Four quark state

— a nature interpretation of the Ds(2632)

Yu-Qi Chen & Xue-Quan Li

hep-ph/0407062

Outline

1. Selex experiments

2. Four quark state interpretation of Ds(2632)

3. Ds(2317), Ds(2460)

4. Predictions

5. Outlook

1. SELEX experiments

Fixed target at Fermilab

600 GeV Σ- +π-

Selex hep-ex/0406045

2. Four-quark state interpretation of Ds(2632)

Possible interpretations

• cs excited state

Ds(2632) → DK OZI allowed

expect to have large decay width

• csg, csgg hybrid state

mass too large ? decay width large?

• 4 quark state - nature

4-quark interpretation

(2 6 3 2)sc s s s D

Possible color

configurations

1 1

8 8

33

6 6

( ) ( )

( ) ( )

( ) ( )

( ) ( )

c s s s

c s s s

c s s s

c s s s

Flavor SU(3) partner (2 3 1 7)( ) sc s u u d d D

(2 4 6 0)( ) sc s u u d d D Spin excitation

molecule

repulsive

diaquark - antidiaquark

repulsive

s

Decay modes

s

c

ssD

c

s

s

c

s

D

K

,d u

,d u

suppression

• s s quark final state destructive interference like D+ decay

2s i n

• ss annihilation higher order process

• color match

•.

2

1

cN

3. Ds(2317), Ds(2460)

In heavy quark chiral effective theory

are chiral partner of Ds(1996), D*s(2112)

Surprising mass relations

* * (2 4 6 0) (2 3 1 7) 1 4 0 M e Vs s s sD D D D D DM M M M M M

Bardeen, Eichten, & Hill

Nowak, Rho, & Zahed

Ds(2317), Ds(2460)

0+ 1+ 0- 1-

Mass splittings are given by Godberg-Trieman relation

In mc →∞ limit

(1 ) (1 ) (0 ) (0 )/ 3 ~ 3 1 0 M e V

s s s spD D D D

M M M M m

Questions: no such partners of D and D* mesons satisfy this relation

Molecular picture Barnes, Close & LipkinBeveren & RuppCheng & Hou

The mass difference DK and D*K threshold 40 MeV

are dominated by D*K and DK molecular states Ds(2317), Ds(2460)

Ds(2317), Ds(2460)

The relation of the mass differences

can be understood in the molecular picture K

* (2 4 6 0) (2 3 1 7) 1 4 0 M e Vs sD D D DM M M M

Mass difference is caused by the spin-flip interaction

Suppressed by 1/mc ,

pseudoscalar meson K is blind to the spin of charm

Decays:

below the DK threshold

dominated by isospin violated process

*

(2 3 1 7)

(2 4 6 0)

s s

s s

D D

D D

Belle

Electromagnetic decay

CLEO

Question: molecular state is not so good in explaining the electromagnetic decays

4. Predictions

(2 6 3 2)sc s s s D (2 3 1 7)( ) sc s u u d d D

(2 4 6 0)( ) sc s u u d d D*(1 )sc s s s D

s

Main Decay modes

s

c

s

*sD

cs

s

c

s

*D

K

,d u

,d u

In the molecular picture, mass is around 2770 MeV

50 MeV deviation is acceptable

5. Outlook

Ds(2632) as well as Ds(2317) , Ds(2460)

are very interesting states

Ds(2632) needs confirmation !!!

BaBar scan from B decay did not see signal