resonances and thresholds in charmonium spectra

Resonances and Resonances and thresholds in thresholds in

charmonium spectracharmonium spectraYu.S.Kalashnikova, ITEP

CharmoniumCharmonium

2

2

4

3

cc

sSS SO T

pH m V

m

V r V V Vr

2Yu.S.Kalashnikova, ITEP

3

3000

3250

3500

3750

4000

4250

0-+ 1-- 0++ 1++ 2++ 1+- 2-- 3-- 2-+

M, MeV

Theory: Godfrey-Isgur

DD

?

??

Yu.S.Kalashnikova, ITEP

1++(3872) 1--(4260)

JPC?(4430)

I=1 !?

4

Weird charmoniaWeird charmoniaand relevant thresholdsand relevant thresholds

Yu.S.Kalashnikova, ITEP 5

X(3872) D0D0* 3872 MeVD+D-* 3879 MeV

Y(4260) DD1 4285 MeV

Y(4325) D*D0 4360 MeV

(4430) D*D1 4430 MeV

Threshold affinity means that the admixture of D-meson pairs in the wavefunction is large

Molecular charmonium

D

D*

uu* vector

D

D*

D*

D

Q exch not enough

exchange drives attraction

1++(3872)


S-wave 1- - (1-+ !)

D1

D*

psi

pi

D

D1

D*

D0

pi

Q exch gives cc* + … final statesVerify JPC seek other final states

Other places should occur…

exchange drives attraction

S-wave 0- (I=0 and I=1)also 1- 2-

D*

D1

D1

D*

pi

1--(4260)

JPC?(4460)

I=1 !?

8

DD DD ccc (cc (cccg, cg, cccqqqq))

D

D

D

D

cc

=

+cc

D

D

D

D

DD

D

DD

D


Coupling to bare state drives attraction


Doubling of states in DD Doubling of states in DD c ccc system system

Spectral density w(M) of the cc state

w(M)

M

Difference between bound Difference between bound states of states of quarksquarks and and

hadronshadrons

Yu.S.Kalashnikova, ITEP 10

Hadrons can go on-shell -> non-analyticities

Quark loop

Hadron loop

Polynomial in E

i(E)1/2 + polynomial, E>0

-(-E)1/2 + polynomial, E<0

Should lead to observable Should lead to observable differencedifference


The case of XThe case of X

Focus on resonances very close Focus on resonances very close to thresholdto threshold

12

X(3872) X(3872) J/ J/

M(X) = 3871.2 M(X) = 3871.2 0.5 MeV 0.5 MeV


X(3875) X(3875) D0D0 D0D000


X(3872) X(3872) X(3875) ? X(3875) ?

15

FlattFlattèè analysis analysis

Assumptions:

1++ quantum numbers for the X

X -> D0D*0 -> D0D00 decay chain

J/ and J/ are the main non – DD*

decay modes of the X


DD* S-waveDD* S-wave


Differential Rates:Differential Rates:

0 0 012

2

1 2

( ) 10.62

2

( / ) 1

2

( )2

below j-th threshold

f

j j

gkdBr B KD D

dE D

dBr B K J

dE D

iD E E gk gk

ik

B

B

D0*->D00

B->KX


Results (generalities)Results (generalities)

++--J/J/ peak exactly @ D0D0 peak exactly @ D0D0**

peak width 2.3 MeVpeak width 2.3 MeV

D0D0D0D0** coupling is large coupling is large

scaling of Flattè parametersscaling of Flattè parameters

g->g, Ef->Ef, ->, B->B

18

ABelle

a(D0D0*) =(-3.98 –i0.46)

fm

J/

J/

DD

DD

19

X(3872) as a X(3872) as a virtualvirtual state:state:

+-J/ cusp

Large and negative real part of the scattering length (and small imaginary part)

Scaling behaviour of Flattè parameters

Dynamical nature of the X



Why virtual state?Why virtual state?

Br(X -> D0D00)

Br(X -> J/) 9.7 9.7 3.4 3.4

21

Scattering length Scattering length approximation:approximation:

2 21

2 21

0 *01

2 21

2

01 1

1

( / ), 0

( )

( / ), 0

( )

( )

( )

( / )( )

2im

re im

im

re im

im

re im

re im

re re

ai

dBr JE

dE k

dBr JE

dE

kdBr D D

dE k

dBr JE

dE

re>0

22

Bound state is below threshold, and decays only because D*0

has finite width. In the limit of infinitely narrow widththe bound state is stable. As (D*0->D00) 42 keV,

(Xbound -> D0D*00)

In the B-meson decay, together with the bound statecontribution to the rate, there is also continuum contribution. The latter is nonzero even in the narrow-

widthapproximation.

2*42 keV naively

(2-4)*42 keV with FSI interference


23

In the B-meson decay, the D0D*0 continuum provides the main contribution to D0D00 rate. In the case of the virtual state it is much larger, than for the bound state. So the large ratio

tells that X is a virtual state. It is similar to the virtualstate in the 1S0 nucleon-nucleon scattering rather thanto the deuteron: the system is almost bound.


Br(B -> KX) Br(X -> DD)

Br(B -> KX) Br(X -> J/)

24

ConclusionsConclusions

The X(3875) can only be related to the The X(3875) can only be related to the X(3872) if we assume the X to be of dynamical X(3872) if we assume the X to be of dynamical originorigin

(molecular charmonium)(molecular charmonium)

However, it is not a bound state, but a virtual However, it is not a bound state, but a virtual oneone

Only much better resolution on Only much better resolution on J/J/ lineshape could confirm or rule out this lineshape could confirm or rule out this

solutionsolution

If the cusp-like lineshape is ruled out, the If the cusp-like lineshape is ruled out, the X(3875) and X(3872) are two different particles X(3875) and X(3872) are two different particles



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resonances and thresholds in charmonium spectra

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