phase VP

a

a g3C F MiMs

ssB

t

e

2

/3)(

Four equations for four unknowns:

Haber, PRD32, 2961 (1985)

continuum

The universal -90°phase J/ψVP

Two solutionsWith oppositeSign!

The universal -90°phase ψ(2S)VP

Assuming Rψ(2S)=RJ/ψ

Hep-ph/0303144With continuum!

PRD63, 054021 (2001)Without continuum!

1. Can’t rule out (nearly) orthogonal phase

2. The phase is negative

The universal -90°phase ψ(2S)PP

A’ (π﹢π﹣) and A’+B’ (K﹢K﹣) known,KS KL is needed to extract the phase between A’ and B’.

φ

ψ(2S) π﹢π﹣

ψ(2S) K﹢K﹣

ψ(2S) KS KL

When extract A’/B’ from experimental information, Continuum contribution should be considered!

The universal -90°phase

DASP:

ψ(2S)PP

BESI:

MKIII:

–80° 120 °

B ((2S)

KS K

L

) =5.25

10 – 5

Yuan, Wang, Mo

PLB567 (2003)73

K+K– & + inputs ;Input 1:DASP;Input 2:BESI ;Input 3: K+K–

from BESI & + by form factor.

The universal -90°phase ψ(2S)PP

BESIIpreliminary

The universal -90°phase ψ(3770)ρπ

Using mixing angle θ=12°, assuming ψ(2S)ρπ completely missing, ψ(3770)ρπ is enhanced!

or

Using ωπ form factor to estimate ρπ form factor: Comparable!

Interference?

The universal -90°phase ψ(3770)ρπ

To measure B(ψ(3770)ρπ), the best way is to do the energy scan!

The band is for non-zero B(ψ(2S)ρπ)!

Hep-ph/0308041,To appear in PLB.

MK3 UL (<6.3pb)Favors φ= 90°!﹣

σ(K*0K0+c.c.)For φ= 90°!﹣

Missing ρπ signal and/orenhanced K*0K0 signal indicate BRs at 10-4 level.

The universal -90°phase Concluding Remarks

1. A universal 90°phase﹣ can accommodate all experimental information in the OZI suppressed vector charmonia decays;

2. The minus sign is determined with the help of the continuum amplitude;

3. The existing ψ(2S) and ψ(3770) data samples at BESII and CLEOc will help to clarify the situation;

4. The orthogonal phase with minus sign is probably also true for bottomonium decays.

0

2

4

6

8

10

12

14

MKI MKII MKIII CBAL BESI BESII CLEOc

ψ(2S) Sample in Million

14

1.5

05101520253035404550

MKIII BES CLEOc CLEOc

ψ(3770) Sample In pb-1

2fb-1planned by CLEOc

M/EcmCLEO, hep-ex/0307035

Summary1. Continuum amplitude was overlooked for a long time in e﹢e﹣

charmonium experiments, new generation experiments should consider it seriously to get reliable physics outputs

2. 0 and ﹢﹣ form factors at ψ(2S) mass are calculated and compared with predictions

3. A universal -90°phase between OZI suppressed strong and electromagnetic amplitudes of charmonia decays is favored by the experiment information

4. The universal phase may be extended to bottomonia

5. High precision experimental information are desired to test above conclusions

Thanks a lot!Thanks a lot!